Fast Modular Exponentiation with Huge Exponents

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Sujet : Fast Modular Exponentiation with Huge Exponents
De : 3883 (at) *nospam* sugar.bug (SugarBug)
Groupes : sci.crypt
Date : 11. Apr 2024, 14:35:22
Autres entêtes
Organisation : Baggy Jeans Mafia (sybershock.com)
Message-ID : <b1fbf007d052918737b3ad5b1987fa27$1@sybershock.com>
User-Agent : 3883.7766
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.

--
    3883@sugar.bug | sybershock.com | sci.crypt



Date Sujet#  Auteur
11 Apr 24 * Fast Modular Exponentiation with Huge Exponents5SugarBug
11 Apr 24 +* Re: Fast Modular Exponentiation with Huge Exponents3Peter Fairbrother
12 Apr 24 i`* Re: Fast Modular Exponentiation with Huge Exponents2SugarBug
12 Apr 24 i `- Re: Fast Modular Exponentiation with Huge Exponents1SugarBug
16 Apr 24 `- Re: Fast Modular Exponentiation with Huge Exponents1Phil Carmody

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