标准编号：ISO/IEC 18032:2020
中文名称：信息安全 素数生成
英文名称：Information security — Prime number generation
发布日期：2020-12
标准范围
This document specifies methods for generating and testing prime numbers as required in
cryptographic protocols and algorithms.
Firstly, this document specifies methods for testing whether a given number is prime. The testing
methods included in this document are divided into two groups:
— probabilistic primality tests, which have a small error probability. All probabilistic tests described
here can declare a composite to be a prime;
— deterministic methods, which are guaranteed to give the right verdict. These methods use so-called
primality certificates.
Secondly, this document specifies methods to generate prime numbers. Again, both probabilistic and
deterministic methods are presented.
NOTE It is possible that readers with a background in algorithm theory have already had previous encounters
with probabilistic and deterministic algorithms. The deterministic methods in this document internally still
make use of random bits (to be generated via methods described in ISO/IEC 18031), and “deterministic” only
refers to the fact that the output is correct with probability one.
Annex A provides error probabilities that are utilized by the Miller-Rabin primality test.
Annex B describes variants of the methods for generating primes so that particular cryptographic
requirements can be met.
Annex C defines primitives utilized by the prime generation and verification methods.
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