Abstract: Montgomery exponentiators and methods modulo exponentiate a generator (g) to a power of an exponent (e). The Montgomery exponentiators and methods include a first multiplier that is configured to repeatedly square a residue of the generator, to produce a series of first multiplier output values at a first multiplier output. A second multiplier is configured to multiply selected ones of the series of first multiplier output values that correspond to a bit of the exponent that is binary one, by a partial result, to produce a series of second multiplier output values at a second multiplier output. By providing two multipliers that are serially coupled as described above, Montgomery exponentiation can be accelerated.

Abstract: Montgomery multipliers and methods modular multiply a residue multiplicand by a residue multiplier to obtain a residue product, using a scalar multiplier, a first vector multiplier and a second vector multiplier. A controller is configured to control the scalar multiplier, the first vector multiplier and the second vector multiplier, to overlap scalar multiplies using a selected digit of the multiplier and vector multiplies using a modulus and the multiplicand. The scalar multiplier is configured to multiply a least significant digit of the multiplicand by a first selected digit of the multiplier, to produce a scalar multiplier output. The first vector multiplier is configured to multiply the scalar multiplier output by a modulus, to produce a first vector multiplier output. The second vector multiplier is configured to multiply a second selected digit of the multiplier by the multiplicand, to produce a second vector multiplier output.