Cryptographers who develop encryption technologies may not be sleeping very well these days.OpenAI and Anthropic both said Monday that their internal AI models had disproven the Exponential Time Hypothesis, a longstanding computer science theorem that predicts the minimum difficulty…
An elliptic curve E over a finite field F consists of the set of points (x, y) satisfying the equation y² = x³ + ax + b with x and y in F. Typically in cryptography the field F is the integers mod p where p…
Enter to search English articles · Esc to close · ↑↓ to move Translated from the Japanese original Based on the reproduction code and the explanation of base points published by Anthropic, what has been found about the five NIST prime-field curves can…
Buterin, co-founder of Ethereum, is concerned about the potential cryptographic threats posed by the speedy development of AI-based mathematics. He’s not suggesting an immediate push to move all money off of systems relying on mathematical facts as security, but it’s…
A research team from the University of California, San Diego, and the French National Institute for Digital Science and Technology (Inria) has demonstrated in large-scale computational experiments that an attack can forge a 1024-bit RSA signature without factoring the RSA…
The idea of using computers to assist with proofs is not new. The first major computer-assisted proof was published in 1976, the proof of the four color theorem by Kenneth Appel and Wolfgang Haken. The authors reduced the proof of the…
Introduction Every blockchain needs a way to determine what is valid. When a transaction enters a decentralized network, independent …
Apple Machine Learning Research Interactive Proofs for General Distribution Properties Suppose Alice has collected a small number of samples from an unknown distribution, and would like to learn about the distribution. Bob, an untrusted data analyst, claims to have run…
Generative AI provides core idea to link two jamming theories, with proof validated and completed by physicists A 10-year-old mathematical puzzle explaining the phenomenon of jamming, in which particles suddenly freeze like a traffic jam after moving around, has been…
Researchers at La Sapienza University in Rome have successfully proven a decade-old mathematical conjecture regarding the physics of jamming, marking a notable milestone in human-AI scientific collaboration. The breakthrough, detailed in a recent publication in the Journal of Statistical Mechanics:…
The mathematics of cryptography: elliptic curves, number theory and codes in encryption, and mathematicians and AI cracking cryptographic puzzles.
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