Divide and capture: An improved cryptanalysis of the encryption standard algorithm RSA

• Main Authors: SUSILO, Willy, TONIEN, Joseph, YANG, Guomin
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2021
• Subjects: RSA; Wiener; Boneh-Durfee; Short key attack; Continued fractions; Information Security; Theory and Algorithms
• Online Access: https://ink.library.smu.edu.sg/sis_research/7292; https://ink.library.smu.edu.sg/context/sis_research/article/8295/viewcontent/Divide_and_capture__An_improved_cryptanalysis_of_the_encryption_standard_algorithm_RSA.pdf
• Institution: Singapore Management University

RSA is a well known standard algorithm used by modern computers to encrypt and decrypt messages. In some applications, to save the decryption time, it is desirable to have a short secret key d compared to the modulus N. The first significant attack that breaks RSA with short secret key given by Wiener in 1990 is based on the continued fraction technique and it works with d < 1/4 root 18 N-.(25). A decade later, in 2000, Boneh and Durfee presented an improved attack based on lattice technique which works with d < N-.(292). Until this day, Boneh-Durfee attack remain as the best attack on RSA with short secret key. In this paper, we revisit the continued fraction technique and propose a new attack on RSA. Our main result shows that when d < root t (2 root 2 + 8/3) N-.(75)/root e, where e is the public exponent and t is a chosen parameter, our attack can break the RSA with the running time of O(tlog (N)). Our attack is especially well suited for the case where e is much smaller than N. When e approximate to N, the Boneh-Durfee attack outperforms ours. As a result, we could simultaneously run both attacks, our new attack and the classical Boneh-Durfee attack as a backup.