Cryptanalysis of RSA: A Special Case of Boneh-Durfee's Attack [article]

Majid Mumtaz, Ping Luo
2020 IACR Cryptology ePrint Archive  
Boneh-Durfee proposed (at Eurocrypt 1999) a polynomial time attacks on RSA small decryption exponent which exploits lattices and sub-lattice structure to obtain an optimized bounds d < N 0.284 and d < N 0.292 respectively using lattice based Coppersmith's method. In this paper we propose a special case of Boneh-Durfee's attack with respect to large private exponent (i.e. d = N > e = N α where and α are the private and public key exponents respectively) for some α ≤ , which satisfy the condition
more » ... d > φ(N ) − N . We analyzed lattices whose basis matrices are triangular and non-triangular using large decryption exponent and focus group attacks respectively. The core objective is to explore RSA polynomials underlying algebraic structure so that we can improve the performance of weak key attacks. In our solution, we implemented the attack and perform several experiments to show that an RSA cryptosystem successfully attacked and revealed possible weak keys which can ultimately enables an adversary to factorize the RSA modulus.
dblp:journals/iacr/MumtazL20 fatcat:sgoegczurrfatbbcuvcw7dzrya