NP-Complete Sets for Computing Discrete Logarithms and Integer Factorization

Integer Factorization and Computing Discrete Logarithms in Maple

As part of our MITACS research project at Simon Fraser University, we have investigated algorithms for integer factorization and computing discrete logarithms. We have implemented a quadratic sieve algorithm for integer factorization in Maple to replace Maple’s implementation of the MorrisonBrillhart continued fraction algorithm which was done by Gaston Gonnet in the early 1980’s. We have also ...

Primality Testing, Integer Factorization, and Discrete Logarithms

Integer factorization and Discrete Logarithm problem are neither in P nor NP-complete

Though integer factorization and discrete logarithm problem are both practically and theoretically important, the computational complexity of these problems remained unknown. By comparing integer factorization problem with a problem in P and NP-complete problems, I show that the decision problem version of integer factorization problem is neither in P nor NP-complete. In addition, integer facto...

Implementing Swati Verma’s Digital Signature Schemes based on Integer Factorization and Discrete Logarithms

A digital signature is a cryptographic method for verifying the identity of an individual. It can be a process, computer system, or any other entity, in much the same way as a handwritten signature verifies the identity of a person. Digital signatures use the properties of public-key cryptography to produce pieces of information that verify the origin of the data. Several digital schemes have b...

Splitting NP-Complete Sets

We show that a set is m-autoreducible if and only if it is m-mitotic. This solves a long standing open question in a surprising way. As a consequence of this unconditional result and recent work by Glaßer et al., complete sets for all of the following complexity classes are m-mitotic: NP, coNP, ⊕P, PSPACE, and NEXP, as well as all levels of PH, MODPH, and the Boolean hierarchy over NP. In the c...