Aurura modexp #111
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Aurura modexp #111
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Migrate all maven coordinates that were `.native.` to `.nativelib.`. The old coordinate name presented problems in some auto-module systems for the JPMS. Signed-off-by: Danno Ferrin <[email protected]>
Signed-off-by: Danno Ferrin <[email protected]>
Signed-off-by: Danno Ferrin <[email protected]>
Port over aurora's modexp implementaiton. Signed-off-by: Danno Ferrin <[email protected]>
Signed-off-by: Danno Ferrin <[email protected]>
garyschulte
reviewed
Aug 3, 2023
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| This function takes the base, exponent and modulus as big-endian encoded bytes and returns the result in big-endian as well. | ||
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| This crate is meant to be an efficient implementation, using as little memory as possible (for example, it does not copy the exponent slice). | ||
| The exponentiation is done using the ["binary method"](https://en.wikipedia.org/wiki/Exponentiation_by_squaring). | ||
| The multiplication steps within the exponentiation use ["Montgomery multiplication"](https://en.wikipedia.org/wiki/Montgomery_modular_multiplication). | ||
| In the case of even modulus, Montgomery multiplication does not apply directly. | ||
| However we can reduce the problem to one involving an odd modulus and one where the modulus is a power of two. | ||
| These two sub-problems can be solved efficiently (the former using Montgomery multiplication, the latter the modular arithmetic is trivial on a binary computer), | ||
| then the results are combined using the [Chinese remainder theorem](https://en.wikipedia.org/wiki/Chinese_remainder_theorem). | ||
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| The primary academic references for this implementation are: | ||
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| 1. [Analyzing and Comparing Montgomery Multiplication Algorithms](https://www.microsoft.com/en-us/research/wp-content/uploads/1996/01/j37acmon.pdf) | ||
| 2. [Montgomery Reduction with Even Modulus](http://www.people.vcu.edu/~jwang3/CMSC691/j34monex.pdf) | ||
| 3. [A Cryptographic Library for the Motorola DSP56000](https://link.springer.com/content/pdf/10.1007/3-540-46877-3_21.pdf) | ||
| 4. [The Art of Computer Programming Volume 2](https://www-cs-faculty.stanford.edu/~knuth/taocp.html) |
garyschulte
approved these changes
Aug 3, 2023
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