The method enables authentication data to be communicated and checked between a transponder device (1) and a reader unit (2) of a vehicle in order to authorize access to the vehicle. The device includes a logic circuit (11), a non-volatile memory (13), an encryption and/or decryption circuit (12) and a first transmission and reception module (14, 16) of data signals (S.sub.D). The reader unit includes a microprocessor unit (21), a memory (22), a random number generator (24) and a second module (23, 25) for transmitting and receiving data signals (S.sub.D). A random number (RN1) generated in the reader unit is transmitted with a first encrypted function obtained using the random number and a secret key. The transponder device receives the random number and the first encrypted function. A new first encrypted function is calculated in the transponder device using a secret key identical to the secret key of the reader unit. This new first function is compared with the first received encrypted function. A second encrypted function is also calculated in the transponder device in order to be transmitted to the reader unit solely if the new first encrypted function is equal to the first received encrypted function. The validity of the second encrypted function is checked in the reader unit in order to authorize access to the vehicle. The number of bits of the random number, of the first and second encrypted functions can be configured in the transponder device and/or in the reader unit with a determined length.