Engineering / Mathematics — Computation and Sources
Parameter Sizes, Records and Live References
Where to obtain current key size recommendations, factoring records and post-quantum guidance, and why they are not reproduced here.
Executive summary
Key size recommendations, computational records and migration timelines all change, and a static page carrying them becomes misleading rather than merely stale.
This page records the durable method for deriving a recommendation and routes to maintained sources for the figures.
Learning objectives
- Understand how key size recommendations are derived.
- Identify the categories of authoritative source.
- Recognise which facts are durable and which are not.
01The sourcing policy
The same policy applies across the KEVOS mathematics collections. The durable layer — definitions, algorithms, complexity results and the reasoning by which parameters are chosen — is authored here. Numeric data with a shelf life is routed to maintained sources.
| Durable | Not durable |
|---|---|
| Why NFS has L(1/3) complexity | The current factoring record |
| How a key size follows from a record | The recommended key size |
| Why quantum computers break RSA | The migration deadline |
| What a security level means | Which algorithms meet it today |
02How a recommendation is derived
Take a completed record
A published factorisation or discrete logarithm computation with its effort accounting in core-years.
Extrapolate by the complexity formula
The L(1/3) expression predicts effort at other parameter sizes.
Project hardware improvement
Allow for cost per operation falling over the intended protection period.
Add a margin for algorithmic risk
Allow for improvements to the algorithms themselves, which cannot be predicted.
Publish a minimum size
Standards bodies convert the result into recommendations by protection period.
The extrapolation also assumes no algorithmic breakthrough. A materially better factoring algorithm would invalidate every recommendation simultaneously.
03Categories of source
Standards bodies
National and international organisations publish key length recommendations by protection period, revised periodically.
Comparison services
Maintained sites aggregating the recommendations of different bodies side by side, which makes the spread of expert opinion visible.
Record announcements
Published by the teams performing the computations, with full effort accounting — the primary data for extrapolation.
Post-quantum guidance
Migration timelines and algorithm selections, published separately and currently moving faster than classical guidance.
For any specific decision, consult a current source at the time of the decision. The reasoning on this page tells you what to look for and how to interpret it; it deliberately does not tell you the answer, because the answer changes.
04Frequently asked questions
Why not include figures with a review date?
Because pages are read long after they are written and the review date is easily missed. Routing to a maintained source is more reliable than dating a static figure, and it fails safe.
Does the Riemann hypothesis affect key sizes?
No. It concerns the distribution of primes, not the difficulty of factoring. A proof would sharpen various estimates and settle conditional theorems, and would supply no factoring algorithm.
How urgent is post-quantum migration?
Urgent for data requiring long-term confidentiality, because encrypted traffic captured now could be decrypted once a sufficiently large quantum computer exists. Current guidance from standards bodies is the appropriate source for timelines.
Sources and method
Structural reference: Victor Shoup, A Computational Introduction to Number Theory and Algebra, Version 1, Cambridge University Press, 2005 — orientation page, no single source section.
This page carries the durable method layer only: definitions, constructions, algorithms, complexity results and selection criteria, authored originally for KEVOS. No text is transcribed or paraphrased from the source, and no numeric tables or benchmark data are reproduced — these are routed to live authoritative sources instead.
Forward reference: this page extends beyond the source text and is flagged as post-source.
Author: Kevin Jogin. Last reviewed 2026-08-07.