Abstract: The discrete logarithm problem (DLP) is the basis for several cryptographic primitives. Since Shor’s work, it has been known that the DLP can be solved by combining a polynomial-size quantum ...

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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 ...

The original version of this story appeared in Quanta Magazine. The simplest ideas in mathematics can also be the most perplexing. Take addition. It’s a straightforward operation: One of the first ...

In case you've faced some hurdles solving the clue, Results of addition problems, we've got the answer for you. Crossword puzzles offer a fantastic opportunity to engage your mind, enjoy leisure time, ...

A new proof illuminates the hidden patterns that emerge when addition becomes impossible. The simplest ideas in mathematics can also be the most perplexing. Take addition. It’s a straightforward ...

Sir Timothy Gowers, the world-renowned Cambridge mathematician, and a team of distinguished colleagues are taking on for-profit academic journal publishers with today's launch of Discrete Analysis, a ...

In recent years the Elliptic Curve Cryptography approach has become popular due to its high efficiency and strong security. The purpose of this article is to present this topic in a relatively clearer ...

A new proof about prime numbers illuminates the subtle relationship between addition and multiplication — and raises hopes for progress on the famous abc conjecture. One morning last November, the ...

The Power Line is a newsletter series that reviews key stories in the electric power sector—ranging from grid reliability, transmission issues, and emergent technology and business models. The Power ...

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 ...