To suppress the relation between the value of the decryption key and the temporal structure of the calculating steps, through a masking mechanism that does not appreciably lengthen the calculations, nor would necessitate inordinate hardware facilities in modular exponentiation.

An encrypting exponentiation modulo M is effected by a modular multiplication X*YmodM, where M is a modulus. The method involves an iterative series of steps. Each step executes one or two first multiplications to produce a first result, and a trim-down reduction of the size of the first result by one or more second multiplications to produce a second result. The method postpones substantially any subtraction of the modulus as pertaining to the measure to a terminal phase of the modular exponentiation. This is possible through choosing in an appropriate manner one or more parameters figuring in the method.