Cryptology ePrint Archive: Report 2013/866

Compact Ring-LWE based Cryptoprocessor

Sujoy Sinha Roy and Frederik Vercauteren and Nele Mentens and Donald Donglong Chen and Ingrid Verbauwhede

Abstract: In this paper we propose an efficient and compact processor for a ring-LWE based encryption scheme. We present three optimizations for the Number Theoretic Transform (NTT) used for polynomial multiplication: we avoid pre-processing in the negative wrapped convolution by merging it with the main algorithm, we reduce the fixed computation cost of the twiddle factors and propose an advanced memory access scheme. These optimization techniques reduce both the cycle and memory requirements. Finally, we also propose an optimization of the ring-LWE encryption system that reduces the number of NTT operations from five to four resulting in a 20\% speed-up. We use these computational optimizations along with several architectural optimizations to design an instruction-set ring-LWE cryptoprocessor. For dimension 256, our processor performs encryption/decryption operations in 20/9 $\mu s$ on a Virtex 6 FPGA and only requires 1349 LUTs, 860 FFs, 1 DSP-MULT and 2 BRAMs. Similarly for dimension 512, the processor takes 48/21 $\mu s$ for performing encryption/decryption operations and only requires 1536 LUTs, 953 FFs, 1 DSP-MULT and 3 BRAMs. Our processors are therefore more than three times smaller than the current state of the art hardware implementations, whilst running somewhat faster.

Category / Keywords: Lattice-based cryptography, ring-LWE, Polynomial multiplication, Number Theoretic Transform, Hardware implementation

Date: received 25 Dec 2013, last revised 18 Jun 2014

Contact author: sujoy sinharoy at esat kuleuven be

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Version: 20140618:191822 (All versions of this report)

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