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Charles Guillemet
@P3b7_
CTO at @ledger. Busy securing the blockchain revolution. Cryptography, (Hw) Security, Tech, Blockchain. Previously built the Donjon (@DonjonLedger)
๊ฐ€์ž… September 2018
310 ํŒ”๋กœ์ž‰ ์ค‘    46.3K ํŒฌ
๐Ÿค–ETH (not Ethereum but the Exponential Time Hypothesis) is false. A Lean proof, produced by OpenAI says 3-SAT can be solved in subexponential time. For twenty-five years the field assumed the opposite, and hundreds of "impossible unless ETH fails" results in graphs, biology, databases, and geometry were deduced from a false premise. The problems are not suddenly easy. We have simply lost a fundamental reason we had for refusing to look for a faster algorithm. Sorry, your SAT solver does not get faster. ETH was the strong form of P โ‰  NP. Every polynomial is already subexponential, so a true ETH would have implied P โ‰  NP immediately. A false ETH does not imply P = NP. Subexponential is still FAR more than polynomial. This has no impact on cryptography. Signatures, hashes, discrete logs, and lattices are average-case questions about specific functions. A faster worst-case algorithm for Boolean formulas does not forge a signature, invert SHA-256, or change the cost of a Bitcoin block. Classical cryptography needs one-way functions, and those cannot exist if P = NP. Whenever P = NP is proven, our simulation must be reset.
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