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Recently, there has been considerable debate concerning key sizes for publ i c key based cry p t o graphic methods. Included in the debate have been considerations about equivalent key sizes for diffe rent methods and considerations about the minimum re q u i red key size for diffe rent methods. In this paper we propose a method of a n a lyzing key sizes… (More)

- Kevin T. Rowney, Robert D. Silverman
- ACM SIGSAM Bulletin
- 1989

We present the implementation of an extensive system of routines, in Macsyma, which allows finite field arithmetic and manipulation of symbolic objects in finite fields,

A number of cryptographic standards currently under development call for the use of strong primes in the generation of an RSA key. This paper suggests a fast way of generating random strong primes that also satisfy a number of other cryptographic requirements. The method requires no more time to generate strong primes than it takes to generate random primes.

- Robert D. Silverman, Sidney J. Stuart
- Softw., Pract. Exper.
- 1989

- Robert D. Silverman
- IEEE Computer
- 1999

A modification, due to Peter Montgomery, of Pomerance's Quadratic Sieve for factoring large integers is discussed along with its implementation. Using it, allows factorization with over an order of magnitude less sieving than the basic algorithm. It enables one to factor numbers in the 60-digit range in about a day, using a large minicomputer. The algorithm… (More)

- Thomas R. Caron, Robert D. Silverman
- The Journal of Supercomputing
- 1988

A new version of the Quadratic Sieve algorithm, used for factoring large integers, has recently emerged. The new algorithm, called the Multiple Polynomial Quadratic Sieve, not only considerably improves the original Quadratic Sieve but also adds features that ideally suit a parallel implementation. The parallel implementation used for the new algorithm, a… (More)

Much asymptotic analysis has been devoted to factoring algorithms. We present a practical analysis of the complexity of the elliptic curve algorithm, suggesting optimal parameter selection and run-time guidelines. The parameter selection is aided by a novel use of Bayesian statistical decision techniques as applied to random algorithms. We discuss how… (More)

- Robert D. Silverman
- Commun. ACM
- 1991

Over the last 15 years the increased availability of computers and the introduction of the RSA cryptosystem has led to a number of new and remarkable algorithms for finding the prime factors of large integers. Factoring numbers is an arithmetic problem so simple to understand that school children are asked to do it. While multiplying or adding two very… (More)

A weakness has been found in the ISO 9796 signature standard using RSA. The padding method proposed by the standard is the origin of the problem and will require probable changes in ISO 9796 parts 1 and 2. This weakness was discovered by Gemplus’ cryptography division and the ENS and UCL cryptography groups while implementing the standard. A paper reporting… (More)