On primes, semiprimes and their applications

This article proves: the (Sophie Germain prime numbers are numbers of the type Nβ = 6a + 5 with a ∈ N, a ≥ 0 ; b) there are infinites germain prime numbers. This article interests potentially for all those that are researching new and every larger Sophie ...

Cryptography is used for secure communication since ancient days for providing confidentiality, integrity and availability of the information. Public key cryptography is a classification of cryptography having pair of keys for encryption and decryption. ...

Given an elliptic curve $$E$$E over a finite field $$\mathbb {F}_q$$Fq of $$q$$q elements, we say that an odd prime $$\ell \not \mid q$$ýýq is an Elkies prime for $$E$$E if $$t_E^2 - 4q$$tE2-4q is a square modulo $$\ell $$ý, where $$t_E = q+1 - \#E(\...