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Improved definition of magic constants

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tevador
2019-03-13 22:58:22 +01:00
parent 0d9beb5418
commit a2e7e05c40
2 changed files with 39 additions and 14 deletions
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doc/design.md
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@@ -106,9 +106,9 @@ SquareHash was chosen for its relative simplicity (uses only two operations - mu
From a cryptographic standpoint, SquareHash achieves full [Avalanche effect](https://en.wikipedia.org/wiki/Avalanche_effect). SquareHash was originally based on [exponentiation by squaring](https://en.wikipedia.org/wiki/Exponentiation_by_squaring). In the [x86 assembly implementation](https://github.com/tevador/RandomX/blob/master/src/asm/squareHash.inc), if `adc rax, 0` is added after each subtraction, SquareHash becomes the following operation:
<code>
(x+1613783669344650115)<sup>4398046511104</sup> mod 2<sup>64</sup>+1
(x+9507361525245169745)<sup>4398046511104</sup> mod 2<sup>64</sup>+1
</code>,
where <code>4398046511104 = 2<sup>42</sup></code>. The addition of the carry was removed to improve CPU performance. The constant `1613783669344650115` is added to make SquareHash sensitive to zero.
where <code>4398046511104 = 2<sup>42</sup></code>. The addition of the carry was removed to improve CPU performance. The constant `9507361525245169745` is added to make SquareHash sensitive to zero.
#### Generator