Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add hamzabellouch/agent-skills --skill number-theory-and-cryptographygit clone --depth 1 https://github.com/hamzabellouch/agent-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/hamzabellouch/agent-skills/number-theory-and-cryptography)<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/number-theory-and-cryptography"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/number-theory-and-cryptography/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/number-theory-and-cryptography"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/number-theory-and-cryptography.svg" alt="Reviewed on agentmods" width="80" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00077 | $0.00704 |
| Opus 5.5 | $0.00031 | $0.00282 |
| Sonnet 5.5 | $0.00015 | $0.00141 |
| Haiku 4.5 | $0.00008 | $0.00070 |
Grade A, and why
number-theory-and-cryptography scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured today.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 29 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Number Theory & Cryptography
Basics
- Fundamental theorem of arithmetic; gcd via Euclid; Bezout ax + by = gcd (extended Euclid); lcm = ab/gcd.
- Modular arithmetic: a == b (mod n); inverse of a mod n exists iff gcd(a,n) = 1; solve ax == b via inverse.
- Chinese Remainder Theorem for pairwise coprime moduli.
- Fermat: a^(p-1) == 1 (mod p) for p prime, p not dividing a. Euler: a^phi(n) == 1 for gcd(a,n) = 1; phi(n) = n prod (1 - 1/p). Wilson: (p-1)! == -1 (mod p).
- Multiplicative functions: tau, sigma, mu, phi; Moebius inversion; Dirichlet convolution.
- Order of an element, primitive roots (exist mod 1, 2, 4, p^k, 2p^k).
- Quadratic residues: Legendre symbol, Euler's criterion, quadratic reciprocity, Jacobi symbol; sums of two squares (p == 1 mod 4), Lagrange four squares.
- Diophantine: linear ax + by = c solvable iff gcd | c; Pythagorean triples (m^2 - n^2, 2mn, m^2 + n^2); Pell x^2 - Dy^2 = 1 via continued fractions; Fermat's Last Theorem (Wiles); infinite descent; lifting-the-exponent lemma; Zsigmondy.
- Valuations: v_p(n!) = sum floor(n/p^k) (Legendre).
Primes
- Sieve of Eratosthenes; primality tests: Miller-Rabin (probabilistic), AKS (deterministic polynomial); prime number theorem pi(x) ~ x/ln x; Dirichlet's theorem on primes in progressions; twin prime, Goldbach, Riemann hypothesis as open problems.
Cryptography
- RSA: n = pq, e coprime to phi(n), d = e^{-1} mod phi(n); encrypt c = m^e mod n, decrypt m = c^d mod n. Security rests on factoring hardness; use OAEP padding and 2048+ bit keys in practice.
- Diffie-Hellman key exchange, discrete log problem; ElGamal; elliptic curves y^2 = x^3 + ax + b over F_p (group law), ECDH/ECDSA; post-quantum lattice-based (Kyber, Dilithium) as Shor-resistant alternatives; hash functions and signatures.
- Never implement your own crypto in production; use vetted libraries.
Script
scripts/number_theory.py: egcd, modular inverse, CRT, Miller-Rabin, factorization (Pollard rho), phi, primitive root, RSA toy demo.
What ships with it
2 files beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- today First seen · 29 lines · 77 tokens per session scan A 549702544a72
number-theory-and-cryptography is a skill published in the GitHub repository hamzabellouch/agent-skills (8 stars, last pushed today), licensed MIT. It adds 77 tokens to every session and 704 once invoked, about $0.0003 per session on Opus 5.5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-10-17.
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