1. Method for establishing secured communication between a first communicating electronic device known as the device and a second communicating electronic device known as the reader, each having at least one random number generator, a symmetrical encryption algorithm SYM, an asymmetrical encryption algorithm ASYM and a mathematical function F, said device being associated with a cryptographic certificate Cert, a public key n and a private key Kpriv, comprising at least the stages of: engagement, during which said device generates a first random number k and informs said reader of the identity of said device challenge, during which said reader obtains the public key n and subsequently generates a second random number r, encrypts it using said algorithm ASYM and n and transmits it to said device, response, during which said device decrypts the random number r with said algorithm ASYM and said private key Kpriv, encrypts said random number k with said algorithm SYM and the random number r by way of a key, sends this encrypted data to said reader and generates a session key by applying said function F to said random numbers k and r verification, during which said reader decrypts said random number k received with the algorithm SYM and the random number r by way of a key and subsequently generates a session key by applying said function F to said random numbers k and r.