A p-ary MDPC scheme

The McEliece public key cryptosystem is an attractive general construction that has received extensive attention over the years. Recently, a very promising version called QC-MDPC, was proposed. By using binary quasi-cyclic codes, the size of the public key can be decreased significantly. The decryption step involves iterative decoding of moderate density parity check codes (MDPC). In this paper we propose a non-binary version of QC-MDPC. The errors in the new scheme are discrete Gaussian and the decryption involves a new type of iterative decoding with a non-binary alphabet. The resulting scheme improves upon the binary QC-MDPC in that the size of the pubic key can be even smaller.