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FBI Seizes NetNut Proxy Platform, Popa Botnet

from Krebs on Security [alt+shift+b] in technology

The Federal Bureau of Investigation (FBI) said today it worked with industry partners to seize hundreds of domains associated with NetNut, a sprawling residential proxy service operated by the publicly-traded Israeli company Alarum Technologies [NASDAQ: ALAR]. The action comes roughly two weeks after KrebsOnSecurity published findings from multiple security firms connecting NetNut to the Popa botnet, a collection of at least two million devices that have been compromised by malicious software with little or no consent from victims. The NetNut homepage today was replaced by this seizure banner from the FBI. On June 19, three different security firms issued similar findings: That NetNut is a residential proxy network which populates a botnet called Popa, and distributes software for devices commonly found in homes, such as smart TVs and streaming boxes. NetNut’s software turns those systems into always-on residential proxy nodes that are rented to others, who predominantly use them to relay abusive and intrusive Internet traffic, such as mass content scraping, advertising fraud, and account takeover activity. Earlier today, NetNut’s homepage was replaced with a seizure notice from the FBI and the Internal Revenue Service Criminal Investigation division. The seizure notice thanked Google, Lumen, Shadowserver and other industry partners for their help in dismantling hundreds of domains tied to the Popa botnet, which experts say has long been synonymous with NetNut’s residential proxy infrastructure. In a blog post published today, the Google Threat Intelligence Group (GTIG) said NetNut’s proxy network is widely resold and white-labeled by a number of third-party proxy providers, and that its services are heavily sought out by cybercriminals seeking to obfuscate the source of their malicious traffic. The GTIG said that in a single week during June 2026, they observed 316 distinct clusters of threat actors using suspected NetNut exit nodes, including cybercriminal and...
2nd Jul 2026

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FBI Probes Service Selling 153M+ Drivers Licenses

A new identity theft service launched on the dark web this week is selling digital scans of more than 153 million drivers licenses from people in the United States and Canada. Based on interviews with individuals whose licenses are available for purchase on this service, it appears to be siphoning images collected by a widely-used identity verification company based in Louisiana. KrebsOnSecurity also has learned that the New Orleans field office of the Federal Bureau of Investigation (FBI) today launched an official inquiry into the source of the images. A record available at this identity theft service that includes the drivers license for U.S. Defense Secretary Pete Hegseth, who is one of several high-ranking U.S. government officials whose drivers licenses can be found for sale. On Monday, Aug. 31, a source alerted KrebsOnSecurity to a service advertised by a new user on the Russian cybercrime forum Exploit, offering access to digital scans of identity documents on more than 170 million people in North America. The source brought it to my attention because the proprietor of this identity theft service offered my Virginia drivers license as a free sample in their initial sales thread on Exploit. The service, dubbed Nexus, claims to have more than 153 million drivers licenses for people in the United States and Canada, as well as more than 10 million identification cards; more than three million travel documents and/or international IDs; and at least 579,000 medical cards. A quick look around Nexus finds they are likely not exaggerating about that 153 million number: Running a blank search in Nexus (with no search parameters entered) returns approximately 11.5 million pages of results, with roughly 15 results displayed per page. It includes documents from people in both Canada and the United States, but the bulk of these records are on Americans: searching for just Canadian drivers licenses returns approximately 1.1 million results, with the largest concentration from Ontario (473,673 records). Curiously, the identity records include not only drivers licenses but also marijuana dispensary cards. Some of the records list their “source” as “CDL,” presumably short for “commercial drivers license. Other records carry the source notation of “CAC,” which may refer to Common Access Cards, government issued identity cards that grant physical access to government buildings and secure rooms. The people behind Nexus claim the license images are coming from an active breach at “a major identity verification company” whose customers include multiple Fortune 500 companies. The record totals listed by the Nexus identity theft service. The number of drivers license records increased by nearly 400,000 in the span of just 24 hours. “We have been continuously exfiltrating new data for over a year into our private database,” the service enthused in its introductory post on Exploit. “Records are available to preview before purchase with pertinent information redacted. Customer photos are displayed if available.” Indeed, over the past 24 hours, the number of drivers license records listed as available in Nexus has increased by nearly 400,000, suggesting that freshly stolen license data is being harvested and uploaded to this service on a semi-regular basis. The record that features my drivers license includes six image files — three pairs of photos of the license’s front and back — a basic image scan — as well as infrared and ultraviolet versions of the same images. A date and timestamp is appended to each image file, and the timestamp on my license scan corresponds to a date in June 2025 when I took a flight to the midwest United States to attend a family funeral. Some of the 153 million+ license scans — including mine — feature six image files with date and timestamps appended to the filenames. Not all records include photos, and some that do feature photos do not display the associated filenames. Intent on discovering the source of this data, KrebsOnSecurity asked more than a dozen friends and family members for permission to search for their licenses in this service. Each person whose license could be found (nine of them) confirmed having traveled on or very close to the dates in the timestamps attached to their images. It is unclear what timezone these timestamps are in, but from reviewing car rental records shared by several people who helped with this research, it appears the timezone is set to Greenwich Mean Time (GMT). At first, I thought the source of the data might have something to do with airports. However, that theory went out the window when it became apparent there were no passports in this data set. Also, only some of those who helped with this research said they showed their drivers license at the airport on the day of their travel. One person whose license was in Nexus hadn’t flown at all recently, but was renting a car from Hertz for several months around the date of their timestamp. Two of those who agreed to help are federal employees who said they shared other forms of government identification when passing through airport security. However, those individuals each said they shared their state-issued drivers licenses later that day when renting vehicles at their respective destinations, and that both rented their cars from Hertz. After finding a note in my calendar for the day of my June 2025 flight reminding me to bring my passport, I remembered that I also never actually shared my drivers license when I went through security at Reagan National Airport on that day because I did not yet have a Real ID, a security-enhanced drivers license that is now required by the Transportation Security Administration (TSA) for all domestic travel. Instead, I showed the TSA agent my government-issued U.S. passport. Here’s where it gets interesting: I was able to find my mother’s drivers license in this service as well, and the timestamps for her images are just a few seconds apart from mine. That’s notable because we both handed our licenses to the Hertz rental car representative at the same time. According to my mom, the only place she gave her drivers license to that day was the rental car company, and if memory serves that is also true for me. I don’t recall if the rental car representative inserted our licenses into any kind of machine, but I remember they held onto them for several minutes behind the counter while we were signing various forms. KrebsOnSecurity sought comment from Hertz and will update this story in the event they reply. Zach Edwards is a well-known security and privacy researcher who recently launched a service called DecryptAds to help people better understand how online advertisers are tracking them. A scan of Edwards’s drivers license is available for purchase on this identity theft service, and Edwards said the timestamp on his record corresponds to the middle of a trip last month to Las Vegas for the annual DEFCON security conference. Edwards told KrebsOnSecurity that although he did not rent a car in Vegas, he did hand over his license at the TSA checkpoint, at a marijuana dispensary in Vegas, and at his hotel (the Aria). But he said the only one of those three that for sure scanned his ID in some kind of device was the dispensary. To enter Planet13’s weed dispensary in Las Vegas, one must pass through a red telephone booth. Image: Zach Edwards. Edwards said the dispensary he visited that day was Planet13, a multi-state chain with stores in California, Florida, Illinois and Nevada. In 2022, the New Orleans-based identity provider idscan.net published a press release announcing an exclusive identity verification agreement with Planet13’s dispensaries nationally. IDScan says it processes ID verification for more than 1,000 marijuana dispensaries in 19 U.S. states. The “trust” page of idscan.net states that the company provides identity verification services for numerous big brands, including Hertz, Target, Fedex, Motorola Solutions, the financial services giant Jack Henry, and Caesars Entertainment. And as idscan.net’s own documentation states, the technology scans IDs with both infrared and ultraviolet light. Idscan.net says the company’s systems and technology perform more than 21 million verifications monthly, at more than 20,000 locations around the world. Image: idscan.net. Contacted by KrebsOnSecurity, idscan.net said it was investigating the matter, but the company has not yet shared an official statement or a substantive reply to specific questions sent via email. “At this point I’m not able to share any additional information, but the updates you have provided have been welcome, and helpful to our team’s investigation,” wrote Jillian Kossman, a marketing and operations leader at idscan.net. During the course of my research for this story, word apparently got around to the FBI that I was poking at the apparent source of this new identity theft service’s data. Probably they were tipped off when I shared with a trusted source that Nexus also is selling the drivers license information for the assistant director of the FBI (I did not find FBI Director Kash Patel’s license in Nexus). Earlier this afternoon, I was added to a conference call with a half-dozen FBI agents, including senior leaders from the agency’s cyber division. During that call, the FBI shared that earlier today their New Orleans field office opened an official investigation into an apparent breach involving idscan.net. Edwards said that as more in-person and online experiences require sharing drivers licenses, vendors who collect this sensitive data need to be held to a higher standard. “This episode should further strengthen the resolve for people who are fighting back against online ID schemes which are requiring countless providers to ask for drivers licenses in order to access services under the guise of protecting kids,” Edwards told KrebsOnSecurity. “These systems are putting sensitive data into more and more 3rd party vendors, and we don’t have nearly the oversight to ensure they are safe.” Larry Baldwin is principal intelligence researcher at the cybersecurity firm Cybera. Baldwin said a front and back scan of his drivers license available at Nexus contains timestamps that correspond to the date of a car rental from Hertz on a recent vacation. Baldwin said the Nexus identity theft service presents multiple serious security and privacy threats, noting that state-issued drivers licenses are commonly used as proof of one’s identity when opening new lines of credit. Baldwin said the service could also dangerously expose many people who do not wish to be found but who cannot meaningfully change their appearance (or at least not enough to fool today’s AI-based image matching tools). This category of people, he said, includes those fleeing domestic violence, and even people who have been assigned a whole new life and identity as part of the federal government’s witness protection program, which is generally reserved for criminal defendants in racketeering and conspiracy investigations who agree to cooperate with federal authorities. “Just when it seems like we’re making some headway in improving authentication controls through drivers license verification systems, this happens and the very thing those improvements are dependent on are compromised,” Baldwin said. This is a potentially fast-moving story. Any changes or updates will be noted here along with a timestamp.

1st Sep 2026 • 2 votes
Canadian Man Pleads Guilty in Snowflake Extortions

A 26-year-old Canadian man once described as one of the most consequential cybercrime threat actors of 2024 has pleaded guilty to computer fraud and conspiracy to hack and extort more than 165 organizations that used the cloud data storage provider Snowflake. Connor Riley Moucka, of Kitchener, Ontario, also admitted to stealing call and text history records of more than 100 million AT&T customers. A surveillance photo of Connor Riley Moucka, a.k.a. “Judische” and “Waifu,” dated Oct 21, 2024, 9 days before Moucka’s arrest. This image was included in an affidavit filed by an investigator with the Royal Canadian Mounted Police (RCMP). The U.S. Justice Department said between February and October 2024, Moucka and co-conspirators used stolen login credentials to steal cloud-hosted data belonging to at least 165 customers of a U.S.-based software-as-a-service company. The hackers targeted stolen credentials for Snowflake customer accounts that did not enforce multi-factor authentication, and extorted or attempted to extort a host of well-known companies, including TicketMaster, Lending Tree, Advance Auto Parts and Neiman Marcus. Snowflake responded to the data thefts by increasing password complexity requirements and enforcing multi-factor authentication. Moucka adopted new nicknames frequently — sometimes operating multiple identities concurrently — but two of his best-known monikers were “Judische” and “Waifu.” Judische’s admitted role in the Snowflake data thefts was first documented by KrebsOnSecurity in a September 2024 story about the overlap between Western, English-speaking cybercriminals and extremist groups that harass and extort minors into harming themselves or others. That September 2024 story identified Judische as a software engineer from Ontario who has been involved in numerous data breaches and voice phishing attacks against U.S. companies since at least 2020. A little more than a month later, Canadian authorities arrested Moucka on a provisional warrant from the United States. The government says Moucka and others used their unauthorized access to steal billions of sensitive customer records and download terabytes of information, “including individuals’ non-content call and text history records, banking and other financial information, payroll records, Drug Enforcement Administration (DEA) registration numbers, driver’s license numbers, passport numbers, social security numbers and other personally identifiable information. They then extorted victims by threatening to publish data online.” Moucka also threatened and harassed government officials and security researchers who were helping to track him down. The Justice Department said the conspirators made over $2.5 million in ransom payments, and that in at least one instance, Moucka re-extorted a victim with threats of further disclosure of the victim’s stolen data. “Moucka used the stolen data of a government officer and members of a then-former government officer’s immediate family in this re-extortion attempt,” reads a statement from the Justice Department. One of Moucka’s admitted co-conspirators is Cameron “Kiberphant0m” Wagenius, a U.S. Army soldier who pleaded guilty in July 2025 to extorting AT&T and Verizon for their customer account data. Less than a month before Wagenius’s arrest, KrebsOnSecurity published a deep dive into Kiberphant0m’s various Telegram and Discord identities over the years, revealing how the owner of the accounts told others they were in the Army and stationed in South Korea. One of several selfies on the Facebook page of Cameron Wagenius. Kiberphant0m also re-extorted victims. Immediately following Moucka’s arrest, Kiberphant0m posted on hacker forums what he claimed were the AT&T call logs for then President-elect Donald Trump and for then Vice President Kamala Harris, as well schematics allegedly stolen from the U.S. National Security Agency (NSA). Wagenius is set to be sentenced on September 3, 2026. The government says he faces a maximum penalty of 20 years in prison for conspiracy to commit wire fraud, a maximum penalty of five years in prison for extortion in relation to computer fraud, and a mandatory two-year sentence consecutive to any other prison time for aggravated identity theft. The third alleged co-conspirator is John Erin Binns, 26, an elusive American man who fled the United States after being indicted for his admitted role in a 2021 breach at T-Mobile that exposed the personal information of at least 76 million customers. Sources close to the investigation said Binns, also known as “IRDev” and “IntelSecrets,” was until recently incarcerated in a Turkish prison, but that he has since been released and has resurfaced online. Those sources said Binns also recently obtained Turkish citizenship, and under Turkish law a citizen cannot be extradited to a foreign country. An image of a passport that Binns shared in an email to KrebsOnSecurity in Feb. 2023. Moucka pleaded guilty to four criminal counts, including computer fraud, wire fraud, aggravated identity theft, and conspiracy. He is slated to be sentenced on Oct. 27 and faces a mandatory minimum penalty of two years in prison on the aggravated identity theft count, as well as a maximum penalty of 30 years in prison on the remaining counts. Ultimately, it will be up the federal judge how much time Moucka actually serves for his extensive cybercriminal rap sheet. For an interview with Moucka prior to his arrest and a deeper look at Binns, see our original report on Moucka’s arrest.

6th Aug 2026 • 1 votes
Hackers Used Meta’s AI Support Bot to Seize Instagram Accounts

The Instagram accounts for the Obama White House and the Chief Master Sergeant of the U.S. Space Force were briefly defaced with pro-Iranian images and messages over the weekend, after instructions began circulating on Telegram showing how to trick Meta’s “AI support assistant” bot into resetting account passwords. A screenshot from a video released on Telegram claiming to show how Meta’s AI customer support bot could be tricked into resetting a target’s password. On May 31, word began to spread on several Telegram instant message channels that Meta’s AI bot would happily add an email address to an existing account as part of the bot’s standard password reset flow. A video released on Telegram by pro-Iran hackers claimed to document a remarkably simple exploit that appears to have involved using a VPN connection with an IP address that is in or near the target’s usual hometown, requesting a password reset for the account, and then choosing to chat with Meta’s AI support assistant. From there, the video shows the attacker told the bot to link the account in question to a new email address, after which the bot dutifully sent that address a one-time code that allowed a password reset. The Telegram account that posted the video also linked to screenshots of pro-Iran images, videos and messages that defaced the hacked Instagram accounts, saying hackers had used the exploit to hijack a number of valuable (read: short) Instagram account names that allegedly have a resale value of more than a half million dollars. Meta has not responded to requests for comment on the video’s claims, but the company reportedly did acknowledge the dormant Instagram account for the Obama White House was briefly compromised. The security blog thecybersecguru.com reports that Meta pushed an emergency patch over the weekend, and clarified that no back end database was breached. “Instagram has notoriously poor human support infrastructure,” Cybersecguru wrote. “Recovering a locked account – especially a high-value one can take weeks of back-and-forth with an automated ticketing system. Meta’s solution was to deploy a conversational AI layer to handle common recovery workflows: relinking a lost email address, triggering a password reset, verifying account ownership. The assistant, presumably, was supposed to reduce friction for legitimate users stuck in account-access hell.” Ian Goldin, a threat researcher at Lumen’s Black Lotus Labs, said we’re entering unchartered security territory as more large online platforms start allowing AI chatbots to handle sensitive account recovery requests. Just like human customer support employees can be social engineered into providing unauthorized access to someone’s account, AI bots are equally eager to help and vulnerable to persuasion and trickery, he said. “AI chatbots create interesting new attack surface, and we’re likely going to see a lot more of these kinds of attacks,” Goldin said. Securing your various online accounts means taking full advantage of the most secure form of multi-factor authentication (MFA) offered (such as a passkey or security key). In this case, even using the least robust form of MFA that Instagram offers — a one-time code sent via SMS — likely would have blocked the exploit: The hackers who released the video on Telegram said their exploit failed to work against any accounts that had MFA enabled.

1st Jun 2026 • 1 votes
Canvas Breach Disrupts Schools & Colleges Nationwide

An ongoing data extortion attack targeting the widely-used education technology platform Canvas disrupted classes and coursework at school districts and universities across the United States today, after a cybercrime group defaced the service’s login page with a ransom demand that threatened to leak data from 275 million students and faculty across nearly 9,000 educational institutions. A screenshot shared by a reader showing the extortion message that was shown on the Canvas login page today. Canvas parent firm Instructure [NYSE:INST] responded to today’s defacement attacks by disabling the platform, which is used by thousands of schools, universities and businesses to manage coursework and assignments, and to communicate with students. Instructure acknowledged a data breach earlier this week, after the cybercrime group ShinyHunters claimed responsibility and said they would leak data on tens of millions of students and faculty unless paid a ransom. The stated deadline for payment was initially set at May 6, but it was later pushed back to May 12. In a statement on May 6, Instructure said the investigation so far shows the stolen information includes “certain identifying information of users at affected institutions, such as names, email addresses, and student ID numbers, as well as as messages among users.” The company said it found no evidence the breached data included more sensitive information, such as passwords, dates of birth, government identifiers or financial information. The May 6 update stated that Canvas was fully operational, and that Instructure was not seeing any ongoing unauthorized activity on their platform. “At this stage, we believe the incident has been contained,” Instructure wrote. However, by mid-day on Thursday, May 7, students and faculty at dozens of schools and universities were flooding social media sites with comments saying that a ransom demand from ShinyHunters had replaced the usual Canvas login page. Instructure responded by pulling Canvas offline and replacing the portal with the message, “Canvas is currently undergoing scheduled maintenance. Check back soon.” “We anticipate being up soon, and will provide updates as soon as possible,” reads the current message on Instructure’s status page. While the data stolen by ShinyHunters may or may not contain particularly sensitive information (ShinyHunters claims it includes several billion private messages among students and teachers, as well as names, phone numbers and email addresses), this attack could hardly have come at a worse time for Instructure: Many of the affected schools and universities are in the middle of final exams, and a prolonged outage could be highly damaging for the company. The extortion message that greeted countless Canvas users today advised the affected schools to negotiate their own ransom payments to prevent the publication of their data — regardless of whether Instructure decides to pay. “ShinyHunters has breached Instructure (again),” the extortion message read. “Instead of contacting us to resolve it they ignored us and did some ‘security patches.'” A source close to the investigation who was not authorized to speak to the press told KrebsOnSecurity that a number of universities have already approached the cybercrime group about paying. The same source also pointed out that the ShinyHunters data leak blog no longer lists Instructure among its current extortion victims, and that the samples of data stolen from Canvas customers were removed as well. Data extortion groups like ShinyHunters will typically only remove victims from their leak sites after receiving an extortion payment or after a victim agrees to negotiate. Dipan Mann, founder and CEO of the security firm Cloudskope, slammed Instructure for referring to today’s outage as a “scheduled maintenance” event on its status page. Mann said Shiny Hunters first demonstrated they’d breached Instructure on May 1, prompting Instructure’s Chief Information Security Officer Steve Proud to declare the following day that the incident had been contained. But Mann said today’s attack is at least the third time in the past eight months that Instructure has been breached by ShinyHunters. In a blog post today, Mann noted that in September 2025, ShinyHunters released thousands of internal University of Pennsylvania files — donor records, internal memos, and other confidential materials — through what the Daily Pennsylvanian and other outlets later determined was, in part, a Canvas/Instructure-mediated access path. “Penn was the named victim,” Mann wrote. “Instructure was the mechanism. The incident was treated as a Penn-specific story by most of the national press and quietly handled by Instructure as a customer-specific matter. That framing was wrong then. It is dramatically more wrong in light of the May 2026 events, which now look like the planned escalation of an attack pattern that ShinyHunters had been working against Instructure’s environment for at least eight months prior. The September 2025 Penn breach was the proof of concept. The May 1, 2026 incident was the production run. The May 7, 2026 recompromise was ShinyHunters demonstrating publicly that the May 2 ‘containment’ did not happen.” In February, a ShinyHunters spokesperson told The Daily Pennsylvanian that Penn failed to pay a $1 million ransom demand. On March 5, ShinyHunters published 461 megabytes worth of data stolen from Penn, including thousands of files such as donor records and internal memos. ShinyHunters is a prolific and fluid cybercriminal group that specializes in data theft and extortion. They typically gain access to companies through voice phishing and social engineering attacks that often involve impersonating IT personnel or other trusted members of a targeted organization. Last month, ShinyHunters relieved the home security giant ADT of personal information on 5.5 million customers. The extortion group told BleepingComputer they breached the company by compromising an employee’s Okta single sign-on account in a voice phishing attack that enabled access to ADT’s Salesforce instance. BleepingComputer says ShinyHunters recently has taken credit for a number of extortion attacks against high-profile organizations, including Medtronic, Rockstar Games, McGraw Hill, 7-Eleven and the cruise line operator Carnival. The attack on Canvas customers is just one of several major cybercrime campaigns being launched by ShinyHunters at the moment, said Charles Carmakal, chief technology officer at the Google-owned Mandiant Consulting. Carmakal declined to comment specifically on the Canvas breach, but said “there are multiple concurrent and discreet ShinyHunters intrusion and extortion campaigns happening right now.” Cloudskope’s Mann said what happens next depends largely on whether Instructure’s customers — the universities, K-12 districts, and education ministries paying for Canvas — choose to apply pressure or absorb the breach quietly. “The history of education-vendor incidents suggests the path of least resistance is the second one,” he concluded.

8th May 2026 • 1 votes

More in technology

Anecdata: running shucked WD My Book/Easystore 8TB hard drives for over 5 years

Sharing a few data points because some people did not expect these drives to last that long.

9 hours ago • 1 votes
Prove you are not a child

I'm 100% for banning social media for children. I would even extend it to banning it all together in its current form. But I am also against the methods for enforcement. The problem with banning social media for one group and not another is that you have to differentiate the different groups somehow. And right now, in an age where information and personal data means everything, there are several entities that are salivating to get this data. I've written before about all the problems that come from uploading sensitive data online. It doesn't even matter if they delete the data afterward, as long as the data goes through the wire in the first place, there is a chance for a leak. What appears to be the same simple request "please verify your identity", becomes fundamentally different when mediated by technology. The question isn't whether these digital systems will be compromised, but when. And unlike that movie theater clerk who can't perfectly recall my birthdate minutes after seeing it, computers have perfect memory. They store, copy, backup, and transmit our most sensitive information through networks we don't control, to companies we've never heard of, under policies we'll never read. When kids are not allowed to use social media, it's the adult who pays the price. It's the adult who has to prove that they are not children. They have to risk uploading their government ID to a third party, or biometric data that may be saved and backed up forever. I reject this method. I also reject the method where I have to provide my age to the operating system. No system should compel me to provide personal data in order to use it. Especially if this feature is intended to provide the information to a third party. And what happens if I don't provide this information to my freebsd machine? Or worse, what if I provide false information? Am I going to get punished? How does that protect children in any way? Breaking news: Grown up arrested when OS reported forged identity in his laptop. One question I asked myself was what happens when a minor circumvents the ban. What are the consequences? At least in Australia, a country that has implemented a social media ban for those under 16, there are no consequences. The law places legal responsibility on platforms, not children or parents, and it currently applies to Facebook, Instagram, Kick, Reddit, Snapchat, Threads, TikTok, Twitch, X and YouTube. This almost sounds reasonable. Why should you care, if it becomes facebook responsibility when you don't even own a facebook account? But there is always a caveat. When facebook becomes a tool your school uses to communicate with parents. When Google classroom is the service students use to do their homework. When you are required to login on a system to receive government service. You may not care about a particular social media, but they raise the bar for every other entrant in the game. Every website frequented by a large number of people inherently become social media, and demand data you didn't need to provide before. Technology is not a magical thing that can just solve every problem. It is especially weak when it comes to social problems. However, society can use technology to solve their problems. The responsibility of children falls onto their parents. And there are great tools for parents that their kids access on their devices.

13 hours ago • 1 votes
Intuitive Estimation of the Number of Error Correction Bits

Introduction Hamming Distance Intuitive Estimation of Error Correction Bits Digging Deeper Comparing against BCH Codes What about Reed-Solomon Codes? BCH vs Reed-Solomon Codes References Footnotes Introduction I’ve been interested in error correcting codes (ECC) for a while now, and though I haven’t gotten very far, I keep on reading and, occasionally, writing about it. Except for really simple schemes, ECC theory gets complicated quickly. The two codes that I’ve looked at most are Reed-Solomon (RS) and binary Bose–Chaudhuri–Hocquenghem (BCH) codes. They are closely related: both use polynomial math that is normally performed over a Galois Field, though, as shown in my earlier Reed-Solomon blog post, that’s not strictly required. The encoding algorithms are relatively straightforward but the decoding algorithms are significantly more complicated. RS and binary BCH codes differ in the size of their symbols, their alphabet: a symbol of the former consists of multiple bits, often 8 bits, while a symbol of the latter is a bit. Errors are corrected with a granularity of a symbol. One key ECC question is “How many additional bits do I need to correct a given number of errors?” In this blog post, I check if an intuitive approach that I’ve been using matches reality. I’m trying hard to stay away from theory here, which makes the subject hopefully more accessible, but has the flip side that it’s far from being rigorous and exact. Hamming Distance When you look at the theory of error detecting and correcting codes, the discussion immediately turns to Hamming distance: the number of bit flips required to convert one vector of bits to another. The goal of an error correcting code is to transform the input vector, the message, to an output vector, the codeword, so that the minimum Hamming distance between valid codewords is guaranteed to be at least a certain number. The higher the Hamming distance, the higher number of bits that can be flipped in a codeword without destroying the ability to recover the original message. If \(t\)1 is the number of errors that we want to correct, error coding theory gives us the following formula: In words: to correct a codeword with a maximum number of \(t\) bit errors, the Hamming distance between any 2 codewords must be larger than two times \(t\). The theory also tells us the minimum Hamming distance to detect an error without correcting it: In the rest of this blog post, though, we’ll only care about correction, not detection. Here are 2 quick examples where the message is one bit. Adding 1 bit to the message For a one bit message, there are only 2 possible messages, 0 and 1. Let’s use a code that repeats this bit once: 0 becomes 00 and 1 becomes 11. The Hamming distance between these 2 valid codewords is 2 because you need to flip 2 bits to convert 00 into 11. The equation above tells us that a distance of 2 is not sufficient to fix a one-bit error. Indeed, when we receive 01 as a codeword, it’s impossible to tell if the transmitted codeword was 00 or 11: both have a Hamming distance of 1 to the received word of 01. Adding 2 bits to the message When we expand the 1 bit message to 3 bits and repeat the message bit twice, things are different: 0 transforms into 000 and 1 into 111. The Hamming distance between all possible codewords is 3. The theory says that we should be able to correct a codeword for which only 1 bit was flipped. And indeed, if we receive 001 and there is only 1 bit corrupted, we know for sure that the original message was 0. Intuitive Estimation of Error Correction Bits The concept of a minimum required Hamming distance to correct a number of errors is not particularly complicated, but it’s a different matter to use it to determine the number of additional ECC bits for, say, a BCH code. In fact, I still don’t know how to do it. As an alternative, I found myself using a simple model that works like this: Participant A transmits 1000 bits to participant B over a noisy channel B transmits the same 1000 bits back to A over a perfect channel A transmits a 10 bit error index to signal to B which bit it received wrong Or more general: If a message of \(k\) bits has 1 incorrect bit, you need a number of \(r = \lceil \log_2(k) \rceil\) 2 bits to point out the incorrect bit. Let’s call that number the error index3. To correct \(t\) bits, you need up to \(r = t \cdot \lceil \log_2(k) \rceil\) additional bits. That’s it! The model is simple, it’s not exactly practical, and the number of parity bits has to be only a first order estimation, but I felt like it had to be pretty close to reality. But is it? Digging Deeper Let’s consider some of the aspects of this model: There is no way to signal that there was no corruption That can be solved by allocating one error index value extra to signal a perfect transmission and calculate the number of bits as \(r = \lceil \log_2(k+1) \rceil\) instead of \(r = \lceil \log_2(k) \rceil\). E.g. for a 1000-bit message, an error index from 0 to 999 indicates an error location, and 1000 signals perfect transmission. For messages that are not a power of 2, the number of error indicator bits remains the same. The transmitted error indicator bits can be corrupt as well One way to solve this is by going through the same procedure to verify the error index. For a first iteration, it would cost an additional \(\lceil \log_2(\lceil \log_2(k+1) \rceil ) \rceil\) bits, 4 bits for a 10 bit error index. Of course, those 4 bits might be corrupt too! A better approach is to work backwards: start out with the length of the codeword and the number of errors you want to correct and determine the number of input message bits from there. The number of error indicator bits is then calculated over the length of the codeword and you get \(r = \lceil \log_2(n+1) \rceil\). The length of the message is \(k = n - r\). This breaks the simple model where you transmit message and error indicator separately, but that was not a realistic scenario anyway. It doesn’t consider that the same error index can appear only once If the code can correct 2 errors, you’d need \(\lceil \log_2(k+1) \rceil\) bits for the first error index to indicate zero errors or the location of the first error. For the second error, you need one less value because one location has already been corrected, so the number of bits needed is \(\lceil \log_2(k) \rceil\). This suggests that the number of error indicator bits might be an upper bound. It only applies to error correction the way BCH does it Any random bit can be corrected, but it doesn’t work for RS coding because there a whole symbol can be incorrect. That’s fixable though, I get to that later. You don’t need to signal the correct value Since the symbol is 1 bit in size, the location of the error is sufficient. To fix it, the receiver just needs to invert the bit. This also doesn’t work for RS. Comparing against BCH Codes Forget about using the Wikipedia article to compare the intuition against theory: you won’t find anything explicit. I found this presentation from the National Taipei University useful. The key formulas are on the first slide: Block length: \(n = 2^m -1\) Number of parity-check bits: \(n - k \le m t\) Minimum distance: \(d_{min} \ge 2t + 1\)4 In the equations above, \(k\) is still the length of the original message, \(t\) is the number of bits that can be corrected, \(n\) is the length of the codeword. If we rearrange the first equation, we get: Substitute \(m\) in the second equation: \(r\) is the number of error correction bits, so \(r = n - k\) and: Compare this with the intuitive formula that I started with: The only differences are: I used \(k\) instead of \(n+1\). That accounts for the fact that parity bits themselves need error correction too and that a perfect transmission must be signaled. the BCH equation assumes that the total codeword length is always one less than a power of two. instead of an approximation, it defines an upper bound. Theoretically, all BCH and RS codewords have a length \(n = 2^m -1\) symbols. In practice, the transmitted codewords are often shortened by setting a bunch of the symbols in the input message to zero and not transmitting them.5 When using shortened codes, you still have to use the \(m\) value of the parent code for which \(n = 2^m -1\). The intuitive formula works for long codewords and a limited number of errors to correct: \(n \approx k\). What about Reed-Solomon Codes? RS codes correct symbols not bits but you can still use the intuitive formula to identify the corrupted symbol: in a message with, say, 223 bytes you’d need 8 bits to pinpoint an incorrect byte. However, you also need an additional byte to fix the corruption and that is the case for every error byte that needs to be corrected. To repair \(t\) symbols that are \(s\) bits in size in a message of \(k\) symbols, you’d need this number of bits for the error location: And a bunch of bits with the correct values: Note that \(r_{location}\) points to a symbol, not a bit. Just like BCH codes, \(n = 2^s - 1\) for RS codes. Change \(r_{location}\) to use \(n\) instead of \(k\) and you get: The final result is: It turns out, that is exactly what you’ll find in all texts about RS coding: the number of parity symbols must be at least 2 times the number of corrupt symbols you want to correct. BCH vs Reed-Solomon Codes I’m getting a bit off-topic here but with the intuitive formula validated, it’s interesting to see when RS codes are better than BCH and vice versa. Let’s create an example where codewords are 255 bytes or 2040 bits and where we reserve 32 bytes or 256 bits for error correction. For RS, this allows us to correct 16 corrupt bytes that can contain up to 128 corrupt bits, as long as they’re contained within those 16 bytes. For BCH, we need 11 bits per error or \(11 \cdot 23 = 253\) parity bits to correct 23 corrupt bits which fits within the 256 bits that were allocated for RS. RS is the winner if errors happen in bursts: it doesn’t matter if a burst is 1 or 8 bits long, it counts as a single corruption when they fall within the same byte. BCH wins when errors are spread randomly: instead of fixing 16 bit flips, it can fix 23. In practice, communication protocols often used 2 codes in the following scheme: Transmitter: RS Encoder -> Interleaving -> Convolutional Encoder Receiver: Viterbi Decoder -> De-interleaving -> RS Decoder In this setup, RS is called an outer code and convolutional coding the inner code, because they wrap around the transmission in that order. In many transmission mediums, bit error are uncorrelated and burst errors unlikely. One would think that RS coding is the wrong choice then. However, the Viterbi decoder can introduce bursts of errors when it makes a mistake. The RS decoder is used to clean those up. The burst error length can be so long that a single RS codeword can’t deal with them. That’s why there’s an interleaver to increase the length of burst errors that can be corrected, at the expense of latency and memory storage, but that’s a topic for a different blog post. Modern communication protocols, such as DVB-S2 that’s used by satellite TV, use a low density parity check (LDPC) code instead of a convoluational code as inner code. A LDPC decoder has a lower tendency to introduce long error bursts in case of a mistake and instead introduces single bit errors that are spread randomly within a large codeword. This is where BCH codes shine which is why it’s used instead of RS. All words in this blog posts were written by a human. References Reed-Solomon Error Correcting Codes from the Bottom Up National Taipei University - BCH code CMU Introduction to Coding Theory - Notes 4: Elementary bounds on codes NASA - Bandwidth efficient CCSDS coding standard proposals Discusses outer coding/interleaving/inner coding for space communication. There’s an abundance of information in there, which is what you’d expect from a 70 page document! Footnotes In literature, you’ll often see \(k\) being used for this formula, but further down, \(k\) is used as the length of the original message, which is also a literature convention. So I decided to be consistent within this blog post. ↩ \(\lceil x \rceil\) means: round up to nearest integer. ↩ I came up with “error index” myself, but it turns out to be a term that is commonly used in error coding theory and its meaning is exactly what I had in mind! ↩ This is the minimum Hamming distance equation for error correction. ↩ This assumes that a systematic coding scheme is used, where the original message appears unmodified in the codeword. This is the case for most BCH and RS coding schemes that are used in the real world. ↩

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