ISO/IEC 10118-4:1998 PDF

Information technology — Security techniques — Hash-functions — Part 4: Hash-functions using modular arithmetic

First page of standard ISO/IEC 10118-4:1998

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Title (English):

ISO/IEC 10118-4:1998

Information technology — Security techniques — Hash-functions — Part 4: Hash-functions using modular arithmetic

Document status:: Active
Format:: Electronic (PDF)
Number of pages:: 23
Publication date:: December 20, 1998
Edition:: ISO/IEC IS 10118 edition 1 version 1
ICS:: 35.030

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Description (English):

This part of ISO/IEC 10118 specifies two hash-functions which make use of modular arithmetic. These hash-functions, which are believed to be collision-resistant, compress messages of arbitrary but limited length to a hash-code whose length is determined by the length of the prime number used in the reduction-function defined in 7.3. Thus, the hash-code is easily scaled to the input length of any mechanism (e.g., signature algorithm, identification scheme). The hash-functions specified in this part of ISO/IEC 10118, known as MASH-1 and MASH-2 (Modular Arithmetic Secure Hash) are particularly suitable for environments in which implementations of modular arithmetic of sufficient length are already available. The two hash-functions differ only in the exponent used in the round-function.

Technical details

Technical committee: ISO/IEC JTC 1/SC 27 - Information security, cybersecurity and privacy protection
SKU: ISO/IEC 10118-4:1998

Abstract

Overview

ISO/IEC 10118-4:1998 specifies two modular-arithmetic based hash-functions - MASH-1 and MASH-2 (Modular Arithmetic Secure Hash). These functions compress messages of arbitrary but limited length into a fixed-length hash-code. The output length is determined by the length of the prime p used in the standard’s reduction-function, allowing the hash size to be scaled to match the input requirements of other mechanisms (for example, signature algorithms or identification schemes). The algorithms are designed to be collision-resistant under standard number-theoretic assumptions.

Key topics and technical requirements

Modular arithmetic round-function: A round-function φ combines expanded data blocks with previous outputs using modular operations modulo a composite modulus N.
Two variants:
- MASH-1 uses exponent e = 2 in the round-function.
- MASH-2 uses exponent e = 257; otherwise the two differ only by exponent.
Reduction-function (RED): After iterative rounds, a reduction modulo a prime p produces the final hash-code of length determined by p.
Data preparation: The hashing procedure includes padding, appending the original length, splitting into half-blocks, and expansion (inserting fixed half-bytes), as specified in the standard.
Security constraints:
- The modulus N must be a composite integer (product of two primes) chosen so that factoring N is computationally infeasible.
- The factors of N should remain secret (trusted generation or secure multiparty methods).
- The reduction prime p must not divide N, its length is at most half the bit-length of N, and its top three bits should be ones to avoid unbalanced reductions.
Initialization: The initializing value IV is all-zero string of the block length Lφ.
Identifiers: Hash-function identifiers are defined (MASH-1 = 0x41, MASH-2 = 0x42).

Applications and who would use it

Cryptographers and security engineers who need hash-functions compatible with existing modular-arithmetic infrastructure (e.g., systems already supporting large-modulus arithmetic).
Implementers of digital signature schemes and identification protocols where the hash length must match modulus- or key-dependent input sizes.
Standards bodies and evaluators assessing alternative hash constructions based on number-theoretic assumptions.
Suited for environments where modular-root and factoring hardness are acceptable security bases and where efficient modular-arithmetic implementations are available.

Related standards

ISO/IEC 10118-1: General definitions and conventions for hash-functions.
Other parts of ISO/IEC 10118: Part 2 (block-cipher based) and Part 3 (dedicated hash-functions) for alternative hash-function families.

Keywords: ISO/IEC 10118-4:1998, hash-functions, modular arithmetic, MASH-1, MASH-2, collision-resistant, modulus N, prime p, reduction-function, round-function, hash-code.

Related standards

Mentioned in the description and other ISO standards

Abstract

Overview

Key topics and technical requirements

Modular arithmetic round-function: A round-function φ combines expanded data blocks with previous outputs using modular operations modulo a composite modulus N.
Two variants:
- MASH-1 uses exponent e = 2 in the round-function.
- MASH-2 uses exponent e = 257; otherwise the two differ only by exponent.
Reduction-function (RED): After iterative rounds, a reduction modulo a prime p produces the final hash-code of length determined by p.
Data preparation: The hashing procedure includes padding, appending the original length, splitting into half-blocks, and expansion (inserting fixed half-bytes), as specified in the standard.
Security constraints:
- The modulus N must be a composite integer (product of two primes) chosen so that factoring N is computationally infeasible.
- The factors of N should remain secret (trusted generation or secure multiparty methods).
- The reduction prime p must not divide N, its length is at most half the bit-length of N, and its top three bits should be ones to avoid unbalanced reductions.
Initialization: The initializing value IV is all-zero string of the block length Lφ.
Identifiers: Hash-function identifiers are defined (MASH-1 = 0x41, MASH-2 = 0x42).

Applications and who would use it

Cryptographers and security engineers who need hash-functions compatible with existing modular-arithmetic infrastructure (e.g., systems already supporting large-modulus arithmetic).
Implementers of digital signature schemes and identification protocols where the hash length must match modulus- or key-dependent input sizes.
Standards bodies and evaluators assessing alternative hash constructions based on number-theoretic assumptions.
Suited for environments where modular-root and factoring hardness are acceptable security bases and where efficient modular-arithmetic implementations are available.

Related standards

ISO/IEC 10118-1: General definitions and conventions for hash-functions.
Other parts of ISO/IEC 10118: Part 2 (block-cipher based) and Part 3 (dedicated hash-functions) for alternative hash-function families.

Keywords: ISO/IEC 10118-4:1998, hash-functions, modular arithmetic, MASH-1, MASH-2, collision-resistant, modulus N, prime p, reduction-function, round-function, hash-code.

ISO/IEC 10118-4:1998 PDF

Technical details

Abstract

Overview

Key topics and technical requirements

Applications and who would use it

Related standards

Related standards

Abstract

Overview

Key topics and technical requirements

Applications and who would use it

Related standards

Related standards

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