Handbook

The subject covers a variety of topics in number theory and their applications to modern cryptography. The number theory studied includes prime numbers, congruences and residues, Euler's phi-function, linear congruences and the Chinese remainder theorem. Elementary group theory is also introduced as a unifying language for number-theoretical concepts and results. We additionally consider more advanced concepts such as lattices and elliptic curves. The cryptographic applications studied include RSA, ElGamal, Rabin, discrete elliptic curve cryptosystems, and lattice-based cryptosystems, including the NTRU public key cryptosystem.