J. Pollard, Theorems on factorization and primality testing, Proceedings of the Cambridge Philosophical Society, vol. 76, pp. 521-528, 1974. Home/Search Document Not in Database Summary Related Articles Check |
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On Verifiable Function Sharing - Blunden (Correct)
....is believed to be hard for a general n when n is large. Some ingenious methods have been devised in an attempt to factorize large com posite numbers n. Several of these methods are tailored towards those n whose factors have particular properties, an example being Pollard s (p 1) algorithm [36], which efficiently finds any prime factors p of a composite number n provided the prime factors of (p 1) are all less than or equal to a small bound B. Such algo rithms are sometimes referred to as special purpose factoring algorithms [32] For a general number n that is not known to satisfy ....
J. Pollard. Theorems on Factorization and Primality Testing. In Proceedings of the Cambridge Philosophical Society, volume 76, pages 521-528, 1974.
Computational Methods in Public Key Cryptology - Lenstra (2001) (Correct)
....RSA Similarly, log g (h) can be found by comparing g t to h for t = 0; 1; 2; in succession, until g t = h. This takes at most order(g) multiplications in G. There are no realistic practical applications of this method, unless order(g) is very small. 34 4.1. 2 Pollard s p 1 method [88]. According to Fermat s little theorem (see 3.5.2) a p 1 # 1 mod p for prime p and any integer a not divisible by p. It follows that a k # 1 mod p if k is an integer multiple of p 1. Furthermore, if p divides n, then p divides gcd(a k 1; n) This may make it possible to nd a prime ....
J.M. Pollard, Theorems on factorization and primality testing, Proceedings of the Cambridge philosophical society, 76 (1974) 521-528.
A Short Note on Girault's Self-Certified Model - Ed Mod El (2001) (Correct)
....is feasible in practice. There could, however, exist a problem with this scenario. If n is chosen following (1) then the factorization of n becomes feasible as well. On the other hand, if n is chosen following (2) then it is also possible to factorize n with Pollard s p Gamma 1 algorithm [11]. This implies that cheating users can compute d and consequently, other certificates linked to themselves, which enable them to claim later that the authority has cheated. As a matter of fact, generating a composite number such that it is infeasible for the outside world to factorize it, but it ....
J. M. Pollard, "Theorems on factorization and primality testing", Proceedings of the Cambridge Philosophical Society, vol. 76, 1974, pp. 521-528
Some Integer Factorization Algorithms using Elliptic Curves - Brent (1986) (12 citations) (Correct)
....[22, 29] it is easy to evaluate (9.1) in (r O(log r) s=2 multiplications. Using these ideas we obtain a speedup of about 6.6 over the one phase algorithm for p = 10 20 . 9. 2 Other second phases Our birthday paradox idea can be used as a second phase for Pollard s p Gamma 1 algorithm [23]. The only change is that we work over a different group. Conversely, the conventional second phases for Pollard s p Gamma 1 algorithm can be adapted to give second phases for elliptic curve algorithms, and various tricks can be used to speed them up [19] Theoretically these algorithms give a ....
J. M. Pollard, Theorems in factorization and primality testing, Proc. Cambridge Philos. Soc. 76 (1974), 521--528.
A New Public-Key Cryptosystem Based on Higher Residues - Naccache, Stern (1998) (23 citations) (Correct)
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J. Pollard, Theorems on factorization and primality testing, Proceedings of the Cambridge Philosophical Society, vol. 76, pp. 521-528, 1974.
A New Public-Key Cryptosystem Based on - Higher Residues Published (Correct)
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J. Pollard, Theorems on factorization and primality testing, Proceedings of the Cambridge Philosophical Society, vol. 76, pp. 521-528, 1974.
How to Use RSA; or How to Improve the Efficiency of RSA.. - Joye, Paillier (2002) (Correct)
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J.M. Pollard. Theorems on factorization and primality testing. Proc. Camb. Phil. Soc., 76:521-528, 1974.
How to Use RSA; or How to Improve the Efficiency of RSA.. - Joye, Paillier (2002) (Correct)
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J.M. Pollard. Theorems on factorization and primality testing. Proc. Camb. Phil. Soc., 76:521--528, 1974.
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John M. Pollard. Theorems of factorization and primality testing. Proc. Cambridge Phil. Soc., 76:521--528, 1974.
Nonuniform Hard Boolean Functions and Uniform Complexity Classes - Kabanets (2001) (Correct)
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J.M. Pollard. Theorems on factorization and primality testing. Proceedings of the Cambridge Philosophical Society, 76:521-528, 1974.
How to Use RSA; or How to Improve the Efficiency of RSA.. - Joye, Paillier (2002) (Correct)
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J.M. Pollard. Theorems on factorization and primality testing. Proc. Camb. Phil. Soc., 76:521-528, 1974.
A New Public-Key Cryptosystem Based on Higher Residues - Naccache, Stern (1998) (23 citations) (Correct)
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J. Pollard, Theorems on factorization and primality testing, Proceedings of the Cambridge Philosophical Society, vol. 76, pp. 521-528, 1974.
Factorization of the Tenth and Eleventh Fermat Numbers - Brent (1996) (2 citations) (Correct)
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J. M. Pollard, Theorems in factorization and primality testing, Proc. Cambridge Philos. Soc. 76 (1974), 521--528.
A New Public-Key Cryptosystem Based on Higher Residues - Naccache, Stern (1998) (23 citations) (Correct)
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J. Pollard, Theorems on factorization and primality testing, Proceedings of the Cambridge Philosophical Society, vol. 76, pp. 521-528, 1974.
How to Use RSA; or How to Improve the Efficiency of RSA.. - Joye, Paillier (2002) (Correct)
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J.M. Pollard. Theorems on factorization and primality testing. Proc. Camb. Phil. Soc., 76:521--528, 1974.
Are `Strong' Primes Needed for RSA? - Rivest, Silverman (1999) (1 citation) (Correct)
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J. M. Pollard. Theorems on factorization and primality testing. Proceedings Cambridge Philosophical Society, 76:521--528, 1974.
Factorization of the Tenth Fermat Number - Brent (1999) (1 citation) (Correct)
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J. M. Pollard, Theorems in factorization and primality testing, Proc. Cambridge Philos. Soc. 76 (1974), 521--528. MR 50:6992
Security Analysis of Several Group Signature Schemes - Wang (2003) (1 citation) (Correct)
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J.M. Pollard. Theorems on factorization and primality testing. Proc. Cambridge Philos. Soc., 1974, 76: 521-528.
A New Public-Key Cryptosystem Based on Higher Residues - Naccache, Stern (1998) (23 citations) (Correct)
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J. Pollard, Theorems on factorization and primality testing, Proceedings of the Cambridge Philosophical Society, vol. 76, pp. 521-528, 1974.
How to Use RSA; or How to Improve the Efficiency of RSA.. - Joye, Paillier (2002) (Correct)
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J.M. Pollard. Theorems on factorization and primality testing. Proc. Camb. Phil. Soc., 76:521-528, 1974.
On using Carmichael numbers for public key encryption systems - Pinch (1997) (7 citations) (Correct)
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J.M. Pollard, Theorems on factorization and primality testing, Proc. Cambridge Philos. Soc. 76 (1974), 521--528.
A New Special-Purpose Factorization Algorithm - Qi Che Ng (Correct)
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J.M. Pollard. Theorems on factorization and primality testing. Proc. Camb. Phil. Soc., 76(2):521--528, September 1974.
Data Security - CM 0321 - Jones (2004) (Correct)
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J. Pollard. Theorems of factorization and primality testing. Proc. Cambridge Philos. Soc., 76:521-528, 1974.
A New Public-Key Cryptosystem Based on Higher Residues - Naccache, Stern (1998) (23 citations) (Correct)
No context found.
J. Pollard, Theorems on factorization and primality testing, Proceedings of the Cambridge Philosophical Society, vol. 76, pp. 521-528, 1974.
Data Security - CM 0321 - Jones (2001) (Correct)
No context found.
J. Pollard. Theorems of factorization and primality testing. Proc. Cambridge Philos. Soc., 76:521-528,
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