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IEICE ESS FUNDAMENTALS REVIEW

On post-quantum security of symmetric cryptosystems

Akinori Hosoyamada

Published Jun 30, 2023• 0 citations
Publisher

Abstract

素因数分解問題と離散対数問題を多項式時間で解く量子アルゴリズムをShorが発見して以来,ポスト量子公開鍵暗号技術の研究が盛んに行われてきた.近年では,公開鍵暗号技術のみならず共通鍵暗号技術に対しても,量子計算機の使用を前提とした興味深い攻撃アルゴリズムが複数見つかっている.本稿では,共通鍵暗号技術のポスト量子安全性に関するこれまでの研究の流れと最近の動向について,主に攻撃アルゴリズムの観点から概観する.

DOI
10.1587/essfr.17.1_59

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素因数分解問題と離散対数問題を多項式時間で解く量子アルゴリズムをShorが発見して以来,ポスト量子公開鍵暗号技術の研究が盛んに行われてきた.近年では,公開鍵暗号技術のみならず共通鍵暗号技術に対しても,量子計算機の使用を前提とした興味深い攻撃アルゴリズムが複数見つかっている.本稿では,共通鍵暗号技術のポスト量子安全性に関するこれまでの研究の流れと最近の動向について,主に攻撃アルゴリズムの観点から概観する.
最も有名な公開鍵暗号としてRSA暗号とだ円曲線暗号があり,SSL/TLSによる暗号通信や電子政府でのディジタル署名などで広く普及している.一方で,これらの暗号は量子計算機による多項式時間の解読法が知られているため,量子計算機に耐性のある数学問題を利用したポスト量子暗号(Post-Quantum Cryptography)の研究が注目を集めている.実際,2015年8月にアメリカ国家安全性保障局NSAはポスト量子暗号への移行を表明し,2016年2月には米国標準技術研究所NISTがポスト量子暗号の標準化計画を発表している.本稿では,ポスト量子暗号の歴史と標準化計画の概要を紹介し,代表的なポスト量子暗号となる多変数多項式暗号と格子暗号の構成方法と安全性の評価方法を解説する.
This article describes a post-quantum multirecipient symmetric cryptosystem whose security is based on the hardness of the LWE problem. In this scheme a single sender encrypts multiple messages for multiple recipients generating a single ciphertext which is broadcast to the recipients. Each recipient decrypts the ciphertext with her secret key to recover the message intended for her. In this process, the recipient cannot efficiently extract any information about the other messages. This scheme is intended for messages like images and sound that can tolerate a small amount of noise. This article introduces the scheme and establishes its security based on the LWE problem. Further, an example is given to demonstrate the application of this scheme for encrypting multiple images.
The development of large quantum computers will have dire consequences for cryptography. Most of the symmetric and asymmetric cryptographic algorithms are vulnerable to quantum algorithms. Grover’s search algorithm gives a square root time boost for the searching of the key in symmetric schemes like AES and 3DES. The security of asymmetric algorithms like RSA, Diffie Hellman, and ECC is based on the mathematical hardness of prime factorization and discrete logarithms. The best classical algorithms available take exponential time. Shor’s factoring algorithm can solve the problems in polynomial time. Major breakthroughs in quantum computing will render all the present-day widely used asymmetric cryptosystems insecure. This paper analyzes the vulnerability of the classical cryptosystems in the context of quantum computers, discusses various post-quantum cryptosystem families, discusses the status of the NIST post-quantum cryptography standardization process, provides a performance comparison of post-quantum cryptography (PQC) algorithms on different platforms, and finally provides a couple of future research directions in this field.
The development of large quantum computers will have dire consequences for cryptography. Most of the symmetric and asymmetric cryptographic algorithms are vulnerable to quantum algorithms. Grover's search algorithm gives a square root time boost for the searching of the key in symmetric schemes like AES and 3DES. The security of asymmetric algorithms like RSA, Diffie Hellman, and ECC is based on the mathematical hardness of prime factorization and discrete logarithm. The best classical algorithms available take exponential time. Shor's factoring algorithm can solve the problems in polynomial time. Major breakthroughs in quantum computing will render all the present-day widely used asymmetric cryptosystems insecure. This paper analyzes the vulnerability of the classical cryptosystems in the context of quantum computers discusses various post-quantum cryptosystem families, discusses the status of the NIST post-quantum cryptography standardization process, and finally provides a couple of future research directions in this field.