Cryptanalysis of a Special Case of RSA Large Decryption Exponent Using Lattice Basis Reduction Method
Majid Mumtaz, Ping Luo · 2021 IEEE 6th International Conference on Computer and Communication Systems (ICCCS) · 2021
RSA public key cryptosystem is the “de-facto” standard, provides confidentiality and privacy security services over the internet. At Eurocrypt 1999, Boneh and Durfee proposed a polynomial time attacks on RSA small decryption key exponent. Their attacks worked by exploiting the lattice and sub lattice structure using lattice based Coppersmith's method to solve a modular polynomials, when d0.284and d0.292respectively. In this work, we propose a new attack on some special case of Boneh and Durfee's attack method with respect to large decryption exponent (i.e. d = N > e = Nα, where α and ε are the encryption and decryption exponents respectively) for some α ≤ ε. The condition d > φ(N) - Nεsatisfies our devised attack and the experimental outcome certifies that an RSA cryptosystem with large decryption exponent successfully revealed the weak keys through lattice basis reduction method.