Syllabus
LLL algoritm and its applications - factorization of polynomials over Z, Coppersmith's attack on RSA with small public exponent, cryptanalysis of some knapsack-based cryptosystems.
Hash functions, Ajtai's worst case to average case reduction and its application to security proving. Short vector problem is NP-hard.
Cryptosystem NTRU.
Dicrete Gaussians and LWE, fully homomorphic encryption (optional)
Annotation
LLL algoritm and its application: Short vector problem is NP-hard, cryptosystem NTRU., constructions of hash functions, Coppersmith's attack on RSA, knapsack-based cryptosystems.