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My solutions to the assignments for my course "Algorithms for Numbers and Public-Key Cryptography".

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Algorithms for Numbers and Public-Key Cryptography

My solutions to the assignments for my course "Algorithms for Numbers and Public-Key Cryptography".

Exercise 1 includes:

  • Euclid’s Algorithm;
  • Multiplicative inverse;
  • Chinese Remainder Theorem;
  • Jacobi symbol;
  • Square roots and quadratic equations.

Exercise 2 includes:

  • Addition algorithm for positive integers;
  • Application: Fibonacci Sequence;
  • Multiplication algorithm for positive integers;
  • Factorial;
  • Modular Exponentiation.

Exercise 3 includes:

  • Fermat test;
  • Miller-Rabin primality test;
  • RSA.

Exercise 4 includes:

  • Coppersmith Attack on partially known message encryption with RSA
    • Finding small root of a modular polynomial equation of degree 2;
    • Polynomials of degree 3;
    • Application to breaking RSA encryption with small exponent e.

Exercise 5 includes:

  • Fault attacks against RSA signatures
    • Signature generation algorithm using the Chinese Remainder Theorem;
    • Recovering the factorization of N from s, following the Bellcore attack.

Exercise 6 includes:

  • DGHV Somewhat Homormorphic Encryption Scheme.

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My solutions to the assignments for my course "Algorithms for Numbers and Public-Key Cryptography".

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