Mathématiques du Secret
Talk at Camille Sée High School, Paris (December 6th, 2002)
This talk is made for students who specialize in mathematics during their last year in high school. We present fundamental principles of cryptology an describe precisely the RSA public key cryptosystem, for ciphering and signature since it uses almost only elementary arithmetics (fast modular exponentiation, Euclid’s extended algorithm, Fermat-Euler’s Theorem…). We give elements of cryptanalysis of RSA and explain how to build fake smartcards. We conclude by mentioning some other cryptosystems.