Methods and apparatus for Montgomery multiplication process a multiplier
operand in k-bit radix-digits, wherein k corresponds to a radix
r=2.sup.k. A multiplicand operand and a modulus are processed word by
word, and then additional bits of the multiplier operand are selected for
processing. In a radix r=8 example, the multiplier operand is processed
in 3 bit radix-8 digits. A processing kernel is configured to preprocess
the modulus and/or the multiplier operand so that at least some values
can be obtained from lookup tables.