N. I. Chervyakov, A. N. Golovko

Practical realization of algorithm of the enciphering based on a problem of a backpack, possesses concerning high speed of enciphering. However this cryptosystem has a problem of safety because frequently it is possible to crack it polynomial Shamir's with algorithm and Tseppel,. Problems on the basis of « a problem of a backpack » consist in the following. The set of values and their total value with weights is given. It is required to calculate the weights representing superincreasing sequence in which each member is more the than sum of all other members. If sequence normal the problem difficult solution and a unique method of definition of the subjects belonging a backpack, is the full search of possible decisions spent up to a finding of a correct combination. The algorithm of enciphering is presented. Suitable backpacks for practical use should contain not less than 250 elements. The length of each member of superincreasing sequence is 200-400 bits, that leads to necessary length of a key not less than 1024 bats. Cryptosystem Martin-Hellman have cracked Shamir and Tseppel. For prevention of similar attacks it is offered to couple on the basis of a problem of a backpack and криптосистему on elliptic curves. Elliptic curves have additive group of rational points above a final field in which the attacks similar to attacks of Shamir and Tseppel, are inapplicable. Searches of new ways of increase of efficiency of cryptographic data processing have led researchers to the conclusion, that within the limits of usual item (binary or decimal) notations of acceleration of performance of operations it is almost impossible. The given restriction is connected by that operations above greater numbers in an item notation are characterized by a lot of mutual circuits of carry between categories. The idea of a method consists in having a little bit in pairs mutually simple modules and to operate not directly with numbers, and with their rests. Advantage modular codings consists that addition, it is possible to carry out subtraction and multiplication for one cycle of synchronization. The Known cryptosystems on base of the stowage of the rucksack are broken open by polynomial algorithm. Using to base operations in group point elliptical curves on final floor in cryptosystem on base of the problem of the stowage of the rucksack is provided reliable protection from similar attacks. For ensuring the high velocity and reliability of the cryptooperation such cryptosystem is offered use the system of the remaining classes.