Add ‘post-AI’ encryption to your to-do list

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OpenAI’s trove of 400+ math results suggests traditional encryption may be at risk.

Artificial Intelligence

Even as federal agencies move their most sensitive systems to new forms of encryption following an order from the White House in June, the release this month by OpenAI of new results to theoretical math problems has sparked concern about whether even proposed post-quantum encryption will be safe from increasingly capable AI models.

Encryption is what keeps online data secure; encrypting a message means applying mathematical equations to disguise its contents to an attacker. But new math techniques could let an attacker decipher encrypted messages without a key: the equivalent of a safecracker using the click of pins in a lock to find the right combination. If existing encryption algorithms fall, huge swaths of the internet would be at risk of attack.

Plans for post-quantum encryption may need to incorporate stronger multi-layered defenses—and move forward more quickly than the White House anticipated—to protect data that hasn’t yet been collected.

Encryption works now because, in practice, there are ways to make it very easy for someone with the key to apply some math and reveal the original message, but not to find the key or solve the equations by brute force in a reasonable amount of time. But the encryption techniques currently in widespread use haven’t been proven theoretically safe; they’re trusted because nobody has been able to crack them so far. So if new math is discovered that makes solving encryption schemes much easier, the foundations of the internet’s security would be at risk.

AI systems have been churning out math discoveries at an unprecedented rate. In May, an OpenAI model disproved the Erdős unit distance conjecture, a well-known problem in a subfield of math called discrete geometry. And in September, the company announced its AI had a solution to the Navier-Stokes equations. The equations make up one of seven Millennium Prize Problems, some of the most important unsolved problems in mathematics.

“It just solved 400 problems, any of which, if a human had solved it, that could have been the highlight of their career, that could have been their tenure case,” Scott Aaronson, author of Quantum Computing Since Democritus and Chair of Computer Science at UT Austin, said in an interview.

Omer Reingold, computer scientist and co-winner of the Gödel Prize in 2009, wrote before the latest release that, “The world of mathematics, including theoretical computer science, is in turmoil. Even the Millennium Prize Problems…are no longer beyond the reach of LLMs.”

The OpenAI papers showed new results, “in just about all areas of math, but with this very conspicuous exception that there was nothing in cryptography. And that can't possibly be an accident,” Aaronson said.

Justin Drake, a security researcher at the Ethereum Foundation, wrote that he believes there was “backroom interventionism.”

“I've witnessed first-hand the U.S. government censoring academic quantum cryptanalysis results. Backroom interventionism is my base case,” he said.

Regardless of whether OpenAI redacted encryption results from this particular release, the flood of new results has prompted fears that AI systems could find weaknesses in existing encryption algorithms. The cryptocurrency industry, which depends on encryption to safeguard its digital currencies, has been particularly alarmed.

As part of the way cryptocurrencies function, many crypto accounts expose some information about themselves when they send money. On X, formerly known as Twitter, Drake wrote , “Today I call upon the blockchain industry to calmly begin planning for ‘bunker mode’. My personal recommendation is to set in motion a controlled mass migration of assets to fresh addresses.”

A “fresh address” is one that has never been used to send money to another account, limiting the ways future attackers might break its security.

Other cybersecurity experts are skeptical that AI will have much of an effect on concrete security issues. “Cryptographers are incredibly conservative... we put a lot of buffer into [secure encryption], an enormous amount,” said Bruce Schneier, security guru and author of the bestseller Applied Cryptography .

His concern is more on implementation questions in cybersecurity than the possibility of breakthroughs in theoretical math.

“Computer security is so bad. That's the worry. Finding vulnerabilities in code, hacking into systems. Those are the worries, not the math ... Of all the security things going on, math is the strongest we have,” Schneier added.

Emily Wenger, an assistant professor of electrical and computer engineering at Duke University, who has used machine learning to test the security of post-quantum encryption methods, said she doesn’t think “advanced large language models are going to break all encryption.”

“But when you make practical implementation choices... we found in the past that certain instantiations of these algorithms are insecure,” she said. “There's kind of two ways to break these things. You can either prove something about the math problem, or you can look at implementation choices.”

Aaronson noted that undermining the math behind widely used encryption algorithms like RSA would have sweeping consequences. “These mundane vulnerabilities, you can play the game of whack-a-mole. As soon as you find one, you patch it. Whereas if there's a break of RSA ... if all of our public key crypto systems were broken, then we would really have a problem, the way that we have constructed the internet.”

Dan Boneh, a cryptography expert and professor of computer science and electrical engineering at Stanford, said in a video that losing current forms of encryption “would affect the entire internet... it affects the entire digital world. So, home banking, healthcare, government communications, everything [would be] impacted by such a break.”

But some experts are optimistic that security will ultimately become stronger from the increased attention.

“In the past, when someone would make an assumption and build a [cryptography] system based on it, we'd have to wait 10 years before that system could be deployed, to give people enough time to analyze it. And now all of a sudden we can accelerate this process tremendously using these models... we can just let a model run for a month, try to break it, and if the model can't break it, boy, do we have a lot of confidence that the assumption is valid. So we actually have the prospect to have more confidence in our security than ever before,” Boneh said.

Schneier concurred, saying, “It's an arms race. I think AI is the first technology that's potentially flipping that arms race to a defender advantage … Microsoft used AI to patch 900-something vulnerabilities for a Patch Tuesday last month. But they will never again be problems. You're already being attacked at computer speeds. Now you can be defending at computer speeds.”

Still, any transition would be costly. For a typical commercial firm, building “crypto agility,” or the ability to quickly switch the organization’s data to new types of encryption, may be the best response to encryption uncertainty. But for the defense industrial base, adversaries have been collecting their online data in its encrypted form for years, so switching now would have little effect on their ability to decode existing data.

Intelligence agencies both foreign and domestic have long embraced “harvest now, decrypt later” as a method of espionage, collecting encrypted data over time and storing it, in preparation for breakthroughs that would allow them to crack existing encryption.

“You have to assume that intelligence agencies are vacuuming up your data now, and that's all the more true if you think that AI could potentially discover breaks for these systems within the next year or two,” Aaronson said.

For organizations that deal with restricted or classified information, the prospect of AI math breakthroughs adds another ticking clock to the post-quantum future many have only begun to prepare for.

The federal government is targeting a comprehensive move to post-quantum encryption in the coming years. Agencies must follow Executive Order 14412 and OMB memo M-26-15 , requiring them to migrate key systems to post-quantum cryptography in stages from Dec 2030 to 2035. The NSA has its own schedule for national-security systems. Contractors would also be subject to NIST’s cryptographic standards by Dec 2030 under the EO.

But new math results relevant to encryption could require a different approach. Aaronson said of AI undermining classical encryption or post-quantum algorithms, “Either of those could fall without the other. There's no logic.”

The prudent move for organizations may be “crypto agility,” the capacity to swap and layer different algorithms on top of each other as needed. With a proper agility posture, even broken encryption algorithms would not result in widespread harm in most cases.

“You should be getting crypto agility for post-quantum. So you should be doing it already. And if you're not, you should,” Schneier said.

Matthew Green, an associate professor of computer science at the Johns Hopkins Information Security Institute and author of the blog A Few Thoughts on Cryptographic Engineering wrote , “I can’t see the future. Nobody can. But so far, betting against models and in favor of human intelligence being the limit has not worked well for any of us.”

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OpenAI 的 400 多项数学结果表明，传统加密技术可能面临风险。

人工智能

尽管联邦机构在 6 月份接到白宫的命令后，已将其最敏感的系统转移到新的加密形式，但 OpenAI 本月发布的关于理论数学问题的新成果引发了人们的担忧，即即使是拟议的后量子加密也无法抵御日益强大的 AI 模型。

加密是保障在线数据安全的手段；加密信息是指运用数学公式来隐藏信息内容，使其难以被攻击者获取。但新的数学技术可能使攻击者无需密钥即可解密信息：这相当于保险箱窃贼通过拨动锁芯上的弹珠来找到正确的密码。如果现有的加密算法失效，互联网的很大一部分将面临攻击风险。

后量子加密计划可能需要纳入更强大的多层防御措施，并且推进速度要比白宫预期的更快，以保护尚未收集的数据。

加密技术之所以现在有效，是因为在实践中，拥有密钥的人可以通过一些数学运算轻松还原原始信息，但却无法在合理的时间内找到密钥或通过暴力破解的方式解出加密方程。然而，目前广泛使用的加密技术尚未经过理论验证，其安全性尚未得到充分证明；人们之所以信任它们，是因为迄今为止还没有人能够破解它们。因此，如果发现了新的数学方法，使得破解加密方案变得更加容易，那么互联网安全的根基将岌岌可危。

人工智能系统正以前所未有的速度产出数学发现。今年5月，OpenAI的一个模型推翻了埃尔德什单位距离猜想，这是离散几何领域一个著名的难题。9月，该公司宣布其人工智能系统找到了纳维-斯托克斯方程的解。纳维-斯托克斯方程是七大千禧年难题之一，也是数学领域一些最重要的未解难题。

“它解决了 400 个问题，如果这些问题是由人类解决的，那都可能成为他们职业生涯的亮点，成为他们获得终身教职的理由，”《自德谟克利特以来的量子计算》一书的作者、德克萨斯大学奥斯汀分校计算机科学系主任斯科特·阿伦森在一次采访中说道。

计算机科学家、2009 年哥德尔奖共同获得者奥默·雷戈尔德在最新版发布前写道：“包括理论计算机科学在内的数学界正处于动荡之中。即使是千禧年难题……也不再是法学硕士们无法解决的问题了。”

阿伦森说：“OpenAI 的论文展示了新的成果，几乎涵盖了数学的所有领域，但有一个非常明显的例外，那就是密码学领域没有任何进展。这绝不可能是偶然的。”

以太坊基金会的安全研究员贾斯汀·德雷克 (Justin Drake) 写道，他认为存在“幕后干预”。

“我亲眼目睹了美国政府审查学术界的量子密码分析成果。我的初步判断是，这是幕后干预，”他说。

无论OpenAI是否对此次发布的加密结果进行了删减，大量新结果的涌现都引发了人们的担忧：人工智能系统可能会发现现有加密算法的漏洞。依赖加密技术来保护其数字货币的加密货币行业对此尤为警惕。

作为加密货币运作方式的一部分，许多加密账户在转账时会泄露一些个人信息。在 X（前身为 Twitter）上，德雷克写道：“今天，我呼吁区块链行业冷静地开始规划‘避难模式’。我个人建议启动一项有控制的大规模资产迁移计划，将资产转移到新的地址。”

“新地址”是指从未用于向其他账户汇款的地址，这限制了未来攻击者可能破坏其安全性的方式。

其他网络安全专家对人工智能能否对具体的安全问题产生多大影响持怀疑态度。“密码学家非常保守……我们在（安全加密）方面投入了大量的缓冲空间，非常巨大，”安全专家、畅销书《应用密码学》的作者布鲁斯·施奈尔说道。

他更关心网络安全领域的实施问题，而不是理论数学领域取得突破的可能性。

“计算机安全状况非常糟糕。这才是令人担忧的地方。代码漏洞、系统入侵，这些才是真正令人担忧的问题，而不是数学……在所有安全措施中，数学是我们最强大的武器，”施奈尔补充道。

杜克大学电子与计算机工程系助理教授艾米丽·温格曾利用机器学习来测试后量子加密方法的安全性，她说她不认为“先进的大型语言模型会破解所有加密”。

“但当你做出实际的实现选择时……我们过去发现，这些算法的某些实现方式是不安全的，”她说。“有两种方法可以破坏这些算法。你可以证明数学问题本身存在问题，或者你可以检查实现方式。”

阿伦森指出，破坏RSA等广泛使用的加密算法背后的数学原理将会产生深远的影响。“这些普通的漏洞，就像打地鼠游戏一样，发现一个就修补。但如果RSA被破解……如果我们所有的公钥加密系统都被破解了，那么我们构建互联网的方式就真的会出问题了。”

斯坦福大学计算机科学与电子工程教授、密码学专家丹·博内赫在一段视频中表示，失去现有的加密方式“将影响整个互联网……它会影响整个数字世界。因此，家庭银行、医疗保健、政府通信，所有方面都会受到这种漏洞的影响。”

但一些专家乐观地认为，随着人们越来越重视安全问题，安全最终会得到加强。

“过去，如果有人做出假设并基于此构建一个[密码学]系统，我们需要等待十年才能部署该系统，以便有足够的时间进行分析。而现在，我们可以利用这些模型极大地加快这一进程……我们只需让模型运行一个月，尝试破解它，如果模型无法破解，那么我们就对假设的有效性充满信心。因此，我们现在比以往任何时候都更有信心保障我们的安全，”Boneh说道。

施奈尔对此表示赞同，他说：“这是一场军备竞赛。我认为人工智能是第一个有可能扭转这场军备竞赛局面，让防御者占据优势的技术……微软上个月利用人工智能在‘补丁星期二’修复了900多个漏洞。但这些漏洞将不再构成问题。你已经遭受着计算机速度的攻击。现在，你也可以用计算机速度进行防御了。”

然而，任何转型都将代价高昂。对于典型的商业公司而言，构建“加密敏捷性”（即快速将组织数据切换到新型加密方式的能力）可能是应对加密不确定性的最佳方案。但对于国防工业而言，对手多年来一直在以加密形式收集其在线数据，因此现在进行转换对其解码现有数据的能力影响甚微。

国内外情报机构长期以来一直采用“先收集后解密”作为间谍活动的方法，随着时间的推移收集加密数据并将其存储起来，为日后破解现有加密技术做好准备。

“你必须假设情报机构现在正在收集你的数据，如果你认为人工智能有可能在未来一两年内发现这些系统的漏洞，那就更是如此了，”阿伦森说。

对于处理受限或机密信息的组织而言，人工智能数学突破的前景，给许多组织才刚刚开始准备迎接的后量子未来，又增添了一把倒计时的利剑。

联邦政府计划在未来几年全面过渡到后量子加密技术。各机构必须遵守第14412号行政命令和OMB备忘录M-26-15，分阶段将关键系统迁移到后量子密码技术，迁移时间从2030年12月至2035年。美国国家安全局（NSA）有其自身的国家安全系统迁移计划。根据该行政命令，承包商也必须在2030年12月之前遵守美国国家标准与技术研究院（NIST）的密码学标准。

但与加密相关的新数学成果可能需要不同的方法。阿伦森谈到人工智能可能对传统加密或后量子算法造成破坏时说：“这两者中的任何一个都可能失效，而另一个则不会。这不合逻辑。”

对组织而言，明智之举或许是“加密敏捷性”，即根据需要替换和叠加不同算法的能力。只要具备适当的敏捷性，即使加密算法出现漏洞，在大多数情况下也不会造成大范围损害。

施奈尔说：“你应该为后量子时代做好准备，提升加密技术的敏捷性。所以你现在就应该开始这么做了。如果你还没有，那就应该开始了。”

约翰·霍普金斯大学信息安全研究所计算机科学副教授、博客“关于密码工程的几点思考”的作者马修·格林写道：“我无法预知未来。没有人能预知未来。但到目前为止，押注于人类智能是极限而否定模型的做法，对我们任何人来说都没有好结果。”

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