Information security - Prime number generation

This document specifies mechanisms to establish shared symmetric keys between groups of entities. It defines:

— symmetric key-based key establishment mechanisms for multiple entities with a key distribution centre (KDC); and
— symmetric key establishment mechanisms based on a general tree-based logical key structure with both individual rekeying and batch rekeying.

It also defines key establishment mechanisms based on a key chain with group forward secrecy, group backward secrecy or both group forward and backward secrecy.

This document also describes the required content of messages which carry keying material or are necessary to set up the conditions under which the keying material can be established.

This document does not specify information that has no relation with key establishment mechanisms, nor does it specify other messages such as error messages. The explicit format of messages is not within the scope of this document.

This document does not specify the means to be used to establish the initial secret keys required to be shared between each entity and the KDC, nor key lifecycle management. This document also does not explicitly address the issue of interdomain key management.

ISO/IEC 18032:2020(E)

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.