The method and apparatus updates a binary number that will be used in cellular telephone system authentication procedures by applying a first algorithm to a plurality of most significant bits of a first binary number to obtain a second binary number; operates on a plurality of least significant bits of the first binary number with a second algorithm to obtain a third binary number, and applies a block cipher to the concatenation of the second and third numbers to obtain the updated binary number. When the most significant bits of the updated binary number comprise an all-zeroes number they are replaced with the most significant bits of the concatenation of the second and third numbers.