Factorization strategies of N = pq and N = pʳq and relation to its decryption exponent bound - Abubakar, Saidu Isah (2018)
The major RSA underlying security problems rely on the difficulty of factoring a very large composite integer N into its two nontrivial prime factors of p and q in polynomial time, the ability to solve a given Diophantine equation ed = 1 + kφ (N) where only the public key e is known and the parameters d, k and φ (N) are un- known and finally the failure of an adversary to compute the decryption key d from the public key pair (e, N). This thesis develops three new strategies for the factorization of RSA modulus N = pq through analyzing small prime difference satisfying inequalities |b2 p − a2q| < Nγ , |bi p − a jq| < Nγ and |b j p − a jq| < for...