Abstract: Disclosed herein is an apparatus for calculating a cryptographic component R2 mod n for a cryptographic function, where n is a modulo number and R is a constant greater than n. The apparatus comprises a processor configured to set a start value to be equal to R mod n, perform b iterations of a shift and subtract operation on the start value to produce a base value, wherein the start value is set to be equal to the base value after each iteration, set a multiplication operand to be equal to the base value, and perform k iterations of a Montgomery modular multiplication of the multiplication operand with the multiplication operand to produce an intermediate result, wherein the multiplication operand is set to be equal to the intermediate result after each iteration, wherein the shift and subtract operation comprises determining a shifted start value which is equivalent to the start value multiplied by two, and subtracting n from the shifted start value if the shifted start value is greater than or equal to n.

Abstract: Disclosed herein is an apparatus for calculating a cryptographic component R2 mod n for a cryptographic function, where n is a modulo number and R is a constant greater than n. The apparatus comprises an arithmetic logic unit configured to iteratively perform Montgomery multiplication of a first operand with a second operand to produce an intermediate result, wherein the first operand and the second operand are set to the intermediate result after each iteration, responsive to a termination condition being met, determine an adjustment parameter indicative of a difference between the intermediate result and the cryptographic component, and perform Montgomery multiplication of the intermediate result with the adjustment parameter, to calculate the cryptographic component for the cryptographic function.

Abstract: Disclosed herein is an apparatus for calculating a cryptographic component R2 mod n for a cryptographic function, where n is a modulo number and R is a constant greater than n. The apparatus comprises a processor configured to set a start value to be equal to R mod n, perform b iterations of a shift and subtract operation on the start value to produce a base value, wherein the start value is set to be equal to the base value after each iteration, set a multiplication operand to be equal to the base value, and perform k iterations of a Montgomery modular multiplication of the multiplication operand with the multiplication operand to produce an intermediate result, wherein the multiplication operand is set to be equal to the intermediate result after each iteration, wherein the shift and subtract operation comprises determining a shifted start value which is equivalent to the start value multiplied by two, and subtracting n from the shifted start value if the shifted start value is greater than or equal to n.

Abstract: Disclosed herein is an apparatus for calculating a cryptographic component R2 mod n for a cryptographic function, where n is a modulo number and R is a constant greater than n. The apparatus comprises an arithmetic logic unit configured to iteratively perform Montgomery multiplication of a first operand with a second operand to produce an intermediate result, wherein the first operand and the second operand are set to the intermediate result after each iteration, responsive to a termination condition being met, determine an adjustment parameter indicative of a difference between the intermediate result and the cryptographic component, and perform Montgomery multiplication of the intermediate result with the adjustment parameter, to calculate the cryptographic component for the cryptographic function.