Sparsity-Aware Medium-Density Parity-Check Decoder for McEliece Cryptosystems

Abstract

McEliece cryptosystem based on medium-density parity-check (MDPC) codes is one of the finalists for the post-quantum cryptography standard. Although decoder design for low-density parity-check (LDPC) codes used for digital communications is well-investigated, the design of MDPC decoders faces many new challenges due to the different structure in the parity-check matrix. Even though the parity-check matrices of MDPC codes have relatively higher density, they are still very sparse. Previous decoder designs did not explore such sparsity and derive the columns of the parity check matrix one after the other by cyclic shifting. This paper proposes a low-complexity MDPC decoder design by exploiting the sparsity of the parity-check matrix. The processing corresponding to zero segments of each parity check matrix column is skipped to substantially reduce the latency. Moreover, the columns are processed in a novel non-consecutive order to significantly reduce the number of memory writes for deriving all the columns and accordingly the power consumption. For an example MDPC code considered for the standard, the proposed design can reduce both the decoding latency and the number of memory writes by 70% with 35% area saving.