Haskell RSA

Posted on 11 October 2023.

haskell security math

About

RSA implementation in Haskell using https://en.wikipedia.org/wiki/RSA_(cryptosystem)

Example Results

Usage

λ> (public, private) = keygen Int Int

λ> encrypt public [Integral]

λ> decrypt private [Integral]

Key Generation

n is part of the public key and the private key e is part of the public key d is part of the private key

keygen returns a tuple formed by the public and private keys public = (n, e) private = (n, d)

1. n is the product of two primes
2. λ(n) is computed using Carmichael’s totient function but in this case since p and q are primes we can use the lcm formula
3. e is computed such that λ(n) and e are coprime
4. d is equal to the modular multiplicative inverse of λ(n)

Primes Generation

1. Write down the list 2,3…
2. Mark the first value as prime
3. Remove multiples of p from the list
4. Return to step 2

Conclusion

• GitHub Repo