COMPUTATIONAL NUMBER. THEORY AND CRYPTOGRAPHY. Unit Algebraic
Geometry and Number Theory. Department of Mathematics, KULeuven.
SEMINAR ON COMPUTATIONAL NUMBER THEORY AND CRYPTOGRAPHY Unit Algebraic Geometry and Number Theory Department of Mathematics, KULeuven COSIC (Computer Security and Industrial Cryptography) Department of Electrical Engineering-ESAT, KULeuven Organisers: J. Denef (Math.), J. Scholten (ESAT), I. Semaev (Math & ESAT) In the framework of a joint research project sponsored by the Flanders FWO, we organise during the academic year 2002-2003 a seminar on computational number theory and its applications in cryptography. These seminars will take place on Wednesday, starting at 2.30 PM, about two times a month. We will schedule them not to coincide with the COSIC seminars on cryptography. During the first semester Dr. Igor Semaev will give a mini course of 16 hours entitled
Computational Number Theory Methods in Cryptography This course will be given in sessions of each two hours, Wednesday from 2.30 PM to 3.30 PM, and from 4 PM to 5 PM. The first four sessions will be on October 30, November 13, November 27, and December 11, in room B 01.16 of the department of mathematics, Celestijnenlaan 200 B at Heverlee. During the second semester separate talks will be given by researchers in this field, most of them from abroad. Here is an abstract of Semaev’s mini course: • • • • • • • •
•
Complexity of algorithms, one-way functions, finding roots of polynomials modulo N. Basic cryptographic protocols and primitives: RSA, Diffie-Hellman key agreement, hash functions, ElGamal signature scheme and the Digital Signature Algorithm, the subset sum problem and MerkleHellman encryption, elliptic curve cryptography. Finding collisions for hash functions. Security of RSA. Methods from the geometry of numbers. Coppersmith theorem and its applications. Arithmetic of polynomials over integers. NTRU cryptosystem. LLL- lattice basis reduction and security of NTRU. The discrete log problem in finite fields. Pollard rho-method. The Number Field Sieve algorithm. The integer factorisation problem. Quadratic sieve factoring. The Number Field Sieve algorithm.
Everybody is welcome!
