RSA Cryptosystem: An Analysis And Python Simulator

This project involves an exploration of the RSA cryptosystem and the mathematical concepts embedded within it. The first goal is to explain what the cryptosystem consists of, and why it works. Additional goals include detailing some techniques for primality testing, discussing integer factorization, modular exponentiation, and digital signatures, and explaining the importance of these topics to the security and efficiency of the RSA cryptosystem. The final goal is to implement all of these components into a full simulation of the entire RSA cryptosystem using the Python programming language

Cryptanalysis of RSA: A Special Case of Boneh-Durfee’s Attack

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 e = N^α where ε and α are the private and public key exponents respectively) for some α ≤ ε, which satisfy the condition d > φ(N) − N^ε. 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

Successful cryptanalytic attacks upon RSA moduli N = pq

This paper reports four new cryptanalytic attacks which show that t instances of RSA moduli Ns = psqs for s = 1, . . . , t where t ≥ 2 can be simultaneously factored in polynomial time using simultaneous Diophantine approximations and lattice basis reduction techniques. We construct four system of equations of the form esd − ksφ(Ns) = 1, esds − kφ(Ns) = 1, esd − kφ(Ns) = zs and esds − kφ(Ns) = zs using N – [(a i+1/i + b i+1/i / 2(ab) i+1/2i + a 1/j + b 1/j / 2(ab) 1/2j) √N] + 1 as a good approximations of φ(Ns) for unknown positive integers d, ds, ks, k, and zs . In our attacks, we found an improved short decryption exponent bound of some reported attacks