Method for directly exchanging electronic coin data sets between security elements (SE1, SE2, SE3) of terminals (M1, M2, M3), comprising the following steps: - generating a coin data set (C root) in a verifying unit or a transaction database by: defining a number (n) of elements (C x) on the basis of a monetary value (C Max), generating a random number (r); calculating the coin data set (C root) by means of a cryptographic function (f(r) x), the input parameter of which is the random number (r), the random number (r) being the same for all elements (C x) of the coin data set (croot); - receiving (102, 202) the coin data set (C root) in a first security element; - deriving, by means of the security element, a coin data set (C 1, C 3) from the received coin data set (croot); - transmitting (106, 206) the derived coin data set (C 1, C 3) from the first security element to a second security element; and - displaying (107, 210) the possession of the derived coin data set (C 1, C 3) by the second security element on the verifying unit, characterized in that - in the calculating step each element (C x) of the coin data set (C root) is calculated by means of the cryptographic function (f(r) x), the further input parameter of which is a position (x) of the element (C x) in the coin data set (C root), the elements (C x) being individualized by the position in the coin data set (C root), - the received coin data set (C root) has the number (n) of calculated elements (C x), - the random number (r) is not known to the security elements (SE1, SE2, SE3), and - the deriving is effected by taking at least one element (C x) of the received coin data set (C root) and the position (k) thereof in the received coin data set (C root), and - the verifying unit knows the random number (r) and verifies the authenticity of the derived coin data set (C 1, C 3) on the basis of the random number and the position of the element in the coin data set (C root). - generating a coin data set (C root) in a verifying unit or a transaction database by: defining a number (n) of elements (C x) on the basis of a monetary value (C Max), generating a random number (r); calculating the coin data set (C root) by means of a cryptographic function (f(r) x), the input parameter of which is the random number (r), the random number (r) being the same for all elements (C x) of the coin data set (croot); defining a number (n) of elements (C x) on the basis of a monetary value (C Max), generating a random number (r); calculating the coin data set (C root) by means of a cryptographic function (f(r) x), the input parameter of which is the random number (r), the random number (r) being the same for all elements (C x) of the coin data set (croot); - receiving (102, 202) the coin data set (C root) in a first security element; - deriving, by means of the security element, a coin data set (C 1, C 3) from the received coin data set (croot); - transmitting (106, 206) the derived coin data set (C 1, C 3) from the first security element to a second security element; and - displaying (107, 210) the possession of the derived coin data set (C 1, C 3) by the second security element on the verifying unit, - in the calculating step each element (C x) of the coin data set (C root) is calculated by means of the cryptographic function (f(r) x), the further input parameter of which is a position (x) of the element (C x) in the coin data set (C root), the elements (C x) being individualized by the position in the coin data set (C root), - the received coin data set (C root) has the number (n) of calculated elements (C x), - the random number (r) is not known to the security elements (SE1, SE2, SE3), and - the deriving is effected by taking at least one element (C x) of the received coin data set (C root) and the position (k) thereof in the received coin data set (C root), and - the verifying unit knows the random number (r) and verifies the authenticity of the derived coin data set (C 1, C 3) on the basis of the random number and the position of the element in the coin data set (C root).