Public Key Cryptography based on Coding Theory
Dr. Edgar Martinez-Moro / Universidad de Valladolid
All Public Key Cryptosystems (PKCs) are based on the (computational) hardness of some mathematical problem. RSA or hyperelliptic curve cryptosystem are based on the hardness of factorization and of the discrete log respectively. P. Shor showed how, employing a quantum computer, this problems can be solved. This thread has reinitialized the research on some alternative PKCs that are not broken with Shor's approach. This is the case of McEliece PKC based on the hardness of decoding a "random code". Unfortunately the "good guys" need to know how to decode in order to implement the PKC and therefore the code is not so "random". We will see at the end of the talk how some extensions of some classical results on geometry as "the number of points defining a conic" can help us in breaking McEliece PKC in the case that the code is an Algebraic Geometry code.