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[crypto] Add a generic implementation of a Montgomery ladder

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The Montgomery ladder may be used to perform any operation that is
isomorphic to exponentiation, i.e. to compute the result

    r = g^e = g * g * g * g * .... * g

for an arbitrary commutative operation "*", base or generator "g", and
exponent "e".

Implement a generic Montgomery ladder for use by both modular
exponentiation and elliptic curve point multiplication (both of which
are isomorphic to exponentiation).

Signed-off-by: Michael Brown <mcb30@ipxe.org>
This commit is contained in:
Michael Brown
2025-01-22 12:54:52 +00:00
parent c2f21a2185
commit 66b5d1ec81
2 changed files with 194 additions and 34 deletions
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40
src/include/ipxe/bigint.h
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@@ -304,6 +304,24 @@ FILE_LICENCE ( GPL2_OR_LATER_OR_UBDL );
(result)->element, size ); \
} while ( 0 )
/**
* Perform generalised exponentiation via a Montgomery ladder
*
* @v result Big integer result (initialised to identity element)
* @v multiple Big integer multiple (initialised to generator)
* @v exponent Big integer exponent
* @v op Montgomery ladder commutative operation
* @v ctx Operation context (if needed)
* @v tmp Temporary working space (if needed)
*/
#define bigint_ladder( result, multiple, exponent, op, ctx, tmp ) do { \
unsigned int size = bigint_size (result); \
unsigned int exponent_size = bigint_size (exponent); \
bigint_ladder_raw ( (result)->element, (multiple)->element, \
size, (exponent)->element, exponent_size, \
(op), (ctx), (tmp) ); \
} while ( 0 )
/**
* Perform modular exponentiation of big integers
*
@@ -335,6 +353,20 @@ FILE_LICENCE ( GPL2_OR_LATER_OR_UBDL );
#include <bits/bigint.h>
/**
* A big integer Montgomery ladder commutative operation
*
* @v operand Element 0 of first input operand (may overlap result)
* @v result Element 0 of second input operand and result
* @v size Number of elements in operands and result
* @v ctx Operation context (if needed)
* @v tmp Temporary working space (if needed)
*/
typedef void ( bigint_ladder_op_t ) ( const bigint_element_t *operand0,
bigint_element_t *result0,
unsigned int size, const void *ctx,
void *tmp );
/**
* Test if bit is set in big integer
*
@@ -422,6 +454,14 @@ int bigint_montgomery_relaxed_raw ( const bigint_element_t *modulus0,
void bigint_montgomery_raw ( const bigint_element_t *modulus0,
bigint_element_t *value0,
bigint_element_t *result0, unsigned int size );
void bigint_ladder_raw ( bigint_element_t *result0,
bigint_element_t *multiple0, unsigned int size,
const bigint_element_t *exponent0,
unsigned int exponent_size, bigint_ladder_op_t *op,
const void *ctx, void *tmp );
void bigint_mod_exp_ladder ( const bigint_element_t *multiplier0,
bigint_element_t *result0, unsigned int size,
const void *ctx, void *tmp );
void bigint_mod_exp_raw ( const bigint_element_t *base0,
const bigint_element_t *modulus0,
const bigint_element_t *exponent0,