Algorithms for Generating, Testing and Proving Primes: A Survey
Identifieur interne : 000216 ( Main/Exploration ); précédent : 000215; suivant : 000217Algorithms for Generating, Testing and Proving Primes: A Survey
Auteurs : Preda Mih Ilescu [Suisse]Source :
- Progress in Computer Science and Applied Logic ; 2001.
Abstract
Abstract: We survey methods of testing and proving primality and their implementation for generation of cryptographic primes. While discussing a wider variety of primality tests of theoretical or practical relevance, the focus is on criteria for practical use. We give a new model for sources producing prime numbers with biased distributions and use it for measuring the security of biases against unknown attacks (adapted solutions to the discrete logarithm or integer factoring problems) which could make use of knowledge of the bias. Some results can be proved based solely upon the bias distribution, without prior knowledge of the attacks. Thus an important class of sources with polynomially bounded bias are secure in the sense that algorithms which can use the bias with a performance gain, can be turned into improvements to state of the art attacks in presence of uniform distributed sources. The paper concludes with an overview of some outstanding schemes for generation of cryptographic primes. These are compared according to their performance and confidence of decision.
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DOI: 10.1007/978-3-0348-8295-8_10
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