Re: [TLS] Safe ECC usage
"D. J. Bernstein" <djb@cr.yp.to> Thu, 03 October 2013 01:05 UTC
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From: "D. J. Bernstein" <djb@cr.yp.to>
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Subject: Re: [TLS] Safe ECC usage
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We're hypothesizing an attack A that isn't publicly known, and considering the following probabilities: Pr[A succeeds against a NIST P-256 user]; Pr[A succeeds against a brainpoolP256r1 user]; Pr[A succeeds against a Curve25519 user]. NSA had considerable power to manipulate the NIST P-256 curve choice and thus, at least potentially, the first probability. Under a wide range of reasonable assumptions on A this would allow NSA to create a very high first probability. There's far less room for Brainpool manipulation, although still some (why SHA-1? why not right to left? why pi instead of e or sqrt(2)? and so on), maybe enough to exploit. There's essentially zero room for Curve25519 manipulation. We have no basis for comparing the probabilities outside the case of manipulation. Perhaps Pr[A succeeds against a brainpoolP256r1 user] < Pr[A succeeds against a Curve25519 user], but there's zero justification for this guess. Perhaps Pr[A succeeds against a brainpoolP256r1 user] > Pr[A succeeds against a Curve25519 user], but there's also zero justification for this guess. This is wild speculation, completely divorced from rational risk management. Dan Brown writes: > a proof that Brainpool are invulnerable to the "missed attack" with > probability equal to the density of the vulnerable curves There is no such proof, and there never will be any such proof. I hope you're not trying to bamboozle the innocent reader with bogus claims of provability! But that's not the big issue here. The big issue is that, even in a fantasy world of proving the (rather implausible) statement Pr[A succeeds against a brainpoolP256r1 user] = Pr[A succeeds against a user of a random curve], we still wouldn't have any basis for comparing the Brainpool and Curve25519 probabilities. You claim that Pr[A succeeds against a user of a random curve] < Pr[A succeeds against a Curve25519 user] but you have zero justification for this claim. One could just as well claim the opposite, namely that Pr[A succeeds against a user of a random curve] > Pr[A succeeds against a Curve25519 user], which would also have zero justification. Maybe big coefficients are more secure than small coefficients, but maybe they're _less_ secure. ---D. J. Bernstein Research Professor, Computer Science, University of Illinois at Chicago
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- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Stephen Farrell
- [TLS] draft-sheffer-tls-bcp: DH recommendations Yaron Sheffer
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Yaron Sheffer
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Michael D'Errico
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Patrick Pelletier
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Xuelei Fan
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Martin Rex
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Yaron Sheffer
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Yoav Nir
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Yaron Sheffer
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Martin Rex
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Blumenthal, Uri - 0558 - MITLL
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Blumenthal, Uri - 0558 - MITLL
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Yaron Sheffer
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Peter Gutmann
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Yaron Sheffer
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Peter Gutmann
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Yaron Sheffer
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Michael Ströder
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Yaron Sheffer
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Blumenthal, Uri - 0558 - MITLL
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… james hughes
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… james hughes
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Blumenthal, Uri - 0558 - MITLL
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Michael Ströder
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Michael Ströder
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… james hughes
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Blumenthal, Uri - 0558 - MITLL
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Yoav Nir
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Yaron Sheffer
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Bill Frantz
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Ralph Holz
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Martin Rex
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Martin Rex
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Martin Rex
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… james hughes
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Peter Gutmann
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Peter Gutmann
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Yaron Sheffer
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Michael Ströder
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Yaron Sheffer
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… james hughes
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Peter Gutmann
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Michael Ströder
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Michael D'Errico
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Yoav Nir
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Yaron Sheffer
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Yaron Sheffer
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Stephen Farrell
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Patrick Pelletier
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Yoav Nir
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Michael D'Errico
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Yaron Sheffer
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Yaron Sheffer
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Ralph Holz
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… james hughes
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Ralph Holz
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Nikos Mavrogiannopoulos
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Patrick Pelletier
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Patrick Pelletier
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Patrick Pelletier
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Yoav Nir
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Peter Gutmann
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Patrick Pelletier
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Martin Rex
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Peter Gutmann
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Yaron Sheffer
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Alex Elsayed
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Michael D'Errico
- Re: [TLS] draft-sheffer-tls-bcp: DH recommendatio… Peter Gutmann
- [TLS] Safe ECC usage D. J. Bernstein
- Re: [TLS] Safe ECC usage Dan Brown
- Re: [TLS] Safe ECC usage D. J. Bernstein
- Re: [TLS] Safe ECC usage Dan Brown
- Re: [TLS] Safe ECC usage Kyle Hamilton
- Re: [TLS] Safe ECC usage Johannes Merkle
- Re: [TLS] Safe ECC usage Adam Langley
- Re: [TLS] Safe ECC usage Santosh Chokhani
- Re: [TLS] Safe ECC usage Martin Rex
- Re: [TLS] Safe ECC usage Kyle Hamilton
- Re: [TLS] Safe ECC usage Yoav Nir
- Re: [TLS] Safe ECC usage Martin Rex
- Re: [TLS] Safe ECC usage D. J. Bernstein
- Re: [TLS] Safe ECC usage Dan Brown
- Re: [TLS] Safe ECC usage Johannes Merkle
- Re: [TLS] Safe ECC usage Manuel Pégourié-Gonnard
- Re: [TLS] Safe ECC usage Yoav Nir
- Re: [TLS] Safe ECC usage D. J. Bernstein
- Re: [TLS] Safe ECC usage Dan Brown
- Re: [TLS] Safe ECC usage D. J. Bernstein
- Re: [TLS] Safe ECC usage Dan Brown
- Re: [TLS] Safe ECC usage Johannes Merkle
- [TLS] (offline note) Re: Safe ECC usage Rene Struik
- Re: [TLS] Safe ECC usage D. J. Bernstein
- [TLS] (EC)DSA potential problems (ECC "brittlenes… Martin Rex
- Re: [TLS] Safe ECC usage Dan Brown
- Re: [TLS] Safe ECC usage D. J. Bernstein
- Re: [TLS] Safe ECC usage Dan Brown
- Re: [TLS] Safe ECC usage Watson Ladd
- Re: [TLS] Safe ECC usage Dan Brown
- Re: [TLS] Safe ECC usage Johannes Merkle
- Re: [TLS] Safe ECC usage Nico Williams
- Re: [TLS] Safe ECC usage Dan Brown
- Re: [TLS] Safe ECC usage Nico Williams
- Re: [TLS] Safe ECC usage Michael StJohns
- Re: [TLS] Safe ECC usage Dan Brown
- Re: [TLS] Safe ECC usage Nico Williams
- Re: [TLS] Safe ECC usage Bill Frantz
- Re: [TLS] Safe ECC usage D. J. Bernstein
- Re: [TLS] Safe ECC usage Dan Brown
- [TLS] DH group negotiation extension [was: Re: dr… Daniel Kahn Gillmor
- Re: [TLS] DH group negotiation extension [was: Re… Dang, Quynh
- Re: [TLS] DH group negotiation extension [was: Re… Patrick Pelletier
- Re: [TLS] DH group negotiation extension [was: Re… Watson Ladd