Building cryptographic schemes based on elliptic curves over rational numbers

The possibility of using elliptic curves over the rational field non-zero ranks in cryptographic schemes is studied. For first time, construction cryptosystems proposed security which based on complexity solving knapsack problem numbers ranks. A new approach to use for proposed. few experiments have been carried out estimate heights characteristic points infinite order. model a cryptosystem resistant computations quantum computer and an order curve study effectiveness scheme has out. An attack secret search such implemented it shown that exponential. solution can be applied real as well protocols.