When do you think P vs NP problem will be solved? this month or next or later?

Impressive result from Anthropic, well beyond cryptography. Claude reportedly took less than 30 minutes to trace the origins of NIST elliptic curve seeds, a question open for over 25 years. No vulnerability found, but the implications for research are significant. As AI accelerates discoveries, we face a new bottleneck: understanding what matters and adapting existing systems. monstream.io/f/claude-recons…

I don't recommend anyone scramble to move their funds to new wallets today. But we should take the risks to cryptography from AI-accelerated math seriously, and minimize our exposure to not just quantum-vulnerable cryptography, but also potentially AI-vulnerable cryptography. The core new area of risk from this viewpoint is, unfortunately, ML-DSA / FHE / lattices. (and it's also another reason, along with quantum, why ECDSA might fall even faster than expected, hence the "fresh address" recommendation) So far most people have been in the mode of thinking "elliptic curves broken, hashes safe, lattices safe". But there is a good chance that the concrete security of lattices will take serious hits from the next two years of AI math. The basic threat model is: factoring is something that naively takes 2^(n/2) time, but over decades smart people have found and optimized number field sieves, and degraded that to 2^O(n^(1/3)), which is why RSA keys and signatures need to be ~400 bytes (and not 64 bytes). What if there are skeletons in the closet like that, both for elliptic curves and lattices, that we are simply not smart enough to discover - but bots soon will be? This is a major part of the reason why for the past year ethereum's lean roadmap has been going in the "hash-only" direction: no lattices, no ML-DSA, no Falcon, no lattice-based commitments inside ZK proofs, etc. Signatures in lean ethereum are all hash-based, either WOTS or SPHINCS-. For signatures and proofs, we already know how to go hash-only. The bigger challenge is for *public-key encryption* - and this goes far beyond blockchains. Secure communication, anonymizing protocols, lots of things need public-key encryption. And unfortunately there are long-standing mathematical theorems showing why public-key encryption cannot be done with hashes alone. You have to have some kind of trapdoor object that has at least one form of usable "structure" - either group theory (incl. isogenies) or lattices or code-based or potentially in the future even more newfangled and spooky things (local mixing?). But for anything that has structure, you should assume that AI will make at least some progress in breaking that structure. Here, one reasonable inference is that if you want to make something plausibly long-term secure, multiply the key sizes by 10. To me that's a very plausible world and something not at all extreme to predict. If AI will bring us 50 years of math in 2 years, then that 50 years of math may very plausibly include a "naive factoring -> GNFS" level of improvement to our ability to break lattices. In that world, lattices will still exist, but they will have to be significantly bigger to guarantee the same level of safety. And at those new larger sizes, hash-based constructions will beat lattice-based constructions on concrete efficiency in every use case where hash-based constructions are possible at all. Theoretically, of course it's possible that hashes are broken too (eg. P = NP would imply that). But I think P = NP is very unlikely. And intuitively, it's much more likely that a mathematical object has exactly no exploitable structure (like hashes are intended to), than that a mathematical object has exactly ~3 forms of exploitable structure (for elliptic curves: associativity, Schoof, pairings) and not some secret fourth form of structure we have not yet discovered that greatly degrades its security (for elliptic curves, ECDLP and pairing security). Similar for LWE, SVP, RLWE and the zoo of lattice problems. For this reason, we do not yet see any reason to worry and start padding the byte size of hashes (if we start to worry more, we would pad the round count first before doing anything to the byte size). Concrete TLDR, my own personal views: * Hash-based > lattice-based, in those situations where hash-based is possible at all * For anything lattice-based, be much more paranoid on param sizes. Remember that blockchains are only a small portion of the cryptography story; this point goes far beyond blockchains and applies to eg. access to websites, secure messaging, Tor / VPNs ... * For privacy protocols, strongly favor NOT putting encrypted notes onchain. Instead, send them offchain through some third-party mechanism. * If it's not difficult for you, keeping your funds in addresses which have not yet been used to make a transaction is a good idea. If it's easy for you, do it. **But be careful about migrations; I personally have lost more money in botched migrations than I have lost in all hacks combined**. * For multisig wallets, doing confirmations offchain is better than onchain, because this way the signatures of signer wallets do not get exposed to the public, so if ECDSA falls to AI much faster than expected, at least the multisig "gracefully degrades" to a 1-of-1 where the 1 is whoever was gathering the signatures - a much better place to be than "anyone can take the money" firefly.social/post/x/210783…

Happy to share our collaboration with @nvidia and @DualityTech research teams: "Efficient Large-Integer Arithmetic for FHE". Efficient large-integer arithmetic is a key building block of modern fully homomorphic encryption (FHE). In this paper, we discuss the algorithms and implementation techniques behind high-performance arithmetic for vectorized FHE schemes, examine the trade-offs between different approaches, and highlight promising directions for future improvements. It was a pleasure collaborating with researchers from NVIDIA and Duality Technologies on this work.

The US government, citing national security authorities, has issued an export control directive to suspend all access to Fable 5 and Mythos 5 by any foreign national, whether inside or outside the United States, including foreign national Anthropic employees. The net effect of this order is that we must abruptly disable Fable 5 and Mythos 5 for all our customers to ensure compliance. Access to all other Claude models is not affected. We apologize for this disruption to our customers. We believe this is a misunderstanding and are working to restore access as soon as possible. Read our full statement: anthropic.com/news/fable-myt…

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