부호 기반 양자 내성 암호의 이진 필드 상에서 곱셈 연산 양자 게이트 구현 = Implementation of Quantum Gates for Binary Field Multiplication of Code based Post Quantum Cryptography

다국어 초록 (Multilingual Abstract)

The age of quantum computers is coming soon. In order to prepare for the upcoming future, the National Institute of Standards and Technology has recruited candidates to set standards for post quantum cryptography to establish a future cryptography standard. The submitted ciphers are expected to be safe from quantum algorithm attacks, but it is necessary to verify that the submitted algorithm is safe from quantum attacks using quantum algorithm even when it is actually operated on a quantum computer. Therefore, in this paper, we investigate an efficient quantum gate implementation for binary field multiplication of code based post quantum cryptography to work on quantum computers. We implemented the binary field multiplication for two field polynomials presented by Classic McEliece and three field polynomials presented by ROLLO in generic algorithm and Karatsuba algorithm.

참고문헌 (Reference)

1 I. V. Hoof, "Space-efficient quantum multiplication of polynomials for binary finite fields with sub-quadratic Toffoli gate count"

2 R. Feynman, "Simulating Physics with Computers" 21 : 467-, 1982

3 C. A. Melchor, "ROLLO: Rank-Ouroboros, Lake & Locker"

4 S. Kepley, "Quantum circuits for multiplication with subquadratic gate count" 14 (14): 2373-2386, 2015

5 V. Shende, "Quantum Information and Computation" 2008

6 D. S. Steiger, "ProjectQ: An Open Source Software Framework for Quantum Computing. Quantum"

7 D. Cheung, "On the design and optimization of a quantum polynomial-time attack on elliptic curve cryptography" 96-104, 2008

8 Join Extra Crunch, "IBM unveils its first commercial quantum computer"

9 D. J. Bernstein, "Classic McEliece:conservative code-based cryptography"

10 A. G. Aruna, "A Study on Reversible Logic Gates of Quantum Computing" 7 (7): 427-432, 2016