Every online bank transfer, private message and Bitcoin transaction rests on the assumption that some math problems are ...

- 📄 [ConvolutionFFT](src/main/java/com/thealgorithms/maths/ConvolutionFFT.java) - 📄 [CrossCorrelation](src/main/java/com/thealgorithms/maths/CrossCorrelation ...

ABSTRACT: We present a new perspective on the P vs NP problem by demonstrating that its answer is inherently observer-dependent in curved spacetime, revealing an oversight in the classical formulation ...

As far I understand, 1 distinctive feature of such algorithm is it fully works in subgroups/suborders. All other index calculus algorithms can do this only for the linear algebra phase and thus their ...

ABSTRACT: This work introduces a modification to the Heisenberg Uncertainty Principle (HUP) by incorporating quantum complexity, including potential nonlinear effects. Our theoretical framework ...

We estimate the number of physical qubits and execution time by decomposing an implementation of Shor’s algorithm for elliptic curve discrete logarithms into universal gate units at the logical level ...

Abstract: The difficulty in solving the discrete logarithm problem (DLP) is very important to the cryptography since it is widely used in signature schemes, message encryption, authentication, and so ...

FIPS 203 for ML-KEM (also known as CRYSTALS-Kyber) FIPS 204 for ML-DSA (also known as CRYSTALS-Dilithium) FIPS 205 for SLH-DSA (also known as Sphincs+) The publication of these draft standards is an ...

Ms. Angwin is a contributing Opinion writer and an investigative journalist. Social media can feel like a giant newsstand, with more choices than any newsstand ever. It contains news not only from ...

We revisit the quantum algorithm for computing short discrete logarithms that was recently introduced by Ekerå and Håstad. By carefully analyzing the probability distribution induced by the algorithm, ...