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[crypto] Correct harmless arithmetic error in X25519 comments

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Step 3 of the x25519 modular multiplication has a marginally tighter
upper bound than is currently claimed by the comments, due to an
arithmetic error caused by the number 19 occurring too often when
writing about this field prime.

Correct the comments to minimise future confusion.  There is no change
required to the code: the overall bound on the step 3 result remains
as previously stated.

Signed-off-by: Michael Brown <mcb30@ipxe.org>
This commit is contained in:
Michael Brown
2026-08-09 01:07:59 +01:00
parent 257e8faf10
commit e7f0604575
1 changed files with 6 additions and 6 deletions
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src/crypto/x25519.c
+6 -6
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@@ -486,18 +486,18 @@ void x25519_multiply ( const union x25519_oct258 *multiplicand,
* = step2(low 256 bits) + step2(high 11 bits) * 38 (mod p)
*
* There are 6 bits in the constant value 38. The step 3
* multiplication product will therefore have 11+6=19 bits,
* multiplication product will therefore have 11+6=17 bits,
* and the step 3 result (after the addition) will therefore
* have 257 bits.
*
* A loose upper bound for the step 3 result (after the
* addition) is given by:
*
* step3 < ( 2^256 - 1 ) + ( 2^19 - 1 )
* < ( 2^257 - 2^256 - 1 ) + ( 2^19 - 1 )
* < ( 2^257 - 76 ) - 2^256 + 2^19 + 74
* < 4 * ( 2^255 - 19 ) - 2^256 + 2^19 + 74
* < 4p - 2^256 + 2^19 + 74
* step3 < ( 2^256 - 1 ) + ( 2^17 - 1 )
* < ( 2^257 - 2^256 - 1 ) + ( 2^17 - 1 )
* < ( 2^257 - 76 ) - 2^256 + 2^17 + 74
* < 4 * ( 2^255 - 19 ) - 2^256 + 2^17 + 74
* < 4p - 2^256 + 2^17 + 74
*
* and so the step 3 result is strictly less than 4p, and
* therefore lies within the range [0,4p-1].