Abstract: As is well known that the security of RSA depends on the hardness of integer factorization. The integer factorization method ToolBox includes many algorithms: trial division algorithm, ...

A complete, proof-of-concept, C# implementation of the General Number Field Sieve algorithm for factoring very large semi-prime numbers. The focus was on readability and understandability of the code, ...

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Abstract: Large integer factorization is one of the basic issues in number theory and is the subject of this paper. Our research shows that the Pisano period of the product of two prime numbers (or an ...

1 Department of Electrical Engineering and Computer Science, University of Kansas, Lawrence, KS, USA 2 National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, ...

We introduce a set of quantum adiabatic evolutions that we argue may be used as “building blocks,” or subroutines, in the construction of an adiabatic algorithm that executes Quantum Fourier Transform ...

ABSTRACT: In this paper is demonstrated a method for reduction of integer factorization problem to an analysis of a sequence of modular elliptic equations. As a result, the paper provides a ...

ABSTRACT: In this paper is demonstrated a method for reduction of integer factorization problem to an analysis of a sequence of modular elliptic equations. As a result, the paper provides a ...