Twisted Goppa codes with an efficient decoding algorithm and quasi-cyclic properties
Prof. Qin Yue
2023-10-12 10:40-11:40
MCM610
Speaker: Prof. Qin Yue (Nanjing University of Aeronautics and Astronautics)Time: 10:40-11:40 October 12, 2023 (Thursday)
Place: MCM610
Title: Twisted Goppa codes with an efficient decoding algorithm and quasi-cyclic properties
Abstract: In this talk, we introduce twisted Goppa codes, which generalize classical Goppa codes by adding a twisted term. Then we provide an efficient decoding algorithm for twisted Goppa codes. The Niederreiter cryptosystem is bassed on linear error-correcting codes in which the public key is a parity check matrix. When twisted Goppa codes are applied to the Niederreiter cryptosystem, the public key size is overlarge. To reduce the public key size, we construct quasi-cyclic twisted Goppa codes via a non-trivial automorphism group carefully selecting the defining set and the matched polynomial. Moreover, we obtain a family of cyclic twisted Goppa codes.
