Re: [TLS] On Curve25519 and other possibilities (e.g. ietf256p, ietf384p, ietf521p,
Nigel Smart <nigel@cs.bris.ac.uk> Sat, 28 June 2014 16:58 UTC
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Date: Sat, 28 Jun 2014 17:58:16 +0100
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Subject: Re: [TLS] On Curve25519 and other possibilities (e.g. ietf256p, ietf384p, ietf521p,
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Hi > One way to attempt to unify the diverse world of ECC curves is to focus > on the underlying field, as opposed the curve itself. Consider Fp > operations with p=2^255-19 or p=2^256-189. In other words, for > n={256,384,512}, chose the closest C: p=2^n-C is a prime and make this p > "MUST". People who demand random primes will have to play along and > accept less "randomness" in their curves. Alas there could be some issues with primes close to powers of two. See our recent side channel attacks on EC-DSA with the Eurovision titles on ePrint "Just a Little Bit" etc. Such a p forces the group order to also be close to a power of two (by Hasse's Theorem). Whilst these papers show there are problems with the NIST choices in this respect, the above choices of p would be even worse. So unifying in this respect would be a bad idea IMHO. Nigel -- Prof. Nigel P. Smart | Tel +44 (0)117 9545163 Computer Science Department, | Fax +44 (0)117 9545208 Woodland Road, | Email nigel@cs.bris.ac.uk Bristol, BS8 1UB, UK | http://www.cs.bris.ac.uk~nigel
- [TLS] On Curve25519 and other possibilities (e.g.… Michael StJohns
- Re: [TLS] On Curve25519 and other possibilities (… Blumenthal, Uri - 0558 - MITLL
- Re: [TLS] On Curve25519 and other possibilities (… Eric Rescorla
- Re: [TLS] On Curve25519 and other possibilities (… Hanno Böck
- Re: [TLS] On Curve25519 and other possibilities (… Martin Thomson
- Re: [TLS] On Curve25519 and other possibilities (… Blumenthal, Uri - 0558 - MITLL
- Re: [TLS] On Curve25519 and other possibilities (… Adam Langley
- Re: [TLS] On Curve25519 and other possibilities (… Viktor Dukhovni
- Re: [TLS] On Curve25519 and other possibilities (… Watson Ladd
- Re: [TLS] On Curve25519 and other possibilities (… Salz, Rich
- Re: [TLS] On Curve25519 and other possibilities (… Peter Gutmann
- Re: [TLS] On Curve25519 and other possibilities (… Peter Gutmann
- Re: [TLS] On Curve25519 and other possibilities (… Watson Ladd
- Re: [TLS] On Curve25519 and other possibilities (… Viktor Dukhovni
- Re: [TLS] On Curve25519 and other possibilities (… Alyssa Rowan
- [TLS] Hardware Implementations .. Re: On Curve255… Hannes Tschofenig
- Re: [TLS] Hardware Implementations .. Re: On Curv… Joachim Strömbergson
- Re: [TLS] On Curve25519 and other possibilities (… Paul Hoffman
- Re: [TLS] Hardware Implementations .. Re: On Curv… Hannes Tschofenig
- Re: [TLS] On Curve25519 and other possibilities (… Stephen Farrell
- Re: [TLS] On Curve25519 and other possibilities (… Blumenthal, Uri - 0558 - MITLL
- Re: [TLS] On Curve25519 and other possibilities (… Andrey Jivsov
- Re: [TLS] On Curve25519 and other possibilities (… Nigel Smart
- Re: [TLS] On Curve25519 and other possibilities (… Watson Ladd
- Re: [TLS] On Curve25519 and other possibilities (… Alyssa Rowan
- Re: [TLS] On Curve25519 and other possibilities (… Michael StJohns
- Re: [TLS] On Curve25519 and other possibilities (… Andrey Jivsov
- Re: [TLS] On Curve25519 and other possibilities (… Eric Rescorla
- Re: [TLS] On Curve25519 and other possibilities (… Andrey Jivsov
- Re: [TLS] On Curve25519 and other possibilities (… Michael StJohns
- Re: [TLS] On Curve25519 and other possibilities (… Michael StJohns
- Re: [TLS] On Curve25519 and other possibilities (… Andrey Jivsov
- Re: [TLS] On Curve25519 and other possibilities (… Eric Rescorla
- Re: [TLS] On Curve25519 and other possibilities (… Salz, Rich
- Re: [TLS] On Curve25519 and other possibilities (… Michael StJohns
- Re: [TLS] On Curve25519 and other possibilities (… Watson Ladd
- Re: [TLS] On Curve25519 and other possibilities (… Michael StJohns
- Re: [TLS] On Curve25519 and other possibilities (… Eric Rescorla
- Re: [TLS] On Curve25519 and other possibilities (… Dan Brown
- Re: [TLS] On Curve25519 and other possibilities (… Stephen Farrell
- Re: [TLS] On Curve25519 and other possibilities (… Michael StJohns
- Re: [TLS] On Curve25519 and other possibilities (… Michael StJohns
- Re: [TLS] On Curve25519 and other possibilities (… Eric Rescorla
- Re: [TLS] Off-topic: RC4 Peter Yee
- [TLS] On counting Paul Hoffman
- Re: [TLS] On Curve25519 and other possibilities (… Salz, Rich
- Re: [TLS] On counting Adam Caudill
- [TLS] Off-topic: RC4 Paul Hoffman
- Re: [TLS] On Curve25519 and other possibilities (… Salz, Rich
- Re: [TLS] On Curve25519 and other possibilities (… Watson Ladd
- Re: [TLS] On Curve25519 and other possibilities (… Michael StJohns
- Re: [TLS] On Curve25519 and other possibilities (… Michael StJohns
- Re: [TLS] On Curve25519 and other possibilities (… Watson Ladd
- Re: [TLS] On Curve25519 and other possibilities (… Salz, Rich
- Re: [TLS] On Curve25519 and other possibilities (… Nigel Smart
- Re: [TLS] On Curve25519 standardization Michael StJohns
- Re: [TLS] On Curve25519 and other possibilities (… Michael StJohns
- Re: [TLS] On Curve25519 and other possibilities (… Watson Ladd
- Re: [TLS] On Curve25519 and other possibilities (… Fedor Brunner
- Re: [TLS] On Curve25519 and other possibilities (… Peter Gutmann
- Re: [TLS] On Curve25519 and other possibilities (… Johannes Merkle
- Re: [TLS] On Curve25519 and other possibilities (… Watson Ladd
- Re: [TLS] On Curve25519 and other possibilities (… Andrey Jivsov
- Re: [TLS] On Curve25519 and other possibilities (… Johannes Merkle
- Re: [TLS] On Curve25519 and other possibilities (… Alyssa Rowan
- Re: [TLS] On Curve25519 and other possibilities (… Johannes Merkle
- Re: [TLS] On Curve25519 and other possibilities (… Blumenthal, Uri - 0668 - MITLL