# Clause 7 Discrete logarithms over a composite modulus

This family moves the discrete logarithm problem to a composite modulus, which changes both the arithmetic and the trust model. It keeps the coupon strategy for the claimant and adds a second mode with its own key size, so the parameter record has to say which mode a deployment uses.

## What it asks

Record the mode, the modulus construction, the base and the private key size for each deployment, and show that the mode in the design matches the mode in the configuration. Test the transition between modes if both are supported, because a mixed configuration is the usual source of a silent downgrade.

## What the revision does

The fourth edition keeps the family and will restate it. No public copy of the revised text exists.

## Who it binds

The cryptography owner and the configuration manager.

## Evidence an auditor samples

- The mode and parameter record per deployment (configuration management database)
- The modulus and base generation record (key management)
- The test that a mixed mode configuration is rejected (test suite)

## The test you can run

Read the design note and the running configuration. If they name different modes, the deployment is unowned.

## Common failures

- The mode is a runtime flag with no recorded default.
- A fallback to the weaker mode happens silently on a parameter error.

## How to close it

Make the mode explicit in configuration and remove the silent fallback. A downgrade path that nobody chose is the one an attacker will use, and it takes one test to prove it is gone.

## Source

ISO/IEC 9798-5:2009(E), Clause 7, 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.