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Magic Internet Math · Today · 1 hr 9 min

Exponential Got Less Exponential

In this episode, we picked back up on our red-team tour of Bitcoin cryptography and tried to make sense of the last few weeks of fast-moving math news. We unpacked why the recent excitement around the exponential time hypothesis mattered, how it relates to the discrete log problem behind Bitcoin’s elliptic curve cryptography, and why “less exponential” is not the same thing as “Bitcoin is broken.” Along the way, we revisited the different doors an attacker would have to walk through to weaken secp256k1, from generic algorithmic improvements to curve symmetries, lifting tricks, and the bigger backstop of P vs NP. The goal wasn’t to declare victory or panic, but to get clearer on what has actually changed, what remains theoretical, and where AI seems to fit as a theorem-grinder rather than a magic cryptography-breaking button. We also spent time on the emerging tooling around formal verification and hash-based signatures. That took us into sig.golf, Lean proofs, OpenAI’s public math repository, and the growing idea that part of Bitcoin’s future safety may depend not just on us verifying systems, but on us proving that machines can verify them too. We talked through why libsecp256k1 deserves far more appreciation, why Jonas Nick’s post-quantum work keeps showing up at the center of these conversations, and why experiments around Lean, Bitcoin consensus rules, and AI-assisted proof generation feel increasingly important. If this show is our attempt to build a bridge into the math, this was one of those episodes where the bridge got a little longer — and a lot more interesting. Magic Internet Math: https://magicinternetmath.com/ Plan ₿ Forum Lugano: https://planb.lugano.ch/planb-forum/ libsecp256k1: https://github.com/bitcoin-core/secp256k1 Bitcoin Core: https://bitcoin.org/en/bitcoin-core/ OpenAI Math Repository: https://github.com/openai/math Lean Programming Language and Theorem Prover: https://lean-lang.org/ sig.golf: https://sig.golf/ lean Ethereum by Justin Drake: https://blog.ethereum.org/2025/07/31/lean-ethereum Joseph Lubin at Consensys: https://consensys.com/about/joseph-lubin-founder-of-consensys Jonas Nick at Blockstream: https://blog.blockstream.com/author/jonas/ Neal Koblitz: https://sites.math.washington.edu/~koblitz/ A Course in Number Theory and Cryptography: https://link.springer.com/book/10.1007/978-1-4419-8592-7 Robin Linus: https://robinlinus.com/ Antoine Riard: https://gist.github.com/ariard rust-bitcoin: https://github.com/rust-bitcoin/rust-bitcoin Cashu: https://cashu.space/ Lightning Network / Core Lightning: https://blockstream.com/lightning/ DeepSeek: https://www.deepseek.com/ Kaggle: https://www.kaggle.com/ BIP 42: https://github.com/bitcoin/bips/blob/master/bip-0042.mediawiki BIP 66: https://github.com/bitcoin/bips/blob/master/bip-0066.mediawiki BIP 113: https://github.com/bitcoin/bips/blob/master/bip-0113.mediawiki

0:00 · Welcome back and why math literacy matters-1:09:31
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In this episode, we picked back up on our red-team tour of Bitcoin cryptography and tried to make sense of the last few weeks of fast-moving math news. We unpacked why the recent excitement around the exponential time hypothesis mattered, how it relates to the discrete log problem behind Bitcoin’s elliptic curve cryptography, and why “less exponential” is not the same thing as “Bitcoin is broken.” Along the way, we revisited the different doors an attacker would have to walk through to weaken secp256k1, from generic algorithmic improvements to curve symmetries, lifting tricks, and the bigger backstop of P vs NP. The goal wasn’t to declare victory or panic, but to get clearer on what has actually changed, what remains theoretical, and where AI seems to fit as a theorem-grinder rather than a magic cryptography-breaking button.

We also spent time on the emerging tooling around formal verification and hash-based signatures. That took us into sig.golf, Lean proofs, OpenAI’s public math repository, and the growing idea that part of Bitcoin’s future safety may depend not just on us verifying systems, but on us proving that machines can verify them too. We talked through why libsecp256k1 deserves far more appreciation, why Jonas Nick’s post-quantum work keeps showing up at the center of these conversations, and why experiments around Lean, Bitcoin consensus rules, and AI-assisted proof generation feel increasingly important. If this show is our attempt to build a bridge into the math, this was one of those episodes where the bridge got a little longer — and a lot more interesting.

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