C. Pomerance, The number eld sieve, Proc. Symp. Appl. Math. 48 (1994) 465480. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Computational Methods in Public Key Cryptology - Lenstra (2001) (Correct)
....of more than two large primes, so that relatively small factor bases can be used during sieving. The relation collection stage can be distributed over almost any number of loosely coupled processors, similar to quadratic sieve. For an introductory description of the number eld sieve, refer to [63, 66, 93]. For complete details see [65] and the references given there. The latest developments are described in [21, 81] The largest special number factored using the special number eld sieve is 2 773 1 (see [33] This was done by the same group that achieved the current general number eld ....
C. Pomerance, The number eld sieve, Proc. Symp. Appl. Math. 48 (1994) 465480.
How To Find Small Factors Of Integers - Bernstein (2000) (2 citations) (Correct)
.... array size allows a reduction in the size of n; see, e.g. 52] Pollard s number eld sieve, as generalized by Buhler, Lenstra, and Pomerance, seems to always succeed in time exp( 64=9 o(1) 1=3 (log D) 1=3 (log log D) 2=3 ) See [138] 104] 105] 3] 44] 139] 60] 24] 41] [145], 121] 82] 19] 69] 148] 72] 73] 74] 76] 61] 75] 123] 126] 130] and [127] The algorithm in this paper can again be used to indirectly speed up sieving and reduce the size of n. Coppersmith s number eld sieve variant in [54] seems asymptotically faster, with 64=9 ....
Carl Pomerance, The number eld sieve, in [78] (1994), 465-480. MR 96c:11143.
Recent Progress and Prospects for Integer Factorisation Algorithms - Brent (4 citations) (Correct)
....= d X j=0 a j x j ; it is clear that f(x) and g(x) have a common root m mod N . This method of polynomial selection is called the base m method. In principle, we can proceed as in SNFS, but many diculties arise because of the large coecients of g(x) For details, we refer the reader to [36, 37, 41, 47, 48, 62]. Suce it to say that the diculties can be overcome and the method works Due to the constant factors involved it is slower than MPQS for numbers of less than about 110 decimal digits, but faster than MPQS for suciently large numbers, as anticipated from the theoretical run times given in x2. ....
C. Pomerance, The number eld sieve, Proceedings of Symposia in Applied Mathematics 48, Amer. Math. Soc., Providence, Rhode Island, 1994, 465-480.
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