A React + TypeScript toolkit of calculators for modular number theory and common cryptography tasks. Made for convenience and for reinforcing concepts from a Master’s cryptography course.

https://zamilbahri.github.io/mod-calculator-suite

1. RSA Calculator

   • Supports RSA encryption/decryption with configurable key inputs and key derivation tools.
   • Implemented encoding modes:
     • Direct Integer
     • Fixed-width numeric slicing
     • Radix (b-adic) packing
     • PKCS#1 v1.5 padding
   • Includes a Recover primes decryption option for moduli where N < 2^72.
     • Prime recovery is multithreaded and uses up to two web workers.
     • Before worker scans begin, divisibility is prechecked for small prime factors up to and including 997.
     • For an n-bit RSA modulus N, the worker ranges are split as:
       • balanced: from max(nextPrimeAfterPrecheck, 2^(floor(n/2)-1)) (inclusive) to floor(sqrt(N)) + 1 (exclusive), where nextPrimeAfterPrecheck is currently 1009.
       • low: from nextPrimeAfterPrecheck (inclusive) to max(nextPrimeAfterPrecheck, 2^(floor(n/2)-1)) (exclusive).

2. Prime Generator

   • Generates probable primes by bit size or digit size.
   • Supports generation of up to 10 primes, with count limits by size policy:

   Max Prime Size (bits)	Max Count	Warning Starts At
   1536	10	11 (No warning)
   2048	10	5
   3072	4	2
   4096	4	1

   • Prime generation is multithreaded, and the user can set the number of worker threads.

3. Prime Checker

   • Uses Baillie-PSW and Miller-Rabin primality testing.
   • For n < 2^64, Baillie-PSW is used.
   • For larger values, Miller-Rabin is used with a default of 24 rounds.
   • The user can configure the number of Miller-Rabin rounds.

1. EGCD and Modular Inverse Calculator

   • Computes gcd(a, b), Bézout coefficients, and modular inverses.

2. Fast Exponentiation

   • Computes a^n mod m using square-and-multiply.

3. CRT Solver

   • Solves systems of congruences with pairwise coprime moduli.

1. Matrix Modular Determinant, RREF, and Inverse Calculator

   • Normalizes a matrix A mod m, and computes det(A) mod m, RREF(A) mod m, and A^-1 mod m.

2. Matrix Multiplcation Caluclator

   • Calculates the product of two matrices A x B mod m.

1. Polynomial Arithmetic over GF(2)

   • Supports addition, multiplication, division, and remainder for polynomials in $GF(2)$.

2. Polynomial GCD over GF(2)

   • Computes the Greatest Common Divisor (GCD) using the Euclidean algorithm.

3. Polynomial Inverse over GF(2)

   • Computes modular inverses using the Extended Euclidean Algorithm (EEA) with steps.

• Node.js 20+
• npm

npm install

npm run dev

npm run build

This project is licensed under the MIT License - see the LICENSE file for details.