Abstract: The essence of the invention is an effective method for generating the multiplicative inverse in a finite field GF(p) where p is prime, i.e. for generating the modular inverse. This method is derived from the Extended Euclidean Algorithm (EEA). The method is for binary execution of operations during the process of generating the modular inverse, with respect to the lowest number of addition, subtraction and shift operations possible. The proposed method avoids redundant operations for converting odd and negative values, which are performed in methods currently in use. To achieve that, negative numbers are represented in the two's complement code, values in the control part of the EEA are shifted to the left, and a new definition of the boundary and control conditions is utilized in the procedure. Minimizing the number of additions and subtractions is desirable for calculations with large numbers often encountered in cryptography.

Abstract: The essence of the invention is an effective method for generating the multiplicative inverse in a finite field GF(p) where p is prime, i.e. for generating the modular inverse. This method is derived from the Extended Euclidean Algorithm (EEA). The method is for binary execution of operations during the process of generating the modular inverse, with respect to the lowest number of addition, subtraction and shift operations possible. The proposed method avoids redundant operations for converting odd and negative values, which are performed in methods currently in use. To achieve that, negative numbers are represented in the two's complement code, values in the control part of the EEA are shifted to the left, and a new definition of the boundary and control conditions is utilized in the procedure. Minimizing the number of additions and subtractions is desirable for calculations with large numbers often encountered in cryptography.