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Abstract: Recently, and contrary to the common belief, Rivest and Silverman argued that the use of strong primes is unnecessary in the RSA cryptosystem. This paper analyzes how valid this assertion is for RSA and its extensions to elliptic curves. Over elliptic curves, the analysis is more di#cult because the underlying groups are not always cyclic. (Update)
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BibTeX entry: (Update)
Marc Joye, Jean-Jacques Quisquater, and Tsuyoshi Takagi. How to choose secret parameters for RSA and its extensions to elliptic curves. Designs, Codes and Cryptography, 23(3):297-316, 2001. http://citeseer.ist.psu.edu/article/joye01how.html More
@article{ joye01how,
author = "Marc Joye and Jean-Jacques Quisquater and Tsuyoshi Takagi",
title = "How to Choose Secret Parameters for {RSA}-Type Cryptosystems over Elliptic Curves",
journal = "Designs, Codes and Cryptography",
volume = "23",
number = "3",
pages = "297-316",
year = "2001",
url = "citeseer.ist.psu.edu/article/joye01how.html" }
Citations (may not include all citations):1529 A method for obtaining digital signatures and public-key cry.. - Rivest, Shamir et al. - 1978
1065 Handbook of applied cryptography (context) - Menezes, van Oorschot et al. - 1997
257 Elliptic curve cryptosystems (context) - Koblitz - 1987
237 The Arithmetic of Elliptic Curves (context) - Silverman - 1986
228 Use of elliptic curves in cryptography (context) - Miller
170 Elliptic curve public key cryptosystems (context) - Menezes - 1993
134 Factoring integers with elliptic curves (context) - Lenstra - 1987
68 Prime Numbers and Computer Methods for Factorization (context) - Riesel - 1994
54 New public-key schemes based on elliptic curves over the rin.. - Koyama, Maurer et al. - 1992
47 Protocol failures in cryptosystems (context) - Moore - 1992
40 A new elliptic curve based analogue of RSA (context) - Demytko - 1994
27 Analysis of a simple factorization algorithm (context) - Knuth, Trabb-Pardo - 1976
24 Fast generation of prime numbers and secure public-key crypt.. - Maurer - 1995
18 Remarks on a proposed cryptanalytic attack on the M (context) - Rivest - 1978
16 method of factoring (context) - Williams - 1982
16 public-key cryptosystem (context) - Simmons, Norris et al. - 1977
15 Strong primes are easy to find (context) - Gordon - 1985
14 Factoring via superencryption (context) - Berkovits - 1982
14 Strong RSA keys (context) - Gordon - 1984
13 Critical remarks on some public-key cryptosystems (context) - Herlestam - 1978
12 Rivest-Shamir-Adleman public key cryptosystems do not always.. (context) - Blakey, Borosh - 1979
11 Fast generation of secure RSA-moduli with almost maximal div.. (context) - Maurer - 1990
10 Fast generation of random (context) - Silverman - 1997
8 Are 'strong' primes needed for RSA (context) - Rivest, Silverman - 1997
8 The RSA public-key cryptosystem (context) - for - 1989
7 Security of number theoretic cryptosystems against random at.. (context) - Blakley, Blakley - 1979
7 On using Carmichael numbers for public-key encryption system.. - Pinch - 1997
5 Critical remarks on some public-key cryptosystems (context) - Rivest, on - 1979
4 cient cryptosystems over elliptic curves based on a product .. (context) - Kuwakado, Koyama - 1994
1 Appendix A Lemma 2 Let G p = Z p Z p (context) - Williams, Schmid et al. - 1979
http://www.informatik.tu-darmadt.de/TI/LiDIA
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