R-LWE 암호화를 위한 근사 모듈식 다항식 곱셈기 최적화
Optimization of Approximate Modular Multiplier for R-LWE Cryptosystem
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초록
격자 기반 암호화는 최악의 경우를 기반으로 한 강력한 보안, 비교적 효율적인 구현 및 단순성을 누리기 때문에 포스트 양자 암호화방식 중 가장 실용적인 방식이다. 오류가 있는 링 학습(R-LWE)은 격자 기반 암호화(LBC)의 공개키암호화(Public Key Encryption:PKE) 방식이며, R-LWE의 가장 중요한 연산은 링의 모듈러 다항식 곱셈이다. 본 논문은 R-LWE 암호 시스템의 중간 보안 수준의 매개 변수 집합을 대상으로 하여 근사 컴퓨팅(Approximate Computing: AC) 기술을 기반으로 한 모듈러 곱셈기를 최적화하는 방법을제안한다. 먼저 복잡한 로직을 간단하게 구현하는 방법으로 LUT을 사용하여 근사 곱셈 연산 중 일부의 연산 과정을 생략하고, 2의 보수 방법을 활용하여 입력 데이터의 값을 이진수로 변환 시 값이 1인 비트의 개수를 최소화하여 필요한 덧셈기의 개수를 절감하는 총두 가지 방법을 제안한다. 제안된 LUT 기반의 모듈식 곱셈기는 기존 R-LWE 모듈식 곱셈기 대비 속도와 면적 모두 9%까지 줄어들었고, 2의 보수 방법을 적용한 모듈식 곱셈기는 면적을 40%까지 줄이고 속도는 2% 향상되는 것으로 나타났다. 마지막으로 이 두 방법을모두 적용한 최적화된 모듈식 곱셈기의 면적은 기존대비 43%까지 감소하고 속도는 10%까지 감소하는 것으로 나타났다.
Abstract
Lattice-based cryptography is the most practical post-quantum cryptography because it enjoys strong worst-casesecurity, relatively efficient implementation, and simplicity. Ring learning with errors (R-LWE) is a public key encryption(PKE) method of lattice-based encryption (LBC), and the most important operation of R-LWE is the modular polynomialmultiplication of rings. This paper proposes a method for optimizing modular multipliers based on approximatecomputing (AC) technology, targeting the medium-security parameter set of the R-LWE cryptosystem. First, as a simpleway to implement complex logic, LUT is used to omit some of the approximate multiplication operations, and the 2'scomplement method is used to calculate the number of bits whose value is 1 when converting the value of the inputdata to binary. We propose a total of two methods to reduce the number of required adders by minimizing them. Theproposed LUT-based modular multiplier reduced both speed and area by 9% compared to the existing R-LWE modularmultiplier, and the modular multiplier using the 2's complement method reduced the area by 40% and improved thespeed by 2%. appear. Finally, the area of the optimized modular multiplier with both of these methods applied wasreduced by up to 43% compared to the previous one, and the speed was reduced by up to 10%.
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