## Cryptology ePrint Archive: Report 2017/595

FPGA-based Key Generator for the Niederreiter Cryptosystem using Binary Goppa Codes

Wen Wang and Jakub Szefer and Ruben Niederhagen

Abstract: This paper presents a post-quantum secure, efficient, and tunable FPGA implementation of the key-generation algorithm for the Niederreiter cryptosystem using binary Goppa codes. Our key-generator implementation requires as few as 896,052 cycles to produce both public and private portions of a key, and can achieve an estimated frequency Fmax of over 240 MHz when synthesized for Stratix V FPGAs. To the best of our knowledge, this work is the first hardware-based implementation that works with parameters equivalent to, or exceeding, the recommended 128-bit 'post-quantum security' level. The key generator can produce a key pair for parameters $m=13$, $t=119$, and $n=6960$ in only $3.7$ ms when no systemization failure occurs, and in $3.5 \cdot 3.7$ ms on average. To achieve such performance, we implemented an optimized and parameterized Gaussian systemizer for matrix systemization, which works for any large-sized matrix over any binary field $GF(2^m)$. Our work also presents an FPGA-based implementation of the Gao-Mateer additive FFT, which only takes about 1000 clock cycles to finish the evaluation of a degree-119 polynomial at $2^{13}$ data points. The Verilog HDL code of our key generator is parameterized and partly code-generated using Python and Sage. It can be synthesized for different parameters, not just the ones shown in this paper. We tested the design using a Sage reference implementation, iVerilog simulation, and on real FPGA hardware.

Category / Keywords: post-quantum cryptography, code-based cryptography, Niederreiter key generation, FPGA, hardware implementation.

Original Publication (in the same form): IACR-CHES-2017

Date: received 20 Jun 2017, last revised 22 Jul 2017

Contact author: wen wang ww349 at yale edu

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2017/595

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