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A new report by Capgemini warns that quantum computing may break the widely used public-key cryptographic systems within the next decade — threatening everything from online banking to blockchain ...

Abstract: The discrete logarithm problem has been used as the basis of several cryptosystems. P systems are a cluster of distributed parallel computing devices in a biochemical type. This paper ...

An implementation of the Pohlig-Hellman Algorithm, and using it in solving the Discrete Logarithm Problem in the group of units modulo a prime, with large values.

We present improved quantum circuits for elliptic curve scalar multiplication, the most costly component in Shor’s algorithm to compute discrete logarithms in elliptic curve groups. We optimize ...

Ars Technica has been separating the signal from the noise for over 25 years. With our unique combination of technical savvy and wide-ranging interest in the technological arts and sciences, Ars is ...

A team of French mathematicians and computer scientists has made an important advancement in the field of algorithms for breaking cryptographic codes. In a certain class of problem, the new algorithm ...

Improving over an earlier construction by Kaye and Zalka, Maslov et al. describe an implementation of Shor's algorithm which can solve the discrete logarithm problem on binary elliptic curves in ...

ABSTRACT: Numerous cryptographic algorithms (ElGamal, Rabin, RSA, NTRU etc) require multiple computations of modulo multiplicative inverses. This paper describes and validates a new algorithm, called ...