The invention relates to a process and an apparatus for exponentiation over GF(2n). During an exponentiation in a finite field GF(2n), the squaring operation is carried out by constructing a vector. The components of this vector are constituted, alternately, by the components of the vector which is to be squared and by 0. An apparatus provides for the exponentiation in a finite field GF(2n) and includes three registers only, and furthermore has a regular structure which can be produced through very large scale integration. Application to the authentication of messages, the identification of users and the exchanging of keys. IMAGE
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