p-adic attack of knapsack cryptosystem

The cryptattack of homogeneous knapsack systems is considered. The system is called homogeneous if the message symbols are changed from 0 to q, q/spl ges/1. This attack is based on presentation of the cryptogram and the public key components by p-adic decomposition. The question of cryptattack complexity is brought to the problem of the module p selection while taking into account the transfers expansion limitation only from one digit to next old digit. This attack breaks most of the classic knapsack systems without selection and essentially decreases the selection for knapsack cryptosystems. The developed scheme of attack allows estimating the time of decryption before the cryptogram is received. That leads to essential speeding up of decryption.