UNITED STATES of America, Appellee, v. Ross William ULBRICHT, a/k/a Dread Pirate Roberts, a/k/a Silk Road, a/k/a Sealed Defendant 1, a/k/a DPR, Defendant-Appellant, 858 F.3d 71

GERARD E. LYNCH, Circuit Judge: Defendant Ross William Ulbricht appeals from a judgment of conviction and sentence to life imprisonment entered in the United States District Court for the Southern District of New York (Katherine B. Forrest, /.). A jury convicted Ulbricht of drug trafficking and other crimes asso-dated with his creation and operation of Silk Road, an online marketplace whose users primarily purchased and sold illegal goods and services.

He challenges several aspects of his conviction and sentence, arguing that (1) the district court erred in denying his motion to suppress evidence assertedly obtained in violation of the Fourth Amendment; (2) the district court committed numerous errors that deprived him of his right to a fair trial, and incorrectly denied his motion for a new trial; and (3) his life sentence is both procedurally and substantively unreasonable. Because we identify no reversible error, we AFFIRM Ulbricht’s conviction and sentence in all respects.

BACKGROUND In February 2015, a jury convicted Ross William Ulbricht on seven counts arising from his creation and operation of Silk Road under the username Dread Pirate Roberts (“DPR”). Silk Road was a massive, anonymous criminal marketplace that operated using the Tor Network, which renders Internet traffic through the Tor browser extremely difficult to trace. Silk Road users principally bought and sold drugs, false identification documents, and computer hacking software. Transactions on Silk Road exclusively used Bitcoins, an anonymous but traceable digital currency.

The site also contained a private message system, which allowed users to send messages to each other (similar to communicating via email), a public forum to discuss topics related to Silk Road, and a “wiki,” which is like an encyclopedia that users could access to receive advice about using the site. Silk Road customers and vendors could also access a support

section of the website to seek help from the marketplace’s administrators when an issue arose. According to the government, between 2011 and 2013, thousands of vendors used Silk Road to sell approximately $183 million worth of illegal drugs, as well as other goods and services. Ulbricht, acting as DPR, earned millions of dollars in profits from the commissions collected by Silk Road on purchases. In October 2013, the government arrested Ulbricht, seized the Silk Road servers, and shut down the site. I.

Silk Road Investigation After Ulbricht created Silk Road in 2011, the site attracted the interest of at least two separate divisions of the Department of Justice: the United States Attorney’s Offices for the District of Maryland and for the Southern District of New York. Throughout the investigations, law enforcement agents knew that the person using Dread Pirate Roberts as his or her Silk Road username had created and managed the site, but they did not know DPR’s actual identity.

In 2012 and 2013, agents from both offices investigated several individuals who the government suspected were operating Silk Road as DPR. Those individuals included Ulbricht, Anand Atha-vale, and Mark Karpeles. Ultimately, the New York office identified Ulbricht as DPR, but the Maryland office had investigated and later abandoned the theory that either Athavale or Karpeles might have been Dread Pirate Roberts.

Two aspects of the pre-arrest investigation into Ulbricht are particularly relevant to this appeal: (1) the pen/trap orders that the government obtained to monitor Internet Protocol (“IP”) address traffic to and from various devices associated with Ul-bricht; and (2) the corrupt behavior of two Baltimore agents who worked on the Silk Road investigation. A. The Pen/Trap Orders In September 2013, after Ulbricht became a primary suspect in the DPR investigation, the government obtained five “pen/trap” orders. See 18 U.S.C. §§ 3121-27 (“Pen/Trap Act”).

The orders authorized law enforcement agents to collect IP address data for Internet traffic to and from Ulbricht’s home wireless router and other devices that regularly connected to Ulbricht’s home router. According to the government’s applications for the pen register and trap and trace device, “[ejvery device on the Internet is identified by a unique number” called an IP address. S.A. 73. “This number is used to route information between devices, for example, between two computers.” Id. at 73-74.

In other words, an “IP address is analogous to a telephone number” because “it indicates the online identity of the communicating device without revealing the communication’s content.” Id. at 74. Ulbricht does not dispute that description of how IP addresses function. The pen/trap orders thus did not permit the government to access the content of Ulbricht’s communications, nor did the government “seek to obtain[ ] the contents of any communications.” Id. at 75.

According to Ulbricht, the government’s use of his home Internet routing data violated the Fourth Amendment because it helped the government match Ulbricht’s online activity with DPR’s use of Silk Road. Ul-bricht argues that he has a constitutional privacy interest in IP address traffic to and from his home and that the government obtained the pen/trap orders without a warrant, which would have required probable cause. B.

Corrupt Agents Force and Bridges One of the many other tactics that the government used to expose DPR’s identity was to find low-level Silk Road administrators who helped DPR maintain the site, obtain their cooperation, take over their Silk Road usernames, and chat with DPR under those identities. The true owners of the administrator accounts would assist in the investigation by helping the government chat with DPR and access various aspects of the site.

Government agents would also create their own new user-names and pose as drug dealers or buyers to purchase or sell narcotics and occasionally contact DPR directly. One of the government’s principal trial witnesses, Special Agent Jared Der-Yeghiayan, used the former technique to chat with DPR under the name Cirrus. Cirrus had been a member of the Silk Road support staff before the government took over his account, and Der-Yeghiayan frequently used Silk Road’s messaging system to communicate with DPR and other administrators as Cirrus.

Cirrus also gave the government access to the staff chat, a separate program allowing DPR to communicate only with his employees. Two undercover agents involved in the Silk Road investigation are of particular import to this appeal: Secret Service Special Agent Shaun Bridges and Drug Enforcement Administration (“DEA”) Special Agent Carl Force, both of whom were assigned to the Baltimore investigation.

Both Force and Bridges used their undercover access to exploit the site for their own benefit in various ways, and they eventually pleaded guilty to criminal charges in connection with their work on the Silk Road investigation. For example, Force and Bridges took over an administrator account belonging to Curtis Green, who worked for Silk Road under the name Flush.

According to the criminal complaint against Force and Bridges, in January 2013, Bridges used the Flush username to change other users’ passwords, empty their Bitcoin wallets, and keep $350,000 in Bitcoins in offshore bank accounts, all while attempting to hide his activity through a series of transactions. Specifically, the complaint against Force and Bridges alleges that Bridges “act[ed] as an administrator to reset pins and passwords on various Silk Road vendors’ accounts,” then exchanged the Bit-coins for U.S. dollars using the Mt. Gox exchanger. Supp. App’x 180.

Shortly after he committed the January 2013 thefts, Bridges asked' Force to chat with DPR as Nob, Force’s authorized undercover user-name, to get advice about how to liquidate Bitcoins. He also sought Force’s help in convincing Curtis Green (formerly Flush) to help him transfer Bitcoins to other accounts, and he ultimately tried to blame Green for the theft. With the government’s approval, Force also posed as a drug dealer and communicated with DPR as Nob. As part of his official undercover work as Nob, Force agreed to sell fraudulent identification documents to DPR for $40,000 in Bitcoins.

According to the criminal complaint against the agents, Force kept the Bitcoins received by his Nob account in connection with that transaction for his personal use. On another occasion, again as part of his authorized undercover work, Force advised DPR that he had access to information about Silk Road from an invented corrupt government employee. DPR paid Force $50,000 in Bitcoins for purported inside law enforcement information; Force allegedly purloined that payment as well.

Moreover, outside his authorized undercover work, Force operated another account under the name French Maid, through which he again offered to sell DPR information about the government’s Silk Road investigation. Acting as French Maid, Force received about $100,000 in Bitcoins that he kept for his personal use. Force created yet another unauthorized Silk Road account, under the name Death-FromAbove, which was unknown to law enforcement until the defense identified it during trial..Force used the DeathFromA-bove account to try to extort money from DPR.

For example, in one such chat that took place on April 16, 2013, DeathFromA-bove told DPR that he knew that DPR’s true identity was Anand Athavale. Death-FromAbove demanded a payment of $250,000 in exchange for which DeathFro-mAbove would remain silent about DPR’s identity. There is no evidence that DPR made the requested payment to DeathFro-mAbove; indeed, DPR shrugged off the attempted blackmail as “bogus.” App’x 710.

As will be explained in more detail below, the district court prevented Ulbricht from introducing evidence at trial related to Force’s corruption because doing so would have exposed the ongoing grand jury investigation into Force’s conduct. The district court also denied Ulbricht discovery related to the investigation and excluded certain hearsay statements that arguably revealed Force’s corruption. Ul-bricht contends on appeal that the district court’s various rulings concerning evidence related to Force deprived him of a fair trial.

Additionally, Ulbricht did not learn of Bridges’s corrupt conduct until after trial when the criminal complaint against both agents was unsealed. Thus, in his motion for a new trial, he argued that the belated disclosure violated his due process rights under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). Ulbricht contends on appeal that the district court incorrectly denied that motion. II. Ulbricht’s Arrest Ulbricht was arrested in a San Francisco public library on October 1, 2013, after the government had amassed significant evidence identifying him as Dread Pirate Roberts.

The arrest was successfully orchestrated to catch Ulbricht in the act of administering Silk Road as DPR. Federal agents observed Ulbricht enter the public library, and a few minutes later Dread Pirate Roberts came online in the Silk Road staff chat. Der-Yeghiayan, under the undercover administrator username Cirrus, initiated a chat with DPR, asking him to go to a specific place on the Silk Road site to address some flagged messages from users.

Der-Yeghiayan reasoned that this would “force [Ulbricht] to log in under ... his Dread Pirate Roberts account” in the Silk Road marketplace, as well as in the staff chat software. Tr. 331-32. Once Der-Yeghiayan knew that DPR had logged onto the flagged message page in the marketplace, he signaled another agent to effect the arrest. Ulbricht was arrested, and incident to that arrest agents seized his laptop. The same chat that Der-Yeghiayan had initiated with Dread Pirate Roberts a few minutes earlier was open on Ulbricht’s screen.

Ulbricht also visited the flagged post in the marketplace that Der-Yeghiayan (as Cirrus) had asked DPR to look at during their chat. While he was chatting with Cirrus, moreover, Ulbricht had accessed Silk Road by using the “Mastermind” page. That page was available only to Dread Pirate Roberts. A great deal of the evidence against Ulbricht came from the government’s search of his laptop and his home after the arrest.

On the day of Ulbricht’s arrest, the government obtained a warrant to seize Ulbricht’s laptop and search it for a wide variety of information related to Silk Road and information that would identify Ul-bricht as Dread Pirate Roberts. Ulbricht moved to suppress the large quantity of evidence obtained from his laptop, challenging the constitutionality of that search warrant. Ulbricht argues on appeal that the district court erred in denying his motion to suppress. More details concerning the search warrant will be described in context below. III.

The Trial Ulbricht’s trial lasted approximately three weeks, from January 13 through February 4, 2015. Judge Forrest handled the complex and contentious trial with commendable patience and skill. Although Ulbricht does not challenge the sufficiency of the evidence to support the jury’s verdict on any of the counts of conviction, we summarize the evidence presented at trial as context for the issues raised on appeal. A.

The Government’s Case The government presented overwhelming evidence that Ulbricht created Silk Road in 2011 and continued to operate the site throughout its lifetime by maintaining its computer infrastructure, interacting with vendors, crafting policies for site users, deciding what products would be available for sale on the site, and managing a small staff of administrators and software engineers. Defense counsel conceded in his opening statement that Ul-bricht did in fact create Silk Road.

According to Ulbricht’s own words in a 2009 email, Ulbricht originally conceived of Silk Road as “an online storefront that couldn’t be traced back to [him] ... where [his] customers could buy [his] products” and pay for them “anonymously and securely.” Tr. 991. From 2009 through 2011, Ulbricht worked to get the site up and running, relying on computer programming assistance from others, including his friend Richard Bates. According to one of the journal entries discovered on his laptop, in 2010 Ulbricht began to grow hallucinogenic mushrooms to sell on the site “for cheap to get people interested.” Tr. 899.

As the site began to garner significant interest in 2011, Ulbricht wrote in his journal that he was “creating a year of prosperity and power beyond what I have ever experienced before. Silk Road is going to become a phenomenon and at least one person will tell me about it, unknowing that I was its creator.” Tr. 899-900. 1. Evidence Linking Ulbricht to Dread Pirate Roberts Around January 2012, the Silk Road user who represented himself as the lead administrator of the site adopted the user-name Dread Pirate Roberts.

The name alludes to the pseudonym of a pirate in the popular novel and film The Princess Bride that is periodically passed on from one individual to another. In order to assure users that posts purporting to be authored by DPR were indeed his own, DPR authenticated his posts using an electronic signature known as a PGP key. Silk Road users had access to a public PGP key, and DPR had a private PGP key that he alone could use to sign his Silk Road posts.

When DPR signed a post using his private key, Silk Road users could run the code in the public key, and if the post was signed with the correct private key the user would receive a message that the authentication was successful. The government recovered DPR’s private PGP key on Ul-bricht’s laptop. Importantly, the public PGP key did not change during the site’s life span, meaning that DPR used the same private key to sign his posts throughout the time that he administered Silk Road. Additional evidence supported the conclusion that Ulbricht was Dread Pirate Roberts.

For example, the instructions that DPR provided to Cirrus (the account that Der-Yeghiayan later used for undercover work) for how to access the staff chat and contact DPR directly were found in a file on Ulbricht’s laptop.

The government also discovered the following evidence, covering the entire period during which DPR managed the Silk Road site, on Ulbricht’s computer: thousands of pages of chat logs with Silk Road employees; detailed journal entries describing Ulbricht’s ownership of the site; a list that tracked Ulbricht’s tasks and ideas related to Silk Road; a copy of Silk Road’s database; and spreadsheets cataloguing both the servers that hosted Silk Road and expenses and profits associated with the site.

The government seized approximately $18 million worth of Bitcoins from the wallet on Ul-bricht’s laptop and analyzed their transaction history (through blockchain records) to determine that about 89% of the Bit-coins on Ulbricht’s computer came from Silk Road servers located in Iceland. A search of Ulbricht’s home yielded additional evidence linking him with the site. That evidence included two USB hard drives with versions of documents related to Silk Road that were also stored on Ulbricht’s laptop.

There were also handwritten notes crumpled in Ulbricht’s bedroom trash can about ideas for improving Silk Road’s vendor rating system—an initiative that Dread Pirate Roberts had just revealed through a post in a discussion forum on the site. The government also introduced other circumstantial evidence connecting Ul-bricht to DPR’s activity on Silk Road, such as evidence matching Ulbricht’s actual travel history with' DPR’s online discussion of his travel plans. As one concrete example, the government discovered a Tor Chat log on Ulbricht’s laptop memorializing DPR’s chat with a user named H7.

On October 30, 2011, DPR told H7 that he would be traveling soon. On Ulbricht’s Gmail account, which uses an email address that incorporates his full name, the government discovered a travel itinerary from CheapAir that indicated that Ulbricht would be traveling on November 15, 2011. The government introduced several additional examples of DPR discussing travel plans that matched up with travel disclosed in Ulbricht’s email and social media activity.

At one point, for example, Ul-bricht uploaded photos to his Facebook account in an album entitled “Thailand, February 2012.” DPR discussed going to Thailand in a Tor chat on January 27, 2012, indicating that he was in “Thailand now,” attracted by the “allure of a warm beach.” Tr. 1300. He also mentioned in a January 26 chat with a user named “vj,” which stood for Variety Jones, that he was in Thailand to experience the “beaches and jungles.” Id. at 1298.

One of the photos in the Thailand Facebook album depicted Ul-bricht “in front of what appears to be jungles and beaches,” both of which were referenced in DPR’s chats from late January. Id. at 1301, 2. Murders Commissioned by Dread Pirate Roberts The government also presented evidence that DPR commissioned the murders of five-people to protect Silk Road’s anonymity, although there is no evidence that any of the murders actually occurred.

In March 2013, a Silk Road vendor whose username was FriendlyChemist threatened to release “thousands of usernames, ordr [sic] amounts, [and] addresses” of Silk Road customers and vendors if DPR did not ensure that FriendlyChemist received money from another person, Lucy-drop. Tr. 1806. Releasing the information would have destroyed the affected users’ anonymity, undermining the security of the site.

In a later chat with another person, RealLucyDrop, DPR wrote that it would be “terrible” if the personal information were to be released, and thus he needed FriendlyChemist’s “real world identity so I can threaten him with violence if he were to release any names.” Id. at 1811. The episode escalated from there. DPR connected with Redandwhite, who was FriendlyChemist’s supplier, and wrote that “FriendlyChemist is a liability and I wouldn’t mind if he was executed.” Id. at 1822. After negotiating the logistical details of the murder, Ulbricht agreed to pay Redandwhite $150,000 in Bitcoins to kill FriendlyChemist.

DPR paid Redandwhite, who later confirmed that he had received the payment and carried out the murder, and sent what appeared to be a photo of the dead victim to DPR. DPR replied that he had “received the picture and deleted it,” and thanked Redandwhite for his “swift action.” Id. at 1892. Around the same time, Ulbricht recorded in a file on his laptop that he “[g]ot word that the blackmailer was executed.” Id. at 1887. The government was not able to develop any evidence linking these conversations to an actual murder.

A reasonable jury could easily conclude, however, that the evidence demonstrated that Ulbricht ordered and paid for the killing, and that he believed that it had occurred. Later, DPR ordered four other murders through Redandwhite. Dread Pirate Roberts identified another Silk Road user, Tony76, who knew FriendlyChemist and might compromise the site’s anonymity. After some negotiations, DPR agreed to pay Redandwhite $500,000 in Bitcoins to kill Tony76 and three of his associates. DPR then sent the payment to Redand-white.

On April 6, 2013, Ulbricht wrote in a file on his laptop that he “[g]ave angels go ahead to find tony76.” Tr. 1900. Two days later, Ulbricht recorded that he “[s]ent payment to angels for hit on tony76 and his three associates.” Id. One of the government’s expert witnesses was able to link the payments for all five murders to Bitcoin wallets located on Ulbricht’s laptop.

Again, while the evidence demonstrates that Ulbricht ordered and paid substantial sums for the murders, there is no evidence that the killings actually took place; the government theorized that Re-dandwhite had tricked Ulbricht into thinking that he actually committed the murders, but that in fact he had not. B. The Defense Case As noted above, Ulbricht conceded at trial that he had created' Silk Road, and he was caught red-handed operating the site at the end of the investigation.

His principal defense strategy at trial—more of an effort at mitigation than outright denial of his guilt of the conspiracy and other charges in the indictment—was to admit his role at the beginning and end of the site’s operation, but to contend that he sold Silk Road to someone else in 2011 and abandoned his role as its administrator, only to be lured back by the successor DPR near the end of its operation to take the blame for operating the site.

The defense attempted on several occasions to implicate as alternative suspects Karpeles and Athavale, both of whom the government had investigated for a possible connection to Silk Road but later abandoned as candidates for DPR’s real-world identity. As part of his alternative-perpetrator defense, Ulbricht theorized that the person or persons who operated as the true Dread Pirate Roberts during the purported interim period planted incriminating evidence on his laptop in order to frame him. For the most part, the defense advanced this theory through cross-examination of government witnesses.

Ulbricht did not testify at trial. One point in the testimony of Richard Bates exemplifies the defense’s approach and the government’s response. Bates, Ul-bricht’s friend who assisted with computer programming issues when Ulbricht launched Silk Road, testified for the government. According to Bates, Ulbricht told him in November 2011 that he had sold Silk Road to someone else, a claim that Bates believed at the time to be true. Moreover, in a February 2013 Google chat between Bates and Ulbricht, Ulbricht wrote that he was “[g]lad” that Silk Road was “not [his] problem anymore.” Tr. 1140-41.

Bates understood that to mean that Ulbricht no longer worked on the site. To mitigate any damage from Bates’s testimony, the government introduced a December 9, 2011 Tor chat between Ul-bricht and vj. In that chat, vj asked Ul-bricht whether anyone else knew about his involvement in Silk Road. Ulbricht responded: “[U]nfortunately yes. There are two, but they think I sold the site and got out and they are quite convinced of it.” Tr. 1191. He further wrote that those two people thought he sold the site “about a month ago,” id., which roughly corresponds to the November 2011 conversation between Bates and Ulbricht.

Significantly, it was shortly after this conversation that vj suggested that Ulbricht change his online identity to DPR. In view of the fictional character it referenced, the government contended that the online moniker DPR was deliberately adopted to support the cover story that the lead administrator of Silk Road changed over time. Thus, although the government elicited testimony that Ulbricht told Bates that he sold the site in 2011, it also presented evidence that Ulbricht had lied to Bates about that sale and continued to operate the site in secret. 1.

Cross-Examination of Government Witnesses Ulbricht’s defense depended heavily on cross-examination of government witnesses, much of which was designed to support the argument that either Karpeles or Athavale was the real DPR, or that multiple people operated as Dread Pirate Roberts during Silk Road’s life span. The district court limited his cross-examination in two ways that Ulbricht challenges on appeal. First, the district court prevented Ulbricht from exploring several specific topics with Der-Yeghiayan, the government’s first witness, through whom it introduced much of its evidence.

Those topics included, inter alia, Der-Yeghiayan’s prior suspicions that Karpeles was DPR. Second, the district court limited Ul-bricht’s ability to cross examine FBI computer scientist Thomas Kiernan, who testified about evidence that he discovered on Ulbricht’s laptop, concerning several specific technical issues related to software on Ulbricht’s computer. More details about those attempted cross-examinations will be discussed in context below. 2. Hearsay Statements Ulbricht also attempted to introduce two hearsay statements in his defense, both of which the district court excluded as inadmissible.

Those hearsay statements comprise: (1) chats between DPR and DeathFromAbove (Force) .concerning Force’s attempt to extort money from DPR in exchange for information about the government’s investigation of Silk Road; and (2) the government’s letter describing a statement by Andrew Jones, a site administrator, concerning one particular conversation that he had with DPR. The contents of those hearsay statements and other relevant facts will be discussed in more detail below. 3.

Defense Expert Witnesses Long after the trial began on January 13, 2015, and shortly before the government rested on February 2 and the defense rested on February 3, Ulbricht disclosed to the government his intent to call two expert witnesses: Dr. Steven Bellovin and Andreas Antonopoulos.

The Antono-poulos disclosure indicated that he would testify on several subjects relevant to Silk Road, including “the origins of Bitcoin,” “the various purposes and uses of Bitcoin,” “the mechanics of Bitcoin transactions,” “the value of Bitcoin over time since its inception,” and “the concepts of Bitcoin speculating and Bitcoin mining,” among other things. App’x 349.

The Bellovin disclosure followed a similar pattern, indicating that he would testify about “[gjeneral principles of internet security and vulnerabilities,” the “import of some lines of PHP code provided to defense counsel in discovery,” and “[gjeneral principles of public-key cryptography,” among other topics. Id. at 360. Neither disclosure summarized the opinions that the experts would offer on those subjects, nor did either identify the bases for the experts’ opinions. On January 29 and 31, the government moved to preclude the testimony of both proffered experts.

The government argued that the expert notices were untimely and did not contain the information required by Rule 16 of the Federal Rules of Criminal Procedure, including a

summary of the opinions that the experts would offer on the stand. On February 1—three days before the end of the trial—the district court granted the government’s motions and precluded both experts from testifying, concluding that the defendant’s notices were late and that the disclosures were substantively inadequate under Rule 16. Ulbricht claims that the district court erred in precluding his experts from testifying.

In sum, the defense case was limited to cross-examining government witnesses, briefly calling four character witnesses, having a defense investigator authenticate a task list on Ulbricht’s computer, and reading a few of DPR’s posts into the record. Ulbricht contends, however, that his defense was hamstrung by the rulings described above. C. The Verdict and Post-Trial Motion After deliberating for about three and a half hours, the jury returned a guilty ver-diet on all seven counts in the Indictment. As described in more detail below, Ul-bricht then moved for a new trial under Rule 33, Fed. R. Crim. P.

The district court denied the motion, and Ulbricht argues here that it erred in doing so. IV. Sentencing The United States Probation Office prepared the Pre-Sentence Investigation Report (“PSR”) in March 2015. It described the offense conduct in detail and discussed the five murders that Ulbricht allegedly hired Redandwhite to commit. Over Ul-bricht’s objection, the PSR also discussed six drug-related deaths that the government contended, and the district court found, were connected with Silk Road.

Circumstantial evidence linked each of those fatalities with varying degrees of certainty to the decedent’s purchase of drugs on Silk Road. For example, one user died from an overdose of heroin combined with other drugs. The deceased individual was found with a needle and a bag of heroin, as well as a torn-open delivery package. Open on his computer was a Silk Road chat in which a vendor described the package of heroin that was due to arrive that day, including a tracking number that matched the opened package.

Two other individuals whose deaths the PSR described were Silk Road customers who purchased drugs on the site shortly before their deaths. A fourth person died after ingesting a synthetic drug originally purchased on Silk Road that he obtained through an intermediary dealer, and a fifth died after leaping from a balcony while high on a psychedelic drug that he bought from the site.

A sixth person died of pneumonia after placing over thirty orders for heroin and other drugs on Silk Road; the autopsy report theorized that his drug use may have “blunted the deceased’s perception of the severity of his illness,” thus contributing to his premature death. PSR ¶ 83. In arguing that the district court should consider the six deaths, the government explained that they “illustrate the obvious: that drugs can cause serious harm, including death.” App’x 902.

In the first of several sentencing submissions, Ulbricht urged the district court not to consider the six drug-related deaths and to strike them from the PSR. In support of that argument, Ulbricht claimed that Silk Road had harm-reducing effects, meaning that it made drug use less dangerous. Specifically, Ulbricht employed Dr. Fernando Caudevilla (username Doctor X), a physician who provided drug-use advice to the site’s customers.

Caudevilla spent up to two or three hours a day on Silk Road discussion fora and sent over 450 messages providing guidance about illegal drug dosage and administration, as well as information about the harms associated with certain drugs. Caudevilla also provided weekly reports to DPR concerning the advice he gave to the site’s users.

Ulbricht further claimed that Silk Road allowed for better drug quality control because vendors were subject to a rating system, buyers were able to choose from among many different sellers, and the site’s anonymity encouraged free dialogue about drug use that helped mitigate the stigma accompanying drug addiction. According to Caudevilla, when the site received negative feedback about the quality of the drugs sold by a vendor, that vendor was removed from the site.

Finally, Ulbricht claimed that the site reduced violence associated with the drug trade by providing a safe, computer-based method of purchasing drugs. Ulbricht also submitted an expert report from Dr. Mark Taff, which provided an alternative reason for excluding the six deaths from the PSR. In his report, Dr. Taff explained that, based on the information available, it was impossible to know with medical certainty that Silk Road drugs caused the six deaths described in the PSR.

There were “gaping holes” in the investigations into each death, and some were missing autopsy reports, toxicology reports, and death certificates. App’x 911. Moreover, Dr. Taff claimed that it was impossible to know the cause of each death because several of the deceased had ingested multiple drugs prior to their deaths. Ulbricht argued that, absent a clear causal link between the deaths and the offense conduct, the deaths were not relevant to his sentencing at all.

The defense later submitted another sentencing memorandum, which included 97 letters from friends and family describing Ulbricht’s good character as well as academic articles about the myriad problems associated with unduly severe sentences for drug crimes. He also urged the district court not to consider the five murders commissioned by DPR, in part because he claimed only to have fantasized about the murders, implying that he did not expect them to be carried out.

In its sentencing submission, the government requested that the district court impose a sentence substantially above the twenty-year mandatory minimum. Ulbricht’s sentencing hearing took place on May 29, 2015. The district court concluded that Ulbricht’s offense level was 43—the highest possible offense level under the Sentencing Guidelines—and that his criminal history category was I. The high offense level largely resulted from the massive quantity of drugs trafficked using Silk Road, as well as several enhancements, including one for directing the use of violence, U.S.S.G. § 2Dl.l(b)(2).

Ul-bricht does not dispute that calculation. Due to the high offense level, the Guidelines advisory sentence “range” was life in prison, and the U.S. Probation Office recommended that sentence. At the sentencing hearing, the district court resolved several disputed issues of fact. For example, because Ulbricht contested his responsibility for the five commissioned murders for hire, the district court found by a preponderance of the evidence that Ulbricht did in fact commission the murders, believing that they would be carried out.

The district court characterized the evidence of the murders for hire, which included Ulbricht’s journal, chats with other Silk Road users, and the evidence showing that Ulbricht actually paid a total of $650,000 in Bitcoins for the killings, as “ample and unambiguous.” App’x 1465. The court then turned to the six drug-related deaths described in the PSR.

Over Ulbricht’s objection, the district court found that the deaths were “related conduct relevant to his sentencing” because the “question as to whether this information is properly included in the PSR is whether the Court finds, by a preponderance of the evidence[,] that the deaths, in some way, related to Silk Road.” Id. at 1472. It went on to explain that “the relevant offense committed is the unlawful distribution of drugs and the running of a criminal drug enterprise, ... [and] based on the evidence before the Court, the sale of the drugs through Silk Road caused harm to the decedents.” Id. at 1473.

The district court described the facts associated with five of the deaths and specifically found that each was connected to Silk Road, rejecting the defendant’s argument that but-for causation was required in order for the court to consider the deaths as relevant to the offense conduct. Parents of two of the decedents also made statements at the proceeding, describing the emotional impact that the losses had on them and their families.

In the course of explaining its reasons for choosing Ulbricht’s sentence, the district court discussed the facts of Ul-bricht’s offense, his apparent character, and the purposes of criminal punishment. The court described Doctor X as “enabling,” App’x 1530, rather than reducing the harms associated with drug use, emphasized the social costs attendant to expanding the scope of the drug market, discussed the five murders for hire, and stated that the sentence imposed on Ul-bricht could have a powerful general deterrent effect because the case had attracted an unusually large amount of publicity.

The court then sentenced Ul-bricht principally to life imprisonment. This appeal followed. DISCUSSION On appeal, Ulbricht raises a number of claims of error. For purposes of organizational clarity, we group them into three categories, and present them in the order in which the issues arose in the district court.

Accordingly, we discuss first Ul-bricht’s claims that much of the evidence against him should have been suppressed because it was obtained in violation of his Fourth Amendment rights; second, his arguments that the district court’s evidentia-ry errors denied him a fair trial; and third, his objections to his sentence. I. Fourth Amendment Issues Ulbricht claims that the district court erred in denying his motion to suppress evidence obtained in violation of the Fourth Amendment.

On appeal from a denial of a suppression motion, “we review a district court’s findings of fact for clear error, and its resolution of questions of law and mixed questions of law and fact de novo.” United States v. Bohannon, 824 F.3d 242, 247-48 (2d Cir. 2016). Ulbricht raises two principal arguments. First, he contends that the pen/trap orders that the government used to monitor IP address traffic to and from his home router violated the Fourth Amendment because the government obtained the orders without a warrant.

Second, he claims that the warrants authorizing the government to search his laptop as well as his Google and Facebook accounts violated the Fourth Amendment’s particularity requirement. We reject those contentions and affirm the denial of Ulbricht’s motion to suppress. A. Pen/Trap Orders Pursuant to orders issued by United States magistrate judges in the Southern District of New York, the government used five pen registers and trap and trace devices to monitor IP addresses associated with Internet traffic to and from Ulbricht’s wireless home router and devices that regularly connected to that router.

The government obtained the orders pursuant to the Pen/Trap Act, which provides that a government attorney “may make [an] application for an order ... authorizing or approving the installation and use of a pen register or a trap and trace device ... to a court of competent jurisdiction.” 18 U.S.G. § 3122(a)(1).

A “pen register” is defined as a “device or process which records or decodes dialing, routing, addressing, or signaling information transmitted by an instrument or .facility from which a wire or electronic communication is transmitted,” and “shall not include the contents of any communication.” Id. § 3127(3). A “trap and trace” device means “a device or process which captures the incoming electronic or other impulses which identify the originating number or other dialing, routing, addressing, and signaling information reasonably likely to identify the source of a wire or electronic communication.” Id. § 3127(4).

Like pen registers, trap and trace devices may not capture the “contents of any communication.” Id. The statute does not require a search warrant for the use of a pen register or trap and trace device, nor does it demand the kind of showing required to obtain such a warrant. Rather, the statute requires only that the application contain a “certification ... that the information likely to be obtained is relevant to an ongoing criminal investigation.” Id. § 3122(b)(2).

The orders in this case authorized the government to “use a pen register and trap and trace device to identify the source and destination [IP] addresses, along with the dates, times, durations, ports of transmission, and any Transmission Control Protocol (‘TCP’) connection data, associated with any electronic communications sent to or from” various devices, including Ulbricht’s home wireless router and his laptop. S.A. 93. In each order, the government specified that it did not seek to obtain the contents of any communications.

Instead, it sought authorization to collect only “dialing, routing, addressing, and signaling information” that was akin to data captured by “traditional telephonic pen registers and trap and trace devices.” Id. at 130. Ulbricht claims that the pen/trap orders violated the Fourth Amendment because he had a reasonable expectation of privacy in the IP address routing information that the orders allowed the government to collect.

The Fourth Amendment to the United States Constitution provides that: “The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.” The “cornerstone of the modern law of searches is the principle that, to mount a successful Fourth Amendment challenge, a defendant must demonstrate that he personally has an expectation of privacy in the place searched.” United States v.

Haqq, 278 F.3d 44, 47 (2d Cir. 2002) (internal quotation marks omitted). Thus, a “Fourth Amendment 'search[ ]’ ... does not occur unless the search invades an object or area [in which] one has a subjective expectation of privacy that society is prepared to accept as objectively reasonable.” United States v. Hayes, 551 F.3d 138, 143 (2d Cir. 2008). The Supreme Court has long held that a “person has no legitimate expectation of privacy in information he voluntarily turns over to third parties,” including phone numbers dialed in making a telephone call and captured by a pen register. Smith v.

Maryland, 442 U.S. 735, 743-44, 99 S.Ct. 2577, 61 L.Ed.2d 220 (1979). This is so because phone users “typically know that they must convey numerical information to the phone company; that the phone company has facilities for recording this information; and that the phone company does in fact record this information for a variety of legitimate business purposes.” Id. at 743, 99 S.Ct. 2577. Similarly, “e-mail and Internet users ... rely on third-party equipment in order to engage in communication.” United States v. Forrester, 512 F.3d 500, 510 (9th Cir. 2008).

Internet users thus “should know that this information is provided to and used by Internet service providers for the specific purpose of directing the routing of information.” Id. Moreover, “IP addresses are not merely passively conveyed through third party equipment, but rather are voluntarily turned over in order to direct the third party’s servers.” United States v. Christie, 624 F.3d 558, 574 (3d Cir. 2010) (internal quotation marks omitted).

Ulbricht notes that questions have been raised about whether some aspects of modern technology, which entrust great quantities of significant personal information to third party vendors, arguably making extensive government surveillance possible, call for a re-evaluation of the third-party disclosure doctrine established by Smith. See, e.g., United States v. Jones, 565 U.S. 400, 417-18, 132 S.Ct. 945, 181 L.Ed.2d 911 (2012) (Sotomayor, J., concurring); American Civil Liberties Union v. Clapper, 785 F.3d 787, 824 (2d Cir. 2015).

We remain bound, however, by that rule until and unless it is overruled by the Supreme Court. See United States v. Gomez, 580 F.3d 94, 104 (2d Cir. 2009); see also United States v. Wheelock, 772 F.3d 825, 829 (8th Cir. 2014). Moreover, whatever novel or more intrusive surveillance techniques might present future questions concerning the appropriate scope of the third-party disclosure doctrine, the orders in this case do not present such issues.

The recording of IP address information and similar routing data, which reveal the existence of connections between communications devices without disclosing the content of the communications, are precisely analogous to the capture of telephone numbers at issue in Smith. That is why the orders here fit comfortably within the language of a statute drafted with the earlier technology in mind. The substitution of electronic methods of communication for telephone calls does not alone create a reasonable expectation of privacy in the identities of devices with whom one communicates.

Nor does it raise novel issues distinct from those long since resolved in the context of telephone communication, with which society has lived for the nearly forty years since Smith was decided. Like telephone companies, Internet service providers require that identifying information be disclosed in order to make communication among electronic devices possible. In light of the Smith rule, no reasonable person could maintain a privacy interest in that sort of information.

We therefore join the other circuits that have considered this narrow question and hold that collecting IP address information devoid of content is “constitutionally indistinguishable from the use of a pen register.” Forrester, 512 F.3d at 510; see, e.g., Wheelock, 772 F.3d at 828 (holding that the defendant “cannot claim a reasonable expectation of privacy in [the] government’s acquisition of his subscriber information, including his IP address and name,” because it had been “revealed to a third party” (internal quotation marks omitted)); Christie, 624 F.3d at 573 (holding that there is no expectation of privacy in “subscriber information provided to an internet provider,” such as an IP address (internal quotation marks omitted)); see also Guest v.

Leis, 255 F.3d 325, 336 (6th Cir. 2001) (holding that “computer users do not have a legitimate expectation of privacy in their [bulletin board] subscriber information because they have conveyed it to another person”); United States v. Graham, 824 F.3d 421, 432 (4th Cir. 2016) (en banc) (noting that “third-party information relating to the sending and routing of electronic communications does not receive Fourth Amendment protection”); United States v.

Carpenter, 819 F.3d 880, 887 (6th Cir. 2016) (“[C]ourts have not (yet, at least) extended [Fourth Amendment] protections to the internet analogue to envelope markings, namely the metadata used to route internet communications, like ... IP addresses.”). Where, as here, the government did not access the contents of any of Ulbricht’s communications, it did not need to obtain a warrant to collect IP address routing information in which Ul-bricht did not have a legitimate privacy interest. We therefore reject Ulbricht’s contention that the issuance of such orders violated his Fourth Amendment rights.

Ulbricht’s additional arguments are not persuasive. Ulbricht contends generally that pen/trap orders may monitor a communication’s content by tracking metadata, but he does not identify what metadata the government might have collected or explain how the pen/trap orders in this case gave the government information concerning the content of his communications. He also claims that the orders violated the Fourth Amendment by impermissibly monitoring activity within his home, relying on Kyllo v. United States, 533 U.S. 27, 121 S.Ct. 2038, 150 L.Ed.2d 94 (2001).

In Kyllo, the Court held that using thermal-imaging technology from outside the home to discern whether a person was growing marijuana in the home might reveal innocent, non-criminal information in which a resident has a privacy interest. Id. at 38, 121 S.Ct. 2038. Ulbricht contends that monitoring IP address traffic through his router is similar to the thermal-imaging technology because it might reveal when and how Ulbricht used his computer when he was at home.

The same can be said, however, of an ordinary telephone pen register, which can reveal if, when, and how a person uses his or her home phone to make calls. See, Smith, 442 U.S. at 743, 99 S.Ct. 2577. IP address traffic similarly reveals whether an Internet subscriber (or, more precisely, a person who uses the subscriber’s Internet connection) is home and using the Internet.

Nothing in Kyllo suggests that government monitoring of data disclosed to an outside telephone or Internet provider for ordinary business purposes becomes constitutionally suspect when investigators use that information to draw inferences about whether someone is making telephone calls or accessing websites from inside his or her home. We therefore see no constitutional difference between monitoring home phone dialing information and IP address routing data. Thus, we conclude that the pen register and trap and trace orders did not violate the Fourth Amendment. B.

Search Warrants Ulbrieht also contends that the warrants authorizing the search and seizure of his laptop as well as his Facebook and Google accounts violated the Fourth Amendment’s particularity requirement. The Fourth Amendment explicitly commands that warrants must be based on .probable cause and must “particularly describ[e] the place to be searched, and the persons or things to be seized.” U.S. Const. amend.

IV. “It is familiar history that indiscriminate searches and. seizures conducted under the authority of ‘general warrants’ were the immediate evils that motivated the framing and adoption of the Fourth Amendment.” Payton v. New York, 445 U.S. 573, 583, 100 S.Ct. 1371, 63 L.Ed.2d 639 (1980). Those general warrants “specified only an offense,” leaving “to the discretion of the executing officials the decision as to which persons should be arrested and which places should be searched.” Steagald v. United States, 451 U.S. 204, 220, 101 S.Ct. 1642, 68 L.Ed.2d 38 (1981).

The principal defect in such a warrant was that it permitted a “general, exploratory rummaging in a person’s belongings,” Andresen v. Maryland, 427 U.S. 463, 480, 96 S.Ct. 2737, 49 L.Ed.2d 627 (1976) (internal quotation marks omitted), a problem that the Fourth Amendment attempted to resolve by requiring the warrant to “set out with particularity” the “scope of the authorized search,” Kentucky v. King, 563 U.S. 452, 459, 131 S.Ct. 1849, 179 L.Ed.2d 865 (2011). To be sufficiently particular under the Fourth Amendment, a warrant must satisfy three requirements.

First, “a warrant must identify the specific offense for which the police have established probable cause.” United States v. Galpin, 720 F.3d 436, 445 (2d Cir. 2013). Second, “a warrant must describe the place to be searched.” Id. at 445-46. Finally, the “warrant must specify the items to be seized by their relation to designated crimes.” Id. at 446 (internal quotation marks omitted). “Where, as here, the property to be searched is a computer hard drive, the particularity requirement assumes even greater importance.” Id.

A general search of electronic data is an especially potent threat to privacy because hard drives and e-mail accounts may be “akin to a residence in terms of the scope and quantity of private information [they] may contain.” Id. The “seizure of a computer hard drive, and its subsequent retention by the government, can [therefore] give the government possession of a vast trove of personal information about the person to whom the drive belongs, much of which may be entirely irrelevant to the criminal investigation that led to the seizure.” United States v. Ganias, 824 F.3d 199, 217 (2d Cir. 2016) (en banc).

Such sensitive records might include “[t]ax records, diaries, personal photographs, electronic books, electronic media, medical data, records of internet searches, [and] banking and shopping information.” Id. at 218. Because of the nature of digital storage, it is not always feasible to “extract and segregate responsive data from non-responsive data,” id. at 213, creating a “serious risk that every warrant for electronic information will become, in effect, a general warrant,” Galpin, 720 F.3d at 447 (internal quotation marks omitted).

Thus, we have held that warrants that fail to “link [the evidence sought] to the criminal activity supported by probable cause” do not satisfy the particularity requirement because they “lack[ ] meaningful parameters on an otherwise limitless search” of a defendant’s electronic media. United States v. Rosa, 626 F.3d 56, 62 (2d Cir. 2010). The Fourth Amendment does not require a perfect description of the data to be searched and seized, however.

Search warrants covering digital data may contain “some ambiguity ... so long as law enforcement agents have done the best that could reasonably be expected under the circumstances, have acquired all the descriptive facts which a reasonable investigation could be expected to cover, and have insured that all those facts were included in the warrant.” Galpin, 720 F.3d at 446 (internal quotation marks omitted). Moreover, it is important to bear in mind that a search warrant does not necessarily lack particularity simply because it is broad.

Since a search of a computer is “akin to [a search of] a residence,” id., searches of computers may sometimes need to be as broad as searches of residences pursuant to warrants. Similarly, traditional searches for paper records, like searches for electronic records, have always entailed the exposure of records that are not the objects of the search to at least superficial examination in order to identify and seize those records that are. And in many cases, the volume of records properly subject to seizure because of their evidentiary value may be vast.

None of these consequences necessarily turns a search warrant into a prohibited general warrant. 1. Laptop Search Warrant The warrant authorizing the search and seizure of Ulbricht’s laptop (the “Laptop Warrant”) explicitly incorporated by reference an affidavit listing the crimes charged, which at the time included narcotics trafficking, computer hacking, money laundering, and murder-for-hire offenses in violation of 21 U.S.C. § 846, 18 U.S.C. §§ 1030, 1956, and 1958.

See In re 650 Fifth Ave. & Related Properties, 830 F.3d 66, 101 (2d Cir. 2016) (describing the requirements for a criminal search warrant’s incorporation of an affidavit by reference). The affidavit also described the workings of Silk Road and the role of Dread Pirate Roberts in operating the site and included a wealth of information supporting a finding that there was probable cause to believe that Ulbricht and DPR were the same person.

Based on that information, the Laptop Warrant alleged that Ulbricht “use[d] [the laptop] in connection with his operation of Silk Road,” and that there was “probable cause to believe that evidence, fruits, and instrumentalities of the [charged offenses]” would be found on the laptop. S.A. 246. Generally speaking, the Laptop Warrant divided the information to be searched for and seized into two categories.

The first covered evidence concerning Silk Road that was located on the computer, including, inter alia, “data associated with the Silk.Road website, such as web content, server code, or database records”; any evidence concerning servers or computer equipment connected with Silk Road; emails, private messages, and forum postings or “other communications concerning Silk Road in any way”; evidence concerning “funds used to facilitate or proceeds derived from Silk Road,” including Bitcoin wallet files and transactions with Bitcoin exchangers, or “information concerning any financial accounts ... where Silk Road funds may be stored”; and “any evidence concerning any illegal activity associated with Silk Road.” Id. at 246-48.

The second category of information in the Laptop Warrant included “evidence relevant to corroborating the identification of Ulbricht as the Silk Road user ‘Dread Pirate Roberts.’ ” Id. at 248.

In order to connect Ulbricht with DPR, the Laptop Warrant authorized agents to search for: “any communications or writings by Ul-bricht, which may reflect linguistic patterns or idiosyncra[s]ies associated with ‘Dread Pirate Roberts,’ or political/economic views associated with [DPR] ... ”; “any evidence concerning any computer equipment, software, or usernames used by Ulbricht, to allow comparison with” computer equipment used by DPR; “any evidence concerning Ulbricht’s travel or patterns of movement, to allow comparison with patterns of online activity of [DPR] ”; “any evidence concerning Ulbricht’s technical expertise concerning Tor, Bitcoins,” and other computer programming issues; any evidence concerning Ulbricht’s attempts to “obtain fake identification documents,” use aliases, or otherwise evade law enforcement; and “any other evidence implicating Ulbricht in the subject offenses.” Id. at 248-49 (footnote omitted).

After careful consideration of the warrant, the supporting affidavit, and Ul-bricht’s arguments, we conclude that the Laptop Warrant did not violate the Fourth Amendment’s particularity requirement. We note, at the outset of our review, that the warrant plainly satisfies the basic elements of the particularity requirement as traditionally understood.

By incorporating the affidavit by reference, the Laptop Warrant lists the charged crimes, describes the place to be searched, and designates the information to be seized in connection with the specified offenses.' Each category of information sought is relevant to Silk Road, DPR’s operation thereof, or identifying Ulbricht as DPR. We do not understand Ulbricht’s arguments to contest the Laptop Warrant’s basic compliance with those requirements.

Rather, Ulbricht’s arguments turn on the special problems associated with searches of computers which, as we have acknowledged in prior cases, Galpin, 720 F.3d at 447; Ganias, 824 F.3d at 217-18, can be particularly intrusive. These arguments merit careful attention. For example, Ulbricht questions the appropriateness of the protocols that the Laptop Warrant instructed officers to use in executing the search.

Those procedures included opening or “cursorily reading the first few” pages of files to “determine their precise contents,” searching for deliberately hidden files, using “key word searches through all electronic storage areas,” and reviewing file “directories” to determine what was relevant. S.A. 253. Ulbrieht, supported by amicus the National Association of Criminal Defense Lawyers (“NACDL”), argues that the warrant was insufficiently particular because the government and the magistrate judge failed to specify the search terms and protocols ex ante in the warrant. We cannot agree.

As illustrated by the facts of this very case, it will often be impossible to identify in advance the words or phrases that will separate relevant files or documents before the search takes place, because officers cannot readily anticipate how a suspect will store information related to the charged crimes. Files and documents can easily be given misleading or coded names, and words that might be expected to occur in pertinent documents can be encrypted; even very simple codes can defeat a pre-planned word search.

For example, at least one of the folders on Ulbricht’s computer had a name with the misspelling “aliaces.” App’x 309. For a more challenging example, Ul-bricht also kept records of certain Tor chats in a file on his laptop that was labeled “mbsobzvkhwx4hmjt.” Id. at 398. The agents reasonably anticipated that they would face such problems in this case. Operating Silk Road involved using sophisticated technology to mask its users’ identities.

Accordingly, although we acknowledge the NACDL’s suggestions in its amicus submission for limiting the scope of such search terms, the absence of the proposed limitations does not violate the particularity requirement on the facts of this ease.

We therefore conclude that, in preparing the Laptop Warrant, “law enforcement agents [did] the best that could reasonably be expected under the circumstances, [had] acquired all the descriptive facts which a reasonable investigation could be expected to cover, and [had] insured that all those facts were included in the warrant.” Galpin, 720 F.3d at 446 (internal quotation marks omitted). The fundamental flaw in Ul-bricht’s (and the NACDL’

s) argument is that it confuses a warrant’s breadth with a lack of particularity. As noted above, breadth and particularity are related but distinct concepts. A warrant may be broad, in that it authorizes the government to search an identified location or object for a wide range of potentially relevant material, without violating the particularity requirement. For exampie, a warrant may allow the government to search a suspected drug dealer’s entire home where there is probable cause to believe that evidence relevant to that activity may be found anywhere in the residence.

Similarly, “[w]hen the criminal activity pervades [an] entire business, seizure of all records of the business is appropriate, and broad language used in warrants will not offend the particularity requirements.” U.S. Postal Serv. v. C.E.C. Servs., 869 F.2d 184, 187 (2d Cir. 1989). Ulbrieht used his laptop to commit the charged offenses by creating and continuing to operate Silk Road.

Thus, a broad warrant allowing the government to search his laptop for potentially extensive evidence of those crimes does not offend the Fourth Amendment, as long as that warrant meets the three particularity criteria outlined above. It is also true that allowing law enforcement to search his writings for linguistic similarities with DPR authorizes a broad search of written materials on Ulbricht’s hard drive. That fact, however, does not mean that the warrants violated the Fourth Amendment.

The Laptop Warrant clearly explained that the government planned to compare Ulbricht’s writings to DPR’s posts to confirm that they were the same person, by identifying both linguistic patterns and distinctive shared political or economic views. Ulbricht and the NACDL similarly claim that searching for all evidence of his travel patterns and movement violates the Fourth Amendment’s particularity requirement.

Again, the warrant explained that it sought information about Ulbricht’s travel “to allow comparison with patterns of online activity of ‘Dread Pirate Roberts’ and any information known about his location at particular times.” S.A. 248. Thus, the Laptop Warrant connects the information sought to the crimes charged and, more specifically, its relevance to identifying Ulbricht as the perpetrator of those crimes. We remain sensitive to the difficulties associated with preserving a criminal defendant’s privacy while searching through his electronic data and computer hard drives.

In the course of searching for information related to Silk Road and DPR, the government may indeed have come across personal documents that were unrelated to Ulbricht’s crimes. Such an invasion of a criminal defendant’s privacy is inevitable, however, in almost any warranted search because in “searches for papers, it is certain that some innocuous documents will be examined, at least cursorily, in order to determine whether they are, in fact, among those papers authorized to be seized.” Ganias, 824 F.3d at 211, quoting Andresen, 427 U.S. at 482 n.11, 96 S.Ct. 2737.

The Fourth Amendment limits such “unwarranted intrusions upon privacy,” id. (internal quotation marks omitted), by requiring a warrant to describe its scope with particularity. The Laptop Warrant satisfied that requirement. Ulbricht has challenged only the facial validity of the Laptop Warrant and not its execution. Because we have no reason to doubt that the officers faithfully executed the warrant, its execution did not result in an undue invasion of Ulbricht’s privacy. Finally, we note that the crimes charged in this case were somewhat unusual.

This case does not involve a more typical situation in which officers searched for evidence of a physician’s illegal distribution of pain medications, to use the NACDL’s example, which may have electronically-stored data associated with the alleged crimes on a hard drive that largely contains non-criminal information.

Here the crimes under investigation were committed largely through computers that there was probable cause to believe included the laptop at issue, and the search warrant application gave ample basis for the issuing magistrate judge to conclude that evidence related to Silk Road and Ulbricht’s use of the DPR username likely permeated Ul-bricht’s computer. Thus, given the nature of Ulbricht’s crimes and their symbiotic connection to his digital devices, we decline to rethink the well-settled Fourth Amendment principles that the Laptop Warrant may implicate.

A future case may require this Court to articulate special limitations on digital searches to effectuate the Fourth Amendment’s particularity or reasonableness requirements. Such a case is not before us. 2. The Google and Facebook Warrants Ulbricht also challenges the warrants that allowed the government to search his Google and Facebook accounts, although he does not present any specific arguments related to those warrants. Both warrants, through affidavits incorporated by reference, set forth the basis for probable cause to search those accounts for evidence of Ulbricht’s involvement in Silk Road.

The warrants also authorized the government to search his Google and Fa-cebook accounts for “evidence, fruits, and instrumentalities” of the specified offenses, including, inter alia: “any communications or writings by Ulbricht”; “any evidence concerning any computer equipment, software, or usernames used by Ulbricht”; “any evidence concerning Ulbricht’s travel or patterns of movement”; and any “other evidence of the” crimes charged. S.A. 334-35, 393-94. The scope of the Google and Facebook warrants thus substantially paralleled that of the Laptop Warrant.

The Google and Facebook warrants were constitutional for the same reasons that the Laptop Warrant was valid. They satisfied all three of the particularity requirements because they listed the subject offenses, described the things to be searched, and identified the information to be seized in relation to the charged crimes. Ulbricht does not advance any additional arguments specific to the Google and Fa-cebook warrants, nor have we identified any independent reason to find them unconstitutionally lacking in specificity. 3.

Conclusion In sum, the issuance of the pen/trap orders and the three search warrants that Ulbricht challenges in this appeal did not violate the Fourth Amendment. Thus, we affirm the district court’s denial of Ul-bricht’s suppression motion. II.

The District Court’s Trial Rulings and Ulbricht!s Rule 33 Motion Ulbricht contends that he did not receive a fair trial for several reasons: (1) the district court’s rulings surrounding corrupt agents Force and Bridges violated his due process rights; (2) the district court erroneously precluded two defense experts from testifying; (3) the district court abused its discretion when it curtailed Ul-bricht’s cross-examination of two government witnesses; and (4) the district court erred when it ruled that certain hearsay statements were inadmissible.

He also contends that, even if each individual error is harmless, the cumulative effect of those errors prejudiced him to the extent that his trial was fundamentally unfair. We detect no error in the district court’s rulings on any of those issues and therefore conclude that Ulbricht was not deprived of his right to a fair trial. A.

Corrupt Agents Force and Bridges Ulbricht’s principal fair trial argument is that the district court erred in numerous ways by preventing him from relying on information related to the corruption of two federal agents, Force and Bridges, involved in the investigation of the Silk Road site. Before trial, the district court (1) precluded Ulbricht from referring at trial to the secret grand jury proceeding against Force; (2) denied Ulbricht discovery related to the Force investigation; and (3) denied Ulbricht an adjournment- of the trial until the Force investigation was complete.

During trial, the district court excluded as hearsay certain chats that related to Force’s illicit use of Silk Road. Finally, Ulbricht learned after trial that the government was investigating a second corrupt agent, Bridges. Ulbricht contends that the failure to disclose Bridges’s corruption until after the trial violated Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), and that the district court erroneously denied his motion for a new trial on that ground.

Without question, the shocking personal corruption of these two government agents disgraced the agencies for which they worked and embarrassed the many honorable men and women working in those agencies to investigate serious criminal wrongdoing. Even more importantly, when law enforcement officers abuse their offices for personal gain, commit other criminal acts, violate the rights of citizens, or lie under oath, they undermine the public’s vital trust in the integrity of law enforcement. They may also compromise the investigations and prosecutions on which they work.

At the same time, the venality of individual agents does not necessarily affect the reliability of the government’s evidence in a particular case or become relevant to the adjudication of every case in which the agents participated- Courts are obligated to ensure that probative evidence is disclosed to the defense, carefully evaluated by the court for its materiality to the case, and submitted for the jury’s consideration where admissible.

But courts must also take care that wrongdoing by investigators that has no bearing on the matter before the court not be used as a diversion from fairly assessing the prosecution’s case. Like any other potential evidence, information about police corruption must be evaluated by reference to the ordinary rules of criminal procedure and evidence, a task to which we now turn. 1. Background: Pretrial Disclosure of the Force Investigation The government disclosed its investigation into Force’s corruption to the defense about six weeks before trial.

Initially, on November 21, 2014, the government wrote a sealed ex parte letter to the district court seeking permission to disclose to the defense information about the Force grand jury investigation subject to a protective order. The district court granted the application. On December 1, the government provided a copy of the November 21 letter, which otherwise remained sealed, to defense counsel. According to the letter, Force leaked information to DPR in exchange for payment and “corruptly obtain[ed] proceeds from the Silk Road website and converged] them to his personal use.” App’x 649.

The government then undertook to purge its trial evidence of anything arguably traceable to Force. Ulbricht moved to unseal the entire November 21 letter so that he could rely on the information in the letter that related to Force’s corruption at trial, arguing that the letter included Brady information and that he therefore had a particularized need to disclose the information that outweighed the presumption of grand jury secrecy. He also requested discovery and subpoenas under Rules 16 and 17, Fed. R. Crim. P., to learn more about the scope of Force’s corruption.

In the alternative, Ulbricht sought an adjournment of the trial until the Force investigation concluded and information about his corruption might become public through the filing of charges against him. On December 15, the district court held a sealed hearing on that issue and invited further written submissions, including a particularized list of Ulbricht’s discovery requests. One week later, the district court issued a sealed and partially redacted opinion denying all of Ul-bricht’s requests.

The court did indicate, however, that throughout the trial it would “entertain specific requests to use information from the November 21, 2014 Letter on cross-examination.” App’x 700. Moreover, the court explained that it would “entertain a renewed application” for a “particularized disclosure” of facts relevant to Force’s corruption if the government’s trial tactics or evidence “open[ed] the door” to such facts. Id. 2. Preclusion of Force Investigation Evidence: Rule 6(

e) On appeal, Ulbricht claims that the district court erred in denying his motion to unseal the November 21 letter because he demonstrated a particularized need that rebutted the presumption of secrecy that attaches to grand jury investigations. We disagree. “[T]he proper functioning of our grand jury system depends upon the secrecy of grand jury proceedings.” Douglas Oil Co. of California v. Petrol Stops Nw., 441 U.S. 211, 218, 99 S.Ct. 1667, 60 L.Ed.2d 156 (1979). We have described five rationales for such secrecy:

(1) To prevent the escape of those whose indictment may be contemplated; (2) to insure the utmost freedom to the grand jury in its deliberations, and to prevent persons subject to indictment or their friends from importuning the grand jurors; (3) to prevent subornation of perjury or tampering with the witnesses who may testify before the grand jury and later appear at the trial of those indicted by it; (4) to encourage free and untrammeled disclosures by persons who have information with respect to the commission of crimes; (5) to protect the innocent accused who is exonerated from disclosure of the fact that he has been under investigation, and from the expense of standing trial where there was no probability of guilt.

In re Grand Jury Subpoena, 103 F.3d 234, 237 (2d Cir. 1996). Rule 6(e)(6) of the Federal Rules of Criminal Procedure implements this policy of secrecy by requiring that “all records, orders, and subpoenas relating to grand jury proceedings [must] be sealed.” In re Grand Jury Subpoena, 103 F.3d at 237 (emphasis in original). Information falling within Rule 6(e)’s protections is entitled to a “presumption of secrecy and closure.” Id. at 239.

To rebut the presumption of secrecy, the party “seeking disclosure [must] show a particularized need that outweighs the need for secrecy.” Id. (internal quotation marks omitted).

To prove a particularized need, parties seeking disclosure must show that the “material they seek is needed to avoid a possible injustice in another judicial proceeding, that the need for disclosure is greater than the need for continued secrecy, and that their request is structured to cover only material so needed.” Id. (internal quotation marks omitted). “A district court’s decision as to whether the burden of showing a particularized interest has been met will be overturned only if the court has abused its discretion.” Id.

We cannot say that the district court abused its discretion when it denied Ulbricht’s request to unseal the November 21 letter discussing the Force grand jury investigation. It is undisputed that the letter contained information related to a grand jury proceeding that, if made public, would disclose matters occurring before the grand jury. Ulbricht did not demonstrate a particularized need for disclosure because he did not show that the need for disclosure was greater than the need for continued secrecy or that a possible injustice would result if the grand jury investigation was not disclosed.

Specifically, the district court did not err in concluding that revealing the entire letter could have compromised the Force grand jury investigation in a number of ways. For example, potential co-conspirators might have learned of the investigation and attempted to intimidate witnesses or destroy evidence. The investigation was also likely to garner significant media attention, a fact that might influence witnesses or grand jurors. And, although Force knew of the investigation, revealing its existence to the public might have harmed him if the allegations had ultimately proved untrue.

Finally, Ulbricht’s request was not structured to cover only the information needed to avoid any possible injustice; instead, he sought to unseal the entire November 21 letter and did not propose a more narrowly tailored disclosure. In redacted portions of its opinion, the district court also considered ex parte arguments concerning how the Force investigation might be relevant to Ulbricht’s defense. In general terms, Ulbricht argued that the agents’ corruption was critical to his defense because it would reveal the agents’ ability to falsify evidence against him and demonstrate their motive to do so.

According to the district court’s characterization of his ex parte letters, Ulbricht speculated that Force may have used Curtis Green’s (Flush) administrative capabilities to impersonate DPR; Force’s corrupt conduct might have demonstrated technical vulnerabilities in the site that would render it susceptible to hacking; and learning that Force had good information about the Silk Road investigation might have caused the true DPR to recruit Ulbricht as his successor.

The district court reasoned that much of the information that might have arguably supported any of those theories was made available to the defense in discovery. The only new information in the November 21 letter concerned the investigation of Force’s corruption; the fact of that investigation and its scope does not bolster any of the defense theories that Ulbricht described before the district court or on appeal. That Force was personally corrupt and used his undercover identity to steal money from Silk Road and DPR does not suggest either a motive or an ability on his part to frame Ulbricht as DPR.

Absent any explanation of how Force could have orchestrated a massive plant of incriminating information on Ulbricht’s personal laptop, his larcenous behavior does not advance the claim that such a frame-up was possible beyond mere speculation. Thus, Ulbricht was equally capable of presenting his various defense theories to the jury with or without the November 21 letter. The government’s commitment to eliminating all evidence that came from Force’s work on the Silk Road investigation further undermines Ulbricht’s claim that he needed the information to avoid a possible injustice.

Had Force been called as a government witness, or had any of the government’s evidence relied on his credibility, his character for truthfulness would have been at issue during the trial, and information that impeached his credibility would have become highly relevant. Ulbricht’s reliance on the general fact of cooperation among different government agencies and different U.S. Attorney’s Offices does not undermine the government’s explicit representations that none of the evidence presented at trial derived from Force, and nothing in the record suggests that those representations were false.

Ulbricht had no need to rely on the grand jury investigation of Force to attack the credibility of the actual government witnesses or the integrity of its other evidence. In sum, Ulbricht has not shown that the district court abused its discretion in maintaining the secrecy of the Force grand jury investigation. He did not demonstrate to the district court, and has not demonstrated on appeal, that keeping the November 21 letter under seal resulted in any injustice, or that his need for disclosing the investigation was greater than the need for continued secrecy. 3.

Denial of Discovery Related to Force Ulbrieht claims that the district court erred in denying him discovery, including requested subpoenas, related to the Force investigation. Rule 16(a)(1)(E), Fed. R. Crim. P., requires the government to disclose information within its control if the information is “material to preparing the defense” or will be a part of the government

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