Area-Time Efficient Computation of Niederreiter Encryption on QC-MDPC Codes for Embedded Hardware

In this paper, we present a fast implementation for QC-MDPC Niederreiter encryption. Existing high-speed implementations are considerably resource involving but the solution we propose here mitigates such situation while maintaining the high throughputs. In particular, new arithmetic for lightweight Hamming weight computation and a fast sorting network for MDPC decoding are proposed. A novel constant weight coding unit is proposed to enable standard asymmetric encryptions. For now, the design presented in this work is the fastest one of existing QC-MDPC code based encryptions in the public domain. The area-time product of this work drops by at least 53 percent compared to previous fast speed designs of QC-MDPC based encryptions. It is shown for instance that our implementation of encrypting engine can sign one encryption in 3.86 ms on a Xilinx Virtex-6 FPGA with 3371 slices. Our iterative decrypting engine can decrypt one ciphertext in 114.64 ms with 5271 slices and our faster non-iterative decrypting engine can decrypt in 65.76 ms with 8781 slices.