# 6.3 The short exchange in a prime order group

The exchange is a commitment, a challenge and a response checked against the public value. Its security depends on the challenge being fresh and on the verifier recomputing the relation rather than comparing a value the claimant supplied.

## What it asks

Record the exchange and the freshness source, and show the verifier recomputation step in the test. Test a replayed challenge, a response outside the group and a wrong public value, and keep the outputs with the release record.

## What the revision does

The fourth edition will restate the exchange. The revised sequence is not in the public record.

## Who it binds

The implementer and the tester who signs off the verifier.

## Evidence an auditor samples

- The exchange sequence and the freshness source (interface specification)
- The verifier recomputation step, with a code pointer (source repository)
- The three negative tests and their outputs (test report)

## The test you can run

Replace the verifier recomputation with a constant and run the positive test. If it still passes, the test is not testing the verifier.

## Common failures

- The verifier compares a claimant supplied hash instead of recomputing.
- The challenge is reused within a session with no window.

## How to close it

Mutate the verifier and confirm the tests fail. A test suite that passes when the check is removed is a demonstration of the test, not of the mechanism.

## Source

ISO/IEC 9798-5:2009(E), 6.3, 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.