Patent ID: 8352736

Claim:
An authentication method of a first module by a second module, the method comprising the steps of: generating with the second module a random datum; transmitting the random datum to the first module; generating with the first module a first number by starting with said random datum and applying a private key associated with the first module through a bilinear function; wherein the bilinear function is a Tate pairing having, substantially, the form: G 1 ×G 2 →G 3 where G 1 and G 2 are additive groups formed by a set of points of an elliptic curve defined over a ground field GF(q) or an extension field GF(q k ) where q is a prime power and k is an integer, and G 3 is a subgroup of a multiplicative group of GF(q k )*, with the group G 1 being an [l]-torsion subgroup of G 2 such that [l]P=O for all P G 1 where O is the identity element and k being the smallest integer for which l divides (q k −1); and generating with the second module a second number to be directly compared with said first number to authenticate the first module, wherein the generating of the second number is carried out starting from public parameters and is performed independent of the generating of said first number, wherein the steps of generating the first and second numbers are performed concurrently, the first module comprises a smart card, a USB data key, a computer or a cell phone, and the second module comprises a cell phone, a set-top-box, a server or a computer.