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