Re: Fast Modular Exponentiation with Huge Exponents

I am seeking different efficient programming methods (algorithms) for modular exponentiation with huge exponents, viz. 160-bit to 1024-bit integers as exponents and bases. I hope to find something a bit better than repeated squaring to handle the exponent; or at least a better way of chunking it. I will be working with DWORD and QWORD segments, so this should be an interesting hack.
 Example:
 1376059935759825045063891486059888763810529472911 ^
1227306356230802884842928886716272231596711085779 %
1393133130738640234978081120598228122485209166367
 Imagine instead of 160 bits up to to 1024 bits for all integers in the equation, the base, exponent, and modulus.
 I am not the least bit interested in using 3rd party code for this project. Please point the way to _algorithms_, not libraries or units.