In the current state of the art in public key cryptography, all methods require, in one way or another, the use of prime numbers as parameters to the various algorithms. This document presents a set of accepted techniques for generating primes. It is intended that ASC X9 standards that require the use of primes will refer to this document, rather than trying to define these techniques on a case-by-case basis. Standards, as they exist today, may differ in the methods they use for parameter generation from those specified in this document. It is anticipated that as each existing ASC X9 standard comes up for its 5-year review, it will be modified to reference this document instead of specifying its own techniques for generating primes. This standard defines methods for generating large prime numbers as needed by public key cryptographic algorithms. It also provides testing methods for testing candidate primes presented by a third party. 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 with probability less than 2?00. - 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 presents primality certificates for some of the algorithms where it is feasible to do so. The syntax for such certificates is beyond the scope of this document. Primality certificates are never required by this standard. Primality certificates are not needed when a prime is generated and kept in a secure environment that is managed by the party that generated the prime.
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4.1 The term reference as employed in this practice implies that both the glass and the metal of the reference glass-metal seal will be a standard reference material such as those supplied for other physical tests by the National Institute of Standards and Technology, or a secondary reference material whose sealing characteristics have been determined by seals to a standard reference material (see NIST Special Publication 260).4 Until standard reference materials for seals are established by the NIST, secondary reference materials may be agreed upon between producer and user.51.1 This practice covers procedures for preparing and testing reference glass-to-metal bead-seals for determining the magnitude of thermal expansion (or contraction) mismatch between the glass and metal. Tests are in accordance with Test Method F218 (see Section 2).1.2 This practice applies to all glass-metal combinations, established or experimental, particularly those intended for electronic components.1.3 The practical limit of the test in devising mismatch is approximately 300 ppm, above which the glass is likely to fracture.1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.1.5 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
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In the current state of the art in public key cryptography, all methods require, in one way or another, the use of prime numbers as parameters to the various algorithms. This document presents a set of accepted techniques for generating primes. It is intended that ASC X9 standards that require the use of primes will refer to this document, rather than trying to define these techniques on a case-by-case basis. Standards, as they exist today, may differ in the methods they use for parameter generation from those specified in this document. It is anticipated that as each existing ASC X9 standard comes up for its 5-year review, it will be modified to reference this document instead of specifying its own techniques for generating primes. This standard defines methods for generating large prime numbers as needed by public key cryptographic algorithms. It also provides testing methods for testing candidate primes presented by a third party. 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 with probability less than 2?00.?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 presents primality certificates for some of the algorithms where it is feasible to do so. The syntax for such certificates is beyond the scope of this document. Primality certificates are never required by this standard. Primality certificates are not needed when a prime is generated and kept in a secure 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-random number generator is used to generate prime numbers, an ANSI approved random number (or bit) generator (i.e., one that is specified in an ANSI X9 standard) shall be used. This requirement is necessary to ensure security. NOTE鵗he 2-100 failure probability is selected to be sufficiently small that errors are extremely unlikely ever to occur in normal practice. Moreover, even if an error were to occur when one party tests a prime, subsequent tests by the same or other parties would detect the error with overwhelming probability. Furthermore, the 2-100 probability 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 a test is much lower. Accordingly, the 2-100 bound is considered appropriate independent of the size of the prime being generated and the intended security level of the cryptosystem in which the prime is to be employed. For high-assurance applications, however, the deterministic methods may nevertheless be preferable.
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