4 ms·

This is a newbie question, but how are the standard primes created? How is it ensured that they are not selected maliciously, etc? (a link will suffice)

by runn1ng 11y ago

cperciva 11y ago
The standard prime groups have their highest and lowest 64 bits set, and as many as possible of the rest taken from the binary expansion of pi. The group #14 prime for example is p = 2^2048 - 2^1984 - 1 + 2^64 * { [2^1918 pi] + 124476 } The value 124476 is the smallest non-negative value which results in p and (p-1)/2 both being prime and 2 being a quadratic residue mod p; this ensures that the subgroup {2^0, 2^1, 2^2, 2^3, ... } is cyclic. We assume that the binary expansion of Pi is not selected maliciously. ;-)
- cantrevealname 11y ago
  And as an amusing tidbit, here is the actual value in hex: FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AACAA68 FFFFFFFF FFFFFFFF Source: https://tools.ietf.org/html/rfc3526#section-3 https://tools.ietf.org/html/rfc3526#section-3
- webmaven 11y ago
  > We assume that the binary expansion of Pi is not selected maliciously. ;-) Well, I suppose that we must assume that, as assuming otherwise is self-defeating: anyone running the simulation we're living in already has direct access to the plaintexts anyway.
  - qb45 11y ago
    That somebody maliciously caused the circle's circumference to diameter ratio to be insecure in this application is indeed not an issue. However, a possible danger is that somebody maliciously suggested using π instead of e...
    - cperciva 11y ago
      True, but Pi is pretty much tradition now... enough so that when Decorrelated Fast Cipher used e instead, it raised some eyebrows.
wfunction 11y ago
> (a link will suffice) https://en.wikipedia.org/wiki/Nothing_up_my_sleeve_number https://en.wikipedia.org/wiki/Nothing_up_my_sleeve_number
andrius4669 11y ago
pretty good presentation on that by djb: https://projectbullrun.org/surveillance/2015/video-2015.html#bernstein https://projectbullrun.org/surveillance/2015/video-2015.html...

This is a newbie question, but how are the standard primes created? How is it ensured that they are not selected maliciously, etc? (a link will suffice)

by runn1ng 11y ago

This is a newbie question, but how are the standard primes created? How is it ensured that they are not selected maliciously, etc? (a link will suffice)

cperciva 11y ago

The standard prime groups have their highest and lowest 64 bits set, and as many as possible of the rest taken from the binary expansion of pi. The group #14 prime for example is p = 2^2048 - 2^1984 - 1 + 2^64 * { [2^1918 pi] + 124476 } The value 124476 is the smallest non-negative value which results in p and (p-1)/2 both being prime and 2 being a quadratic residue mod p; this ensures that the subgroup {2^0, 2^1, 2^2, 2^3, ... } is cyclic. We assume that the binary expansion of Pi is not selected maliciously. ;-)

cantrevealname 11y ago
And as an amusing tidbit, here is the actual value in hex: FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AACAA68 FFFFFFFF FFFFFFFF Source: https://tools.ietf.org/html/rfc3526#section-3 https://tools.ietf.org/html/rfc3526#section-3
webmaven 11y ago
> We assume that the binary expansion of Pi is not selected maliciously. ;-) Well, I suppose that we must assume that, as assuming otherwise is self-defeating: anyone running the simulation we're living in already has direct access to the plaintexts anyway.
- qb45 11y ago
  That somebody maliciously caused the circle's circumference to diameter ratio to be insecure in this application is indeed not an issue. However, a possible danger is that somebody maliciously suggested using π instead of e...
  - cperciva 11y ago
    True, but Pi is pretty much tradition now... enough so that when Decorrelated Fast Cipher used e instead, it raised some eyebrows.

wfunction 11y ago

> (a link will suffice) https://en.wikipedia.org/wiki/Nothing_up_my_sleeve_number https://en.wikipedia.org/wiki/Nothing_up_my_sleeve_number

andrius4669 11y ago

pretty good presentation on that by djb: https://projectbullrun.org/surveillance/2015/video-2015.html#bernstein https://projectbullrun.org/surveillance/2015/video-2015.html...