# 7.1 The environment for a composite modulus

The environmental clause adds modulus construction and factor custody to the usual domain parameter and trust conditions. The composite setting means the party who built the modulus may hold an advantage, so custody and the domain boundary have to be written down.

## What it asks

Evidence the domain parameters, the modulus construction, the factor custody and the verifier trust path. Show who is allowed to know the factors and what they could do with them, and record the domain boundary so that a claimant from one domain cannot be accepted in another.

## What the revision does

The fourth edition will restate these conditions. The public record stops before the new wording.

## Who it binds

The domain authority, the key management owner and the verifier operator.

## Evidence an auditor samples

- The domain parameter and modulus records (cryptography standard)
- The factor custody record and the permitted uses (key management)
- The domain boundary definition and its enforcement (architecture)

## The test you can run

Ask what the party holding the factors could do. If the answer is not written down, the trust model is implicit.

## Common failures

- The factors are held by the same team that operates the verifiers.
- The domain boundary exists in a document but not in configuration.

## How to close it

Write the trust model as a short paragraph with named roles. The composite setting is safe only when the party with the factors is bounded, and the boundary is the evidence.

## Source

ISO/IEC 9798-5:2009(E), 7.1, publisher preview; replaced by ISO/IEC DIS 9798-5, stage 40.20. Read on 21 October 2026. Our wording, not the instrument's.
https://www.iso.org/standard/89516.html

Not legal advice; does not certify.