A method for directly exchanging electronic coin data sets between security elements (SE1, SE2, SE3) of terminals (M1, M2; M3), comprising the steps of: - receiving a coin data set (C root) in a first security element, wherein the coin data set (C root) is represented by a random number (r) and a number (n) of elements (C x) of the received coin data set (C root) can be calculated, wherein each element (C x) of the received coin data set (C root) can be mapped as a result of a cryptographic function (f(r) x) from the random number (r) and the respective position (x) of the element (C x) in the coin data set (C root); - calculating, in the first security element, at least one element (C k) of the received coin data set (C root) from the random number (r) and the position (k) of the element (C k) in the coin data set (C root) by means of the cryptographic function (f(r) k), - transmitting a first coin data record (C 3) derived from the received coin data record (C root) from the first security element to a second security element, wherein the derived coin data record (C 3) comprises at least the calculated element (C k) of the received coin data record (C root) and the position of the calculated element (k) in the received coin data record (C root); - calculating, in the first security element, at least one further element of the received coin data set (C root) directly following the calculated element (C k) of the first derived coin data set (C 3) from the random number (r) and the position of the directly following further element in the coin data set (C root) by means of the cryptographic function (f(r)), - transmitting a second coin data set (C 4) derived from the received coin data set (C root) to the second security element, the second derived coin data set (C 4) comprising at least the calculated directly following further element of the received coin data set (C root) and the position of the calculated directly following further element in the received coin data set (C root); - combining the first derived coin data set (C 3) with the second derived coin data set (C 4) to obtain a combined derived coin data set (C 6); and - indicating possession of the combined derived coin data set (C 6) from the second security element to a verification unit, whereupon the at least one element (C x) is only redeemable. - receiving a coin data set (C root) in a first security element, wherein the coin data set (C root) is represented by a random number (r) and a number (n) of elements (C x) of the received coin data set (C root) can be calculated, wherein each element (C x) of the received coin data set (C root) can be mapped as a result of a cryptographic function (f(r) x) from the random number (r) and the respective position (x) of the element (C x) in the coin data set (C root); - calculating, in the first security element, at least one element (C k) of the received coin data set (C root) from the random number (r) and the position (k) of the element (C k) in the coin data set (C root) by means of the cryptographic function (f(r) k), - transmitting a first coin data record (C 3) derived from the received coin data record (C root) from the first security element to a second security element, wherein the derived coin data record (C 3) comprises at least the calculated element (C k) of the received coin data record (C root) and the position of the calculated element (k) in the received coin data record (C root); - calculating, in the first security element, at least one further element of the received coin data set (C root) directly following the calculated element (C k) of the first derived coin data set (C 3) from the random number (r) and the position of the directly following further element in the coin data set (C root) by means of the cryptographic function (f(r)), - transmitting a second coin data set (C 4) derived from the received coin data set (C root) to the second security element, the second derived coin data set (C 4) comprising at least the calculated directly following further element of the received coin data set (C root) and the position of the calculated directly following further element in the received coin data set (C root); - combining the first derived coin data set (C 3) with the second derived coin data set (C 4) to obtain a combined derived coin data set (C 6); and - indicating possession of the combined derived coin data set (C 6) from the second security element to a verification unit, whereupon the at least one element (C x) is only redeemable.