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) ...

Post-quantum cryptography is rapidly evolving to counter threats posed by quantum computing, and elliptic curves combined with isogeny methodologies offer a promising avenue. This approach leverages ...

According to one of the world’s leading cryptographers, Bitcoin’s elliptic curve could have a secret backdoor, invalidating all underlying security. A Bitcoin public key is created by applying ...

“Elliptic curve cryptography (ECC), as one of the public key cryptography systems, has been widely applied to many security applications. It is challenging to implement a scalar multiplication (SM) ...

A bounty of $12,288 has been announced for the first person to crack the NIST elliptic curves seeds and discover the original phrases that were hashed to generate them. The bounty will be tripled to ...