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TinyCrypto.jl – Exploring Cryptography in Small Prime Fields

Project Goal TinyCrypto is an educational Julia package that implements foundational cryptographic primitives over tiny prime fields (𝔽ₚ) to make cryptography transparent, auditable, and fun. It’s designed for researchers, teachers, and curious developers who want to explore cryptographic ideas without the distraction of big-number arithmetic or opaque black boxes.

Why TinyCrypto? Cryptographic libraries are often hard to follow, optimized for performance or security. TinyCrypto flips that on its head—emphasizing readability, symbolic clarity, and small, verifiable parameters. It’s a sandbox for learning ECC, field arithmetic, and key management interactively, using simple types and Unicode-rich output.

Features

  • Finite Field Arithmetic Type-safe modular arithmetic via Fp{T,P}, supporting +, -, *, /, ^, inv, with automatic reduction modulo P.

  • Elliptic Curves Supports multiple curve forms: – Weierstrass: y² = x³ + ax + b – Montgomery: By² = x³ + Ax² + x – Edwards & Twisted Edwards: ax² + y² = 1 + dx²y² Includes point addition, doubling, identity detection, and scalar multiplication.

  • ECDSA & Signatures Full keypair generation, message signing, signature verification, and public key recovery (ecrecover).

  • Secret Sharing (in progress) Implements Shamir’s Secret Sharing for secure split/reconstruction of secrets with (k, n) threshold.

  • Symbolic Output Pretty-printed Unicode math: 𝔽ₚ for field primes, 𝔾(x,y) for group generators, ∞ for identity points.

  • Written in Julia Lightweight, high-performance, and idiomatic Julia package with modular structure and type safety throughout.

  • Teaching Focus Operates over small fields (e.g. 𝔽₃₁, 𝔽₉₇), enabling full manual verification and didactic experimentation.

Example Workflows

using TinyCrypto

curve = Edwards(50:100, 1:20, max_cofactor=8)
𝔾 = curve.G                # Generator of the group G
2𝔾 == 𝔾 + 𝔾               # true

priv, pub = genkey(curve) # Generate ECDSA keypair
sig = sign(curve, priv, "hello")
verify(curve, pub, sig, "hello")     # true
pub == ecrecover(curve, "hello", sig) # true

You can generate curves with:

Weierstrass(97:103, 10:15, 2:7)      # y² = x³ + ax + b
Montgomery(30:40, 8:40, 3:40)
TwistedEdwards(50:100, 1:20, 1:20)

And work symbolically with:

const 𝔽₃₁ = Fp{UInt8, 31}
Weierstrass{𝔽₃₁}(6, 9, 37, 1, (0,3))

Learn More and Contribute GitHub: github.com/vargaconsulting/tiny-crypto Docs: vargaconsulting.github.io/tiny-crypto License: MIT