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Some Primality Testing Algorithms
 Notices of the AMS
, 1993
"... We describe the primality testing algorithms in use in some popular computer algebra systems, and give some examples where they break down in practice. 1 Introduction In recent years, fast primality testing algorithms have been a popular subject of research and some of the modern methods are now i ..."
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We describe the primality testing algorithms in use in some popular computer algebra systems, and give some examples where they break down in practice. 1 Introduction In recent years, fast primality testing algorithms have been a popular subject of research and some of the modern methods are now incorporated in computer algebra systems (CAS) as standard. In this review I give some details of the implementations of these algorithms and a number of examples where the algorithms prove inadequate. The algebra systems reviewed are Mathematica, Maple V, Axiom and Pari/GP. The versions we were able to use were Mathematica 2.1 for Sparc, copyright dates 19881992; Maple V Release 2, copyright dates 19811993; Axiom Release 1.2 (version of February 18, 1993); Pari/GP 1.37.3 (Sparc version, dated November 23, 1992). The tests were performed on Sparc workstations. Primality testing is a large and growing area of research. For further reading and comprehensive bibliographies, the interested re...
James Nechvatal Security Technology Group PUBLICKEY CRYPTOGRAPHY
, 1991
"... This publication presents a stateoftheart survey of publickey cryptography circa 1988 1990. In doing so, it covers a number of different topics including: 1. The theory of publickey cryptography. 2. Comparisons to conventional (secretkey) cryptography. 3. A largely selfcontained summary of r ..."
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This publication presents a stateoftheart survey of publickey cryptography circa 1988 1990. In doing so, it covers a number of different topics including: 1. The theory of publickey cryptography. 2. Comparisons to conventional (secretkey) cryptography. 3. A largely selfcontained summary of relevant mathematics. 4. A survey of major existing publickey systems. 5. An exploration of digital signatures and hash functions. 6. A survey of publickey implementations in networks. 7. An introduction to zeroknowledge protocols and probabilistic encryption. 8. An exploration of security issues and key sizes. The treatment of publickey cryptography in this publication includes both theory and practice. Much of the existing published work, including those documents listed in the references, treats