linux-ipsec: "Richard Schroeppel": bigger prime

I asked the author of the primes in the back of the Oakley draft for some larger primes, and for more info on how to determine the estimated strength of the key agreement protocol (so it isn't too much weaker than the block encryption). Here's a better prime that we can use.

        John

Date: Thu, 5 Mar 1998 14:18:47 MST
From: "Richard Schroeppel" <rcs@CS.Arizona.EDU> Subject: bigger prime

Here's a 1536 bit prime I generated for Oakley. The strength parameter is 91 bits. This means that the time to crack a Diffie-Hellman exchange using this prime is estimated at 2^91 DES-encryptions.

Rich rcs@cs.arizona.edu

   The prime is 2^1536 - 2^1472 - 1 + 2^64 * { [2^1406 pi] + 741804 }.    Its decimal value is

         241031242692103258855207602219756607485695054850245994265411
         694195810883168261222889009385826134161467322714147790401219
         650364895705058263194273070680500922306273474534107340669624
         601458936165977404102716924945320037872943417032584377865919
         814376319377685986952408894019557734611984354530154704374720
         774996976375008430892633929555996888245787241299381012913029
         459299994792636526405928464720973038494721168143446471443848
         8520940127459844288859336526896320919633919

   The primality of the number has been rigorously proven.

   The representation of the group in OAKLEY is

      Type of group:                    "MODP"
      Size of field element (bits):      1536
      Prime modulus:                     21 (decimal)
         Length (32 bit words):          48
         Data (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 CA237327 FFFFFFFF FFFFFFFF
      Generator:                         22 (decimal)
         Length (32 bit words):          1
         Data (hex):                     2

      Optional Parameters:
      Group order largest prime factor:  24 (decimal)
         Length (32 bit words):          48
         Data (hex):
            7FFFFFFF FFFFFFFF E487ED51 10B4611A 62633145 C06E0E68
            94812704 4533E63A 0105DF53 1D89CD91 28A5043C C71A026E
            F7CA8CD9 E69D218D 98158536 F92F8A1B A7F09AB6 B6A8E122
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            F242DABB 312F3F63 7A262174 D31BF6B5 85FFAE5B 7A035BF6
            F71C35FD AD44CFD2 D74F9208 BE258FF3 24943328 F6722D9E
            E1003E5C 50B1DF82 CC6D241B 0E2AE9CD 348B1FD4 7E9267AF
            C1B2AE91 EE51D6CB 0E3179AB 1042A95D CF6A9483 B84B4B36
            B3861AA7 255E4C02 78BA3604 6511B993 FFFFFFFF FFFFFFFF
      Strength of group:                 26 (decimal)
         Length (32 bit words)            1
         Data (hex):
            0000005B

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<end of the group definition> Received on Thu Mar 5 18:12:14 1998