This chapter excerpted from Hardware Implementation of Finite-Field Arithmetic, gives an example of finite-field application namely, the implementation of the scalar product (point multiplication) ...

By extending the scope of a key insight behind Fermat’s Last Theorem, four mathematicians have made great strides toward ...

The elliptic curve discrete logarithm problem (ECDLP) lies at the heart of modern public-key cryptography. It concerns the challenge of determining an unknown scalar multiplier given two points on ...

A Note on Elliptic Curves Over Finite Fields, Mathematics of Computation, Vol. 49, No. 179 (Jul., 1987), pp. 301-304 ...

This paper is devoted to the description and analysis of a new algorithm to factor positive integers. It depends on the use of elliptic curves. The new method is obtained from Pollard's (p-1)-method ...

Unless, of course, Bitcoin’s elliptic curve is compromised. Many crypto experts have noticed that Bitcoin’s choice of secp256k1 elliptic curve was unusual for its time, as it was not yet well ...