A quantum computer was able to break a 15-bit elliptic-curve cryptographic key, according to the quantum computing security ...

Michael Oser Rabin has died at the age of 94. He was the only Turing Award recipient born in the German Reich.

ABSTRACT: Quantum technologies, mainly quantum computing and quantum sensing are emerging as new applications of quantum mechanics for practical use. Two notable advancements in quantum computing and ...

Shor’s algorithm is a quantum algorithm for factoring a number N in O((log N)3) time and O(log N) space, ...

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, ...

Abstract: Mathematicians have always been fascinated by the subject of finding the prime numbers of large composite numbers. They have studied various methods and have focused on developing several ...

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 ...