Paper 2018/1029

Reducing the Key Size of McEliece Cryptosystem from Goppa Codes via Permutations

Zhe Li and Chaoping Xing and Sze Ling Yeo

Abstract

In this paper, we propose a new general construction to reduce the public key size of McEliece-based schemes based on Goppa codes. In particular, we generalize the ideas of automorphism-induced Goppa codes by considering nontrivial subsets of automorphism groups to construct Goppa codes with a nice block structure. By considering additive and multiplicative automorphism subgroups, we provide explicit constructions to demonstrate our technique. In addition, we show that our technique can be applied to automorphism-induced Goppa codes to further reduce their key sizes.