Patent ID: 8670559

Claim:
A method of enabling a device to compute an outcome of an exponentiation C x having a base C and an exponent x by means of a white-box implementation of the exponentiation, the method comprising establishing, in a computer processor, the base C of the exponentiation and the exponent x of the exponentiation, comprising establishing the base C in dependence on a key of a cipher, wherein the key of the cipher is to be used by the device for performing a crytographic operation; establishing, in the computer processor, a plurality of values λ i , for i=1, 2, . . . , r, wherein r is an integer and r≧2; establishing, in the computer processor, a plurality of values ω i , for i=1, 2, . . . , r, satisfying ω i =C λ i ; establishing, in the computer processor, a plurality of values φ i , for i=1, 2, . . . , r, satisfying x = ∑ i = 1 r ⁢ λ i ⁢ φ i ; providing the device with information indicative of the plurality of values ω i ; providing the device with information indicative of the plurality of values φ i ; and computing, in the device, P = ∏ i = 1 r ⁢ ω i φ i , thereby hiding the precise values of the base C and the exponent x from a white-box attack.