Factoring p times q through modulus of p plus b times x and q plus e times x Obtaining b times e

摘要

#$%^&*AU2014100414A420140605.pdf#####Factoring p * q through modulus of p + b * x and q + e * x: Obtaining b * e Paul C. Bingham Cheffers 19th April 2014 Abstract An algorithm is shown that can factor p * q if two modulus p + b * x and q+e*x are set so that q+e*x ~ q+,t, p+b*x ~ p+,r/p and q+e*x is a factor of p+b*x by factoring of a e*b modular residue when it is an actual product. It is shown that making p+ b*x a multiple of q+e *x is considerably simpler when x = 4 and when p mod 4 = q mod 4, which is the case in most RSA semiprimes. Finally, the case for when p - b * 4 = q + e * 4 is shown, and this case leads to the discovery of b * e where b + e = (p - q)/4. 1