Arjen K. Lenstra and Eric R. Verheul, The XTR Public Key System. Lecture Notes in Computer Science, Volume 1880, 2000 Home/Search Document Not in Database Summary Related Articles Check |
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Three New Factors Of Fermat Numbers - Brent, Crandall, Dilcher, Van.. (1999) (1 citation) (Correct)
....factor has been found by ECM. Factors of larger numbers are customarily found by trial division [16, 18] 2. The Elliptic Curve Method ECM was invented by H. W. Lenstra, Jr. 23] Various practical refinements were suggested by Brent [1] Montgomery [24, 25] and Suyama [32] We refer to [3, 14, 22, 26, 31] for a description of ECM and some of its implementations. In the following, we assume that ECM is used to find a prime factor p 3 of a composite number N , not a prime power [21, x2.5] The first phase limit for ECM is denoted by B 1 . 1991 Mathematics Subject Classification. 11Y05, 11B83, ....
A. K. Lenstra and M. S. Manasse, Factoring by electronic mail, Proc. Eurocrypt '89, Lecture Notes in Computer Science 434, Springer-Verlag, Berlin, 1990, 355--371.
The GH Public-key Cryptosystem - Gong, Harn, Wu (2001) (Correct)
....p 2 . This algorithm is more ecient than the previously proposed one [5] In Section 4, we will introduce the Duality Law of a pair of reciprocal characteristic sequences. Using this law, we show the property of redundancy in states of characteristic sequences over GF (q) Lenstra and Verheul in [8] have also found this type of redundancy for a special case of characteristic sequences over GF (p 2 ) However the technique used in [8] can not be extended to the general case of the characteristic sequences over either GF (p 2 ) or GF (q) for any arbitrary q. In Section 5, using the linear ....
....characteristic sequences. Using this law, we show the property of redundancy in states of characteristic sequences over GF (q) Lenstra and Verheul in [8] have also found this type of redundancy for a special case of characteristic sequences over GF (p 2 ) However the technique used in [8] can not be extended to the general case of the characteristic sequences over either GF (p 2 ) or GF (q) for any arbitrary q. In Section 5, using the linear feedback shift register concept, we will propose an ecient algorithm to compute the (h dk)th term of a characteristic sequence based on the ....
[Article contains additional citation context not shown here]
A. K. Lenstra and E. R. Verheul, \Key improvements to XTR", the Proceedings of Asiacrypt'2000, Lecture Notes in Computer Science, vol. 1976, 2000.
On Short Representations of Orders and Number Fields - Buchmann, van Sprang (1992) (2 citations) (Correct)
....suppose that we know ae i for some i 2 f1; n Gamma 1g. If deg ae i = n then set ae i 1 = ae i . If deg ae i n then we need to construct ae i 1 as a primitive element of Q(ae i ; i 1 ) over Q. We determine the minimal polynomial of i 1 , and factor it over Q(ae i ) By the result of [7] this can be done in polynomial time. This determines the degree d = Q(ae i ; i 1 ) Q(ae i ) If d = 1 then we set ae i 1 = ae i . Now suppose that d 1. For t 2 f1; 2; n 2 g we form the minimal polynomials of ae i t i 1 , until we find an element of degree d Delta deg ae i ....
A.K. Lenstra Factoring polynomials over algebraic number fields, Lecture Notes in Computer Science 162, Proc. EUROCAL '83 pp. 245, London 1983
Factorization of the Tenth Fermat Number - Brent (1998) (1 citation) (Correct)
.... overcome by the invention of the (special) number field sieve (SNFS) based on a new idea of Pollard [43, 61] In 1990, Lenstra, Lenstra, Manasse and Pollard, with the assistance of many collaborators and approximately 700 workstations scattered around the world, completely factored F 9 by SNFS [44, 45]. The factorization is F 9 = 2424833 Delta 7455602825647884208337395736200454918783366342657 Delta p 99 : In x8 we show that it would have been possible (though more expensive) to complete the factorization of F 9 by ECM. F 10 was the most wanted number in various lists of composite numbers ....
....AP1000, and the ACSys Cooperative Research Centre provided access to eight DEC alphas. 4 R. P. BRENT 2. Variants of ECM The elliptic curve method (ECM) was discovered by H. W. Lenstra, Jr. 46] in 1985. Practical refinements were suggested by various authors [8, 23, 50, 51, 72] We refer to [45, 52, 62, 71] for a general description of ECM, and to [24, 69] for relevant background. Suppose we attempt to find a factor of a composite number N , which we can assume not to be a perfect power [2] 44, x2.5] Let p be the smallest prime factor of N . In practice it is desirable to remove small factors (up ....
[Article contains additional citation context not shown here]
A. K. Lenstra and M. S. Manasse, Factoring by electronic mail, Proc. Eurocrypt '89, Lecture Notes in Computer Science 434, Springer-Verlag, Berlin, 1990, 355--371. MR 91i:11182
Two New Factors of Fermat Numbers - Brent, Crandall, Dilcher (1997) (Correct)
....factor has been found by ECM. Factors of larger numbers are customarily found by trial division [16, 18] 2. The Elliptic Curve Method ECM was invented by H. W. Lenstra, Jr. 22] Various practical refinements were suggested by Brent [1] Montgomery [23, 24] and Suyama [31] We refer to [3, 14, 21, 25, 30] for a description of ECM and some of its implementations. In the following, we assume that ECM is used to find a prime factor p 3 of a composite number N , not a prime power [20, x2.5] The first phase limit for ECM is denoted by B 1 . Although p is unknown, it is convenient to describe ECM in ....
A. K. Lenstra and M. S. Manasse, Factoring by electronic mail, Proc. Eurocrypt '89, Lecture Notes in Computer Science 434, Springer-Verlag, Berlin, 1990, 355--371.
On Short Representations of Orders and Number Fields - Buchmann, van Sprang (1992) (2 citations) Self-citation (Fields) (Correct)
No context found.
A.K. Lenstra Factoring polynomials over algebraic number fields, Lecture Notes in Computer Science 162, Proc. EUROCAL '83 pp. 245, London 1983
Evaluation of real-time aspects of multiparty Security.. - Limmer, Dressler.. (2006) (Correct)
No context found.
Arjen K. Lenstra and Eric R. Verheul, The XTR Public Key System. Lecture Notes in Computer Science, Volume 1880, 2000
Factorization of the Tenth and Eleventh Fermat Numbers - Brent (1996) (2 citations) (Correct)
No context found.
A. K. Lenstra and M. S. Manasse, Factoring by electronic mail, Proc. Eurocrypt '89, Lecture Notes in Computer Science 434, Springer-Verlag, Berlin, 1990, 355--371.
Factorization of the Tenth Fermat Number - Brent (1999) (1 citation) (Correct)
No context found.
A. K. Lenstra and M. S. Manasse, Factoring by electronic mail, Proc. Eurocrypt '89, Lecture Notes in Computer Science 434, Springer-Verlag, Berlin, 1990, 355--371. MR 91i:11182
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