# Clause 3 Notation, symbols and the clause-number trap

The notation clause fixes the symbols for moduli, exponents, witnesses, challenges and responses, and it adds a separate symbol set for each mechanism family. It is the clause that makes a formula portable, and the one where a copied symbol most often hides a different meaning.

## What it asks

Use the clause symbols in every formula you publish or test against, and record which edition the symbols come from. Where a symbol is reused across families with a different meaning, qualify it in the design note so that a reader cannot carry the wrong definition across.

## What the revision does

The fourth edition will restate the symbol sets against the revised clauses. The revised tables are not public.

## Who it binds

The engineer who writes the formula and the test author who turns it into a vector.

## Evidence an auditor samples

- The symbol table used by the design, with its edition (design note)
- The test vectors, with the symbol names the table defines (test suite)
- The review that checked symbols against the edition (review log)

## The test you can run

Take one formula from the design note and one test vector. If the same symbol means a different object in the two, the notation has drifted.

## Common failures

- A symbol is copied from a paper that uses the same letter for a different value.
- The test vector names a symbol the design note never defines.

## How to close it

Version the symbol table with the edition and make the test vectors cite it. A formula without an edition is a formula nobody can reproduce, which is exactly what an assessor will ask you to do.

## Source

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