Abstract: An offline payment method includes communicating a commitment value calculated by an electronic check medium to a terminal configured to receive a payment from the electronic check medium. The commitment value is calculated based on a first authentication code and secret key, wherein the first authentication code is calculated based on a payment amount and secret verification key. The terminal determines and communicates a random/pseudo-random guesstimation to the electronic check medium in response to receiving the verification code, the random/pseudo-random guesstimation being configured to verify that the electronic check medium is authentic. The electronic check medium determines and communicates a second authentication code to the terminal, the second authentication based upon the random/pseudo-random guesstimation.

Abstract: An offline payment method includes communicating a commitment value calculated by an electronic check medium to a terminal configured to receive a payment from the electronic check medium. The commitment value is calculated based on a first authentication code and a secret key, wherein the first authentication code is calculated based on a payment amount and a secret verification key. The terminal determines and communicates a random/pseudo-random guesstimation to the electronic check medium in response to receiving the verification code, the random/pseudo-random guesstimation being configured to verify that the electronic check medium is authentic. The electronic check medium determines and communicates a second authentication code to the terminal, the second authentication based upon the random/pseudo-random guesstimation.

Abstract: A process and arrangement that gives selective access to a security system, particularly in a payment system using debit cards, credit cards, or withdrawal of funds contained in a so-called smart card, and in particular on a chip card. The system comprises at least one first device and at least one second device that must be used in a correct configuration with one another in order to gain access. Access is gained by verifying that a certain coded key K2, held in the second device, is recognized as being valid by the first device, after comparing it with a renewing key K1 and previous versions of the code key K1 contained in the first device.

Abstract: The invention relates to a method and an apparatus for producing a key that is common to two devices that belong to different sets and are intended to implement a common cryptographic procedure. Each device is assigned a mother key (KC, KP) and a daughter key (KP.sub.ck, KC.sub.pi). The daughter key is developed on the basis of the mother key of the other device and of an identification datum specific to the device. When the procedure is performed, the two devices exchange their identification datum (ck, pi), which when processed with the aid of the mother key held by the device will yield the daughter key (KC.sub.pi, KP.sub.ck) of the other device. The pair of keys formed by the daughter key already held and by the daughter key that is calculated constitutes the common key.