The disclosure proposes a method in a first device comprising a transaction history and a generation counter, this device processing transactions with a second device. During a current transaction: receipt of data comprising a public key of the second device, a second generation counter and an identifier of the current transaction; verification that the first and second generation counters coincide; verification that the history comprises an input associated with the public key; approval of the current transaction if the transaction identifier satisfies a condition indicating the uniqueness of the current transaction; storage in the history of a new input with the public key; and update of an account balance to pay a credit to an account. The method also comprises: detection of a risk of saturation of the memory of the first device; update of the first generation counter and eviction of the memory.