ANSI X9.80-2020 pdf free download – Prime Number Generation, Primality Testing, and Primality Certificates.
ln the current state of the art in public key cryptography, all methods require, in one way or another, the use of primenumbers as parameters to the various algorithms. This document presents a set of accepted techniques forgenerating prime numbers, often referred to as simply “primes”.
lt is intended that ASC X9 standards that require the use of primes will refer to this document rather than trying todefine these techniques on a case-by-case basis.Standards, as they exist today, may differ in the methods theyuse for parameter generation from those specified in this document. lt is anticipated that each existing ASC X9standard will be modified to reference this document during its 5-year review instead of specifying its own techniquesfor generating primes.
This Standard defines methods for generating large prime numbers as needed by public key cryptographicalgorithms. It also provides testing methods for iesting candidate primes presented by a third party. Furthermore,the use of prime generation schemes described in the Digital Signature Standard (DSS), FIPS 186-4 (or laterversions) are permitted by this Standard.
This Standard allows primes to be generated either deterministically or probabilistically, where:
– A number shall be accepted as prime when a probabilistic algorithm that declares it to be prime is in error withprobability less than 2-100 , i
-A deterministic prime shall be generated using a method that guarantees that it is prime.
In addition to algorithms for generating primes, this Standard also provides methods for primality certificates whereit is feasible to do so. The syntax for such certificates is beyond the scope of this document. Primality certificatesare never required by this Standard.Primality certificates are not needed when a prime is generated and kept in asecure environment that is managed by the party that generated the prime.
A requirement placed upon the use of this Standard, but out of scope, is as follows:
When a random or pseudo-andom number generator is used to generate prime numbers,an ASC X9-approved random number (or bit) generator (e.g., ane that is specified in an ASC X9 standard) shall be used.This requirement is necessary to ensure security.
NOTEThe 2-10 failure probability is selectad to be sufficiently small that errors are extremely unlikely ever tooccur in normal practice.Moreover, even if an error were to occur when one party tests a prime, subsequent testsby the same or other parties would detect the error with overwhelming probability.Furthermore, the 2-100probability is an upper bound on the worst-case probability that a test declares any non-prime candidate to be prime;not all non-primes may reach this bound, and the probability that a non-prime generated at random passes such atest is much lower. Accordingly, the 2-100 bound is considered appropriate independent of the size of the primebeing generated and the intended security strength of the cryptosystem in which the prime is to be employed. Forhigh-assurance applications, however, the deterministic methods may nevertheless be preferable.
2 Normative References The following referenced documents are indispensable for the application of this Standard. For dated references, only the edition cited applies. Nevertheless, parties to agreements based on this Standard are encouraged to consider applying the most recent edition of the referenced documents indicated below. For undated references, the latest edition of the referenced document (including any amendments) applies. ANSI X9.82: Part 3-2007, Financial Services Industry – Random Number Generation Part 3: Deterministic Random Bit Generators.ANSI X9.80 pdf download.