A method for proving the presence of an identity token in the range of an identity sensor in a cryptographically secure manner and for exchanging at least one random number R T (120,122) of the identity token with a random number Rs (124,126) of the identity sensor, according to which a) the identity sensor transmits an identity sensor ID uniquely assigned to the identity sensor to the identity token and an identity combipass key is formed with an identity token key stored in the identity token by a transformation process, wherein a plurality of corresponding identity combipass keys assigned to the identity token are provided on the identity sensor, b) the identity sensor generates at least one random number Rs and uploads said random number to a radio interface, holding the number in reserve as a confirmation packet for a second random number R T from an identity token arriving in the future, c) the identity token generates a random number R T and sends said random number to the identity sensor, and d) the identity sensor then acknowledges the receipt of the random number R T from the identity token by immediately sending back the random number Rs (124,126) in the form of a single data packet, e) wherein the latency of an identity token for an (answer) random number Rs of less than 300 μs is limited such that the identity token takes into account incoming random numbers Rs only if the identity token recognises that the transmission of the random number Rs has begun within the above-mentioned latency, f) wherein, based on the identity combipass key (116, 118) and the exchanged random numbers Rs (124, 126) and R T (120,122), the identity sensor and the identity token, independently of each other, each determine identity responses (132, 134) which are compared with each other for verifying a permission. a) the identity sensor transmits an identity sensor ID uniquely assigned to the identity sensor to the identity token and an identity combipass key is formed with an identity token key stored in the identity token by a transformation process, wherein a plurality of corresponding identity combipass keys assigned to the identity token are provided on the identity sensor, b) the identity sensor generates at least one random number Rs and uploads said random number to a radio interface, holding the number in reserve as a confirmation packet for a second random number R T from an identity token arriving in the future, c) the identity token generates a random number R T and sends said random number to the identity sensor, and d) the identity sensor then acknowledges the receipt of the random number R T from the identity token by immediately sending back the random number Rs (124,126) in the form of a single data packet, e) wherein the latency of an identity token for an (answer) random number Rs of less than 300 μs is limited such that the identity token takes into account incoming random numbers Rs only if the identity token recognises that the transmission of the random number Rs has begun within the above-mentioned latency, f) wherein, based on the identity combipass key (116, 118) and the exchanged random numbers Rs (124, 126) and R T (120,122), the identity sensor and the identity token, independently of each other, each determine identity responses (132, 134) which are compared with each other for verifying a permission.