Procedure electronic transaction safely and corresponding system.

Procedure secure electronic transaction between an object (O) to be debited by a certain amount (M) and a terminal (T) able to control this debit and check that this debit has been well performed, the wherein method being: a) before any transaction: - for each object defined by an identifier (i) determined, a value (VA) authentication consisting of a digital signature carried by an identifier (i) of the object is calculated, this being produced signature with the use of a private key (SAUT), and can be verified from a public key (PAUT), and is then introduced this value (VA) authentication on the object (O), - is inserted into each terminal (G) the public key (PAUT) authentication, - for each object (O), a diversified key (ki) is determined from a key (KM) base, using the identifier (i) of the object an algorithm ( FKM) of diversificac the object to be debited (O) transmits to the terminal (T) its identifier (i) and -: to Use it base key, and this diversified key (ki) is inserted into the object (O), B) for each transaction ion value (VA) authentication, - the terminal (T) makes a cryptographic calculation applied to the value (VA) authentication using the public key (PAUT (VA) = i) authentication, - the terminal (T) transmits to the object ( O) the amount and parameters (M, j, n) of the transaction, - the object (O) is debited the said amount (M) and calculates a proof of this debit by a cryptographic function (FKI) that It has the secret key its diversified key (ki), and which is applied to the amount (M) and parameters of the transaction and transmits this proof (FKI (M, j, n)) to the terminal (T), - the terminal (T) calculates the diversified key of the object (ki) using a cryptographic function (FKM) used as the secret key base key (KM), and is applied identifier (i) of the object (O) (ki = FKM (i)) and verifies the proof of the debit (FKI (M, j, n)) using this diversified key.