A method and apparatus for cryptographic data processing, includes determining a first modulus having up to a first number of binary digits. A large integer is received which has up to a second number of binary digits that is greater than the first number of binary digits. The first modulus and the large integer are sent to a first processor for computing a first residue of the large integer modulo the first modulus. Before the first processor finishes computing the first residue, the first modulus is also sent to a second processor for computing a second residue of two raised to a power of twice the first number of binary digits modulo the first modulus. The first residue and the second residue are used as input to a third processor that computes a cryptographic result based on the large integer.