Reversible circuits for modular multiplication Cx%M with x M arise as components of modular exponentiation in Shor's quantum number-factoring algorithm. However, existing generic constructions focus ...

Ethereum co-founder Vitalik Buterin proposes removing modular exponentiation precompile, citing severe bottlenecks in zero-knowledge proof generation that slow scaling efforts across layer-2 networks.

ABSTRACT: This experimental study introduces a hybrid quantum-classical framework aiming to improve the noise robustness of Shor’s algorithm. By incorporating a novel hybrid logic gate into the ...

Abstract: Modular exponentiation is a vital function in public key cryptography. Dozens of protocols, including encryption schemes, signature schemes, pseudorandom functions, and more, perform this ...

Is this documented in the sqrt decomposition page? (BTW should be renamed square root to make it easier to search) I saw it in a Project Euler post but probably saw it elsewhere too. Compute queries ...

The team at Google has been developing new, more efficient algorithms, some of which involve building on work done with approximate modular exponentiation. The team has also been working to improve ...

These new IPs expand the security IP product line and enable SoC design teams to build total security solutions. Naperville, Illinois, March 20, 2007 – Jetstream Media Technologies announced today ...

School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing, China As environmental issues and climate change worsen, Smart Grid has become a crucial ...

Abstract: Modular exponentiation with large modulus and exponent, which is usually accomplished by repeated modular multiplications, has been widely used in public key cryptosystems. Typically, the ...

In the mid-1990s, Peter Shor, at AT&T Bell Labs and then one of its heirs, AT&T Labs, devised the first algorithms that one day could exploit the intrinsic parallelism of quantum computing. In ...

This year is the 80th anniversary of a pivotal event during World War II: the decoding of the Enigma machine by the Allied forces. Mathematician Alan Turing, among others, played a crucial role in ...