Secure Number Theoretic Transform and Speed Record for Ring-LWE Encryption on Embedded Processors

摘要

Compact implementations of the ring variant of the Learning with Errors (Ring-LWE) on the embedded processors have been actively studied due to potential quantum threats. Various Ring-LWE implementation works mainly focused on optimization techniques to reduce the execution timing and memory consumptions for high availability. For this reason, they failed to provide secure implementations against general side channel attacks, such as timing attack. In this paper, we present secure and fastest Ring-LWE encryption implementation on low-end 8-bit AVR processors. We targeted the most expensive operation, i.e. Number Theoretic Transform (NTT) based polynomial multiplication, to provide countermeasures against timing attacks and best performance among similar implementations till now. Our contributions for optimizations are concluded as follows: (1) we propose the Look-Up Table (LUT) based fast reduction techniques for speeding up the modular coefficient multiplication in regular fashion, (2) we use the modular addition and subtraction operations, which are performed in constant timing. With these optimization techniques, the proposed NTT implementation enhances the performance by 18.3-22% than previous works. Finally, our Ring-LWE encryption implementations require only 680,796 and 1,754,064 clock cycles for 128-bit and 256-bit security levels, respectively.