Skip to content

Commit 315ec8d

Browse files
aidoaido
committed
Improve efficiency of SSS interpolate() function
1 parent a8e9bba commit 315ec8d

File tree

8 files changed

+57
-106
lines changed

8 files changed

+57
-106
lines changed

‎CHANGELOG.md‎

Lines changed: 10 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -1,5 +1,15 @@
11
# Change log
22

3+
## [1.7.1] - 2024-03-06
4+
### Added
5+
-
6+
7+
### Changed
8+
- Improve efficiency of SSS `interpolate()` function
9+
10+
### Fixed
11+
-
12+
313
## [1.7.0] - 2024-03-03
414
### Added
515
- Added detailed documentation for all SSKR and SSS functions

‎Makefile‎

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -28,7 +28,7 @@ all: default
2828
APPNAME = "Seed Tool"
2929
APPVERSION_M = 1
3030
APPVERSION_N = 7
31-
APPVERSION_P = 0
31+
APPVERSION_P = 1
3232
APPVERSION = "$(APPVERSION_M).$(APPVERSION_N).$(APPVERSION_P)"
3333

3434
APP_LOAD_PARAMS = --appFlags 0x10 $(COMMON_LOAD_PARAMS) --curve secp256k1 --path ""

‎README.md‎

Lines changed: 4 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -5,10 +5,10 @@
55
[![Release](https://img.shields.io/github/release/aido/app-seed-tool)](https://github.com/aido/app-seed-tool/releases)
66
[![License](https://img.shields.io/github/license/aido/app-seed-tool)](https://github.com/aido/app-seed-tool/blob/develop/LICENSE)
77

8-
![nanos](https://img.shields.io/badge/nanos-working-green)
9-
![nanox](https://img.shields.io/badge/nanox-working-green)
10-
![nanosp](https://img.shields.io/badge/nanosp-working-green)
11-
![stax](https://img.shields.io/badge/stax-in_progress-orange)
8+
![nanos](https://img.shields.io/badge/nanos-working-green?logo=data:image/svg%2bxml;base64,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)
9+
![nanox](https://img.shields.io/badge/nanox-working-green?logo=data:image/svg%2bxml;base64,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)
10+
![nanosp](https://img.shields.io/badge/nanosp-working-green?logo=data:image/svg%2bxml;base64,PHN2ZyB3aWR0aD0iMTQ3IiBoZWlnaHQ9IjEyOCIgdmlld0JveD0iMCAwIDE0NyAxMjgiIGZpbGw9Im5vbmUiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyI+PHBhdGggZD0iTTAgOTEuNjU0OFYxMjhINTUuMjkzVjExOS45NEg4LjA1NjMxVjkxLjY1NDhIMFpNMTM4Ljk0NCA5MS42NTQ4VjExOS45NEg5MS43MDdWMTI3Ljk5OEgxNDdWOTEuNjU0OEgxMzguOTQ0Wk01NS4zNzMzIDM2LjM0NTJWOTEuNjUyOUg5MS43MDdWODQuMzg0Mkg2My40Mjk2VjM2LjM0NTJINTUuMzczM1pNMCAwVjM2LjM0NTJIOC4wNTYzMVY4LjA1ODQ0SDU1LjI5M1YwSDBaTTkxLjcwNyAwVjguMDU4NDRIMTM4Ljk0NFYzNi4zNDUySDE0N1YwSDkxLjcwN1oiIGZpbGw9IndoaXRlIi8+PC9zdmc+)
11+
![stax](https://img.shields.io/badge/stax-in_progress-orange?logo=data:image/svg%2bxml;base64,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)
1212

1313
[![Build app-seed-tool](https://github.com/aido/app-seed-tool/actions/workflows/ci-workflow.yml/badge.svg)](https://github.com/aido/app-seed-tool/actions/workflows/ci-workflow.yml)
1414
[![CodeQL](https://github.com/aido/app-seed-tool/actions/workflows/codeql-workflow.yml/badge.svg)](https://github.com/aido/app-seed-tool/actions/workflows/codeql-workflow.yml)

‎src/constants.h‎

Lines changed: 0 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -16,8 +16,6 @@
1616

1717
#pragma once
1818

19-
#define memzero(...) explicit_bzero(__VA_ARGS__)
20-
2119
#define ONBOARDING_WORD_COMPLETION_MAX_ITEMS 8
2220
#define BOLOS_UX_HASH_LENGTH 4 // as on the blue
2321

‎src/sskr/sss/interpolate.c‎

Lines changed: 37 additions & 94 deletions
Original file line numberDiff line numberDiff line change
@@ -23,8 +23,6 @@
2323
// Minimal required bytes for BN storing a GF(256) value
2424
#define GF2_8_MPI_BYTES 1
2525

26-
#define memzero(...) explicit_bzero(__VA_ARGS__)
27-
2826
#ifdef TARGET_NANOS
2927
/**
3028
* @brief Performs a multiplication over GF(2^n).
@@ -135,81 +133,6 @@ cx_err_t cx_bn_gf2_n_mul(cx_bn_t bn_r,
135133
}
136134
#endif
137135

138-
/**
139-
* @brief Performs an invert operation over GF(2^8).
140-
*
141-
* @param[out] bn_r BN index for the result.
142-
*
143-
* @param[in] bn_a BN index of the first operand.
144-
*
145-
* @param[in] bn_n BN index of the modulus.
146-
* The modulus must be an irreducible polynomial over GF(2)
147-
* of degree n.
148-
*
149-
* @param[in] bn_h BN index of the second montgomery constant.
150-
*
151-
* @return Error code:
152-
* - CX_OK on success
153-
* - CX_NOT_LOCKED
154-
* - CX_INVALID_PARAMETER
155-
* - CX_MEMORY_FULL
156-
*/
157-
cx_err_t bn_gf2_8_inv(cx_bn_t bn_r, const cx_bn_t bn_a, const cx_bn_t bn_n, const cx_bn_t bn_h) {
158-
cx_err_t error = CX_OK; // By default, until some error occurs
159-
cx_bn_t bn_x, bn_y, bn_z;
160-
161-
CX_CHECK(cx_bn_alloc(&bn_x, GF2_8_MPI_BYTES));
162-
CX_CHECK(cx_bn_alloc(&bn_y, GF2_8_MPI_BYTES));
163-
CX_CHECK(cx_bn_alloc(&bn_z, GF2_8_MPI_BYTES));
164-
CX_CHECK(cx_bn_copy(bn_x, bn_a));
165-
166-
CX_CHECK(cx_bn_gf2_n_mul(bn_y, bn_x, bn_x, bn_n, bn_h)); // bn_y = bn_x^2
167-
CX_CHECK(cx_bn_gf2_n_mul(bn_y, bn_y, bn_y, bn_n, bn_h)); // bn_y = bn_x^4
168-
CX_CHECK(cx_bn_gf2_n_mul(bn_r, bn_y, bn_y, bn_n, bn_h)); // bn_r = bn_x^8
169-
CX_CHECK(cx_bn_gf2_n_mul(bn_z, bn_r, bn_x, bn_n, bn_h)); // bn_z = bn_x^9
170-
CX_CHECK(cx_bn_gf2_n_mul(bn_r, bn_r, bn_r, bn_n, bn_h)); // bn_r = bn_x^16
171-
CX_CHECK(cx_bn_gf2_n_mul(bn_r, bn_r, bn_z, bn_n, bn_h)); // bn_r = bn_x^25
172-
CX_CHECK(cx_bn_gf2_n_mul(bn_r, bn_r, bn_r, bn_n, bn_h)); // bn_r = bn_x^50
173-
CX_CHECK(cx_bn_gf2_n_mul(bn_z, bn_r, bn_r, bn_n, bn_h)); // bn_z = bn_x^100
174-
CX_CHECK(cx_bn_gf2_n_mul(bn_z, bn_z, bn_z, bn_n, bn_h)); // bn_z = bn_x^200
175-
CX_CHECK(cx_bn_gf2_n_mul(bn_r, bn_r, bn_z, bn_n, bn_h)); // bn_r = bn_x^250
176-
CX_CHECK(cx_bn_gf2_n_mul(bn_r, bn_r, bn_y, bn_n, bn_h)); // bn_r = bn_x^254
177-
178-
CX_CHECK(cx_bn_destroy(&bn_x));
179-
CX_CHECK(cx_bn_destroy(&bn_y));
180-
CX_CHECK(cx_bn_destroy(&bn_z));
181-
182-
end:
183-
return error;
184-
}
185-
186-
/**
187-
* @brief Performs polynomial interpolation on SSS shares.
188-
*
189-
* @details This function interpolates a polynomial that passes through the provided points
190-
* represented by `xi` (x-coordinates) and `yij` (y-coordinate arrays) i.e.
191-
* where:
192-
* xi points to [x0 x1 ... xn-1 ]
193-
* y contains an array of pointers to 32-bit arrays of y values
194-
* y contains [y0 y1 y2 ... yn-1]
195-
* and each of the yi arrays contain [yi_0 yi_i ... yi_31].
196-
*
197-
* This interpolation is used in Shamir's Secret Sharing (SSS) to recover
198-
* the secret from a set of shares.
199-
*
200-
* @param[in] n Number of points to interpolate (length of `xi` and `yij`).
201-
* @param[in] xi Pointer to an array containing the x-coordinates of the points (length `n`).
202-
* @param[in] yl Length of each y-coordinate array in bytes.
203-
* @param[in] yij Pointer to an array of `n` pointers, each pointing to a y-coordinate array of
204-
* length `yl`.
205-
* @param[in] x X-coordinate at which to perform the interpolation.
206-
* @param[out] result Pointer to a buffer where the interpolated value will be stored (must be `yl`
207-
* bytes long).
208-
*
209-
* @return - CX_OK on success
210-
* - A negative error code on failure (specific error codes not defined here,
211-
* consult implementation details for specific error handling)
212-
*/
213136
cx_err_t interpolate(uint8_t n,
214137
const uint8_t* xi,
215138
uint8_t yl,
@@ -220,21 +143,20 @@ cx_err_t interpolate(uint8_t n,
220143
const uint8_t R2[1] = MONTGOMERY_CONSTANT_R2;
221144

222145
cx_err_t error = CX_OK; // By default, until some error occurs
223-
cx_bn_t bn_x, bn_xc_i, bn_xc_j;
224-
cx_bn_t bn_numerator, bn_denominator;
225-
cx_bn_t bn_lagrange, bn_y, bn_result, bn_temp, bn_n, bn_r2;
146+
cx_bn_t bn_x, bn_xc_i;
147+
cx_bn_t bn_numerator, bn_denominator, bn_lagrange;
148+
cx_bn_t bn_result, bn_tempa, bn_tempb, bn_n, bn_r2;
226149
uint32_t result_u32;
227150

228151
CX_CHECK(cx_bn_lock(GF2_8_MPI_BYTES, 0));
229152
CX_CHECK(cx_bn_alloc(&bn_x, GF2_8_MPI_BYTES));
230153
CX_CHECK(cx_bn_alloc(&bn_xc_i, GF2_8_MPI_BYTES));
231-
CX_CHECK(cx_bn_alloc(&bn_xc_j, GF2_8_MPI_BYTES));
232154
CX_CHECK(cx_bn_alloc(&bn_numerator, GF2_8_MPI_BYTES));
233155
CX_CHECK(cx_bn_alloc(&bn_denominator, GF2_8_MPI_BYTES));
234156
CX_CHECK(cx_bn_alloc(&bn_lagrange, GF2_8_MPI_BYTES));
235-
CX_CHECK(cx_bn_alloc(&bn_y, GF2_8_MPI_BYTES));
236157
CX_CHECK(cx_bn_alloc(&bn_result, GF2_8_MPI_BYTES));
237-
CX_CHECK(cx_bn_alloc(&bn_temp, GF2_8_MPI_BYTES));
158+
CX_CHECK(cx_bn_alloc(&bn_tempa, GF2_8_MPI_BYTES));
159+
CX_CHECK(cx_bn_alloc(&bn_tempb, GF2_8_MPI_BYTES));
238160
CX_CHECK(cx_bn_alloc_init(&bn_n, GF2_8_MPI_BYTES, N, sizeof(N)));
239161
CX_CHECK(cx_bn_alloc_init(&bn_r2, GF2_8_MPI_BYTES, R2, sizeof(R2)));
240162

@@ -255,16 +177,38 @@ cx_err_t interpolate(uint8_t n,
255177
// j != i (xi[i]-xi[j])
256178
for (uint8_t j = 0; j < n; j++) {
257179
if (j != i) {
258-
CX_CHECK(cx_bn_set_u32(bn_xc_j, (uint32_t) xi[j]));
180+
CX_CHECK(cx_bn_set_u32(bn_tempa, (uint32_t) xi[j]));
259181

260182
// Calculate the numerator (x - xc[j])
261-
CX_CHECK(cx_bn_xor(bn_numerator, bn_x, bn_xc_j));
183+
CX_CHECK(cx_bn_xor(bn_numerator, bn_x, bn_tempa));
262184

263185
// Calculate the denominator (xc[i] - xc[j])
264-
CX_CHECK(cx_bn_xor(bn_denominator, bn_xc_i, bn_xc_j));
186+
CX_CHECK(cx_bn_xor(bn_denominator, bn_xc_i, bn_tempa));
265187

266188
// Calculate the inverse of the denominator
267-
CX_CHECK(bn_gf2_8_inv(bn_denominator, bn_denominator, bn_n, bn_r2));
189+
// In GF(2^8) the inverse of x = x^254
190+
// bn_result = bn_denominator^2
191+
CX_CHECK(cx_bn_gf2_n_mul(bn_result, bn_denominator, bn_denominator, bn_n, bn_r2));
192+
// bn_result = bn_denominator^4
193+
CX_CHECK(cx_bn_gf2_n_mul(bn_result, bn_result, bn_result, bn_n, bn_r2));
194+
// bn_tempa = bn_denominator^8
195+
CX_CHECK(cx_bn_gf2_n_mul(bn_tempa, bn_result, bn_result, bn_n, bn_r2));
196+
// bn_tempb = bn_denominator^9
197+
CX_CHECK(cx_bn_gf2_n_mul(bn_tempb, bn_tempa, bn_denominator, bn_n, bn_r2));
198+
// bn_tempa = bn_denominator^16
199+
CX_CHECK(cx_bn_gf2_n_mul(bn_tempa, bn_tempa, bn_tempa, bn_n, bn_r2));
200+
// bn_tempa = bn_denominator^25
201+
CX_CHECK(cx_bn_gf2_n_mul(bn_tempa, bn_tempa, bn_tempb, bn_n, bn_r2));
202+
// bn_tempa = bn_denominator^50
203+
CX_CHECK(cx_bn_gf2_n_mul(bn_tempa, bn_tempa, bn_tempa, bn_n, bn_r2));
204+
// bn_tempb = bn_denominator^100
205+
CX_CHECK(cx_bn_gf2_n_mul(bn_tempb, bn_tempa, bn_tempa, bn_n, bn_r2));
206+
// bn_tempb = bn_denominator^200
207+
CX_CHECK(cx_bn_gf2_n_mul(bn_tempb, bn_tempb, bn_tempb, bn_n, bn_r2));
208+
// bn_tempa = bn_denominator^250
209+
CX_CHECK(cx_bn_gf2_n_mul(bn_tempa, bn_tempa, bn_tempb, bn_n, bn_r2));
210+
// bn_denominator = bn_denominator^254
211+
CX_CHECK(cx_bn_gf2_n_mul(bn_denominator, bn_result, bn_tempa, bn_n, bn_r2));
268212

269213
// Calculate the lagrange basis coefficient
270214
CX_CHECK(cx_bn_gf2_n_mul(bn_lagrange, bn_numerator, bn_lagrange, bn_n, bn_r2));
@@ -273,12 +217,12 @@ cx_err_t interpolate(uint8_t n,
273217
}
274218

275219
for (uint8_t j = 0; j < yl; j++) {
276-
CX_CHECK(cx_bn_set_u32(bn_y, (uint32_t) yij[i][j]));
220+
CX_CHECK(cx_bn_set_u32(bn_tempa, (uint32_t) yij[i][j]));
277221
CX_CHECK(cx_bn_set_u32(bn_result, (uint32_t) result[j]));
278222

279-
CX_CHECK(cx_bn_gf2_n_mul(bn_y, bn_lagrange, bn_y, bn_n, bn_r2));
280-
CX_CHECK(cx_bn_copy(bn_temp, bn_result));
281-
CX_CHECK(cx_bn_xor(bn_result, bn_temp, bn_y));
223+
CX_CHECK(cx_bn_gf2_n_mul(bn_tempa, bn_lagrange, bn_tempa, bn_n, bn_r2));
224+
CX_CHECK(cx_bn_copy(bn_tempb, bn_result));
225+
CX_CHECK(cx_bn_xor(bn_result, bn_tempa, bn_tempb));
282226
CX_CHECK(cx_bn_get_u32(bn_result, &result_u32));
283227
result[j] = (uint8_t) result_u32;
284228
result_u32 = 0;
@@ -288,13 +232,12 @@ cx_err_t interpolate(uint8_t n,
288232
// clean up stack
289233
CX_CHECK(cx_bn_destroy(&bn_x));
290234
CX_CHECK(cx_bn_destroy(&bn_xc_i));
291-
CX_CHECK(cx_bn_destroy(&bn_xc_j));
292235
CX_CHECK(cx_bn_destroy(&bn_numerator));
293236
CX_CHECK(cx_bn_destroy(&bn_denominator));
294237
CX_CHECK(cx_bn_destroy(&bn_lagrange));
295-
CX_CHECK(cx_bn_destroy(&bn_y));
296238
CX_CHECK(cx_bn_destroy(&bn_result));
297-
CX_CHECK(cx_bn_destroy(&bn_temp));
239+
CX_CHECK(cx_bn_destroy(&bn_tempa));
240+
CX_CHECK(cx_bn_destroy(&bn_tempb));
298241
CX_CHECK(cx_bn_destroy(&bn_n));
299242
CX_CHECK(cx_bn_destroy(&bn_r2));
300243

‎src/sskr/sss/interpolate.h‎

Lines changed: 2 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -8,6 +8,8 @@
88
#ifndef INTERPOLATE_H
99
#define INTERPOLATE_H
1010

11+
#define memzero(...) explicit_bzero(__VA_ARGS__)
12+
1113
/**
1214
* @brief Performs polynomial interpolation on SSS shares.
1315
*

‎src/sskr/sss/sss.c‎

Lines changed: 0 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -11,8 +11,6 @@
1111
#include "sss.h"
1212
#include "interpolate.h"
1313

14-
#define memzero(...) explicit_bzero(__VA_ARGS__)
15-
1614
/**
1715
* @brief Validates the parameters for Shamir's Secret Sharing (SSS) functions.
1816
*

‎tests/unit/CMakeLists.txt‎

Lines changed: 3 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -46,9 +46,9 @@ function(install_apk_packages)
4646
if(${result} EQUAL 0)
4747
message(STATUS "Installed ${package} package")
4848
else()
49-
message(FATAL_ERROR "Failed to install package :${package}\n"
50-
"Command: ${output}\n"
51-
"Error: ${error}")
49+
message(FATAL_ERROR "Failed to install package: ${package}\n"
50+
"Command: ${output}\n"
51+
"Error: ${error}")
5252
endif()
5353
endforeach()
5454
endfunction()

0 commit comments

Comments
 (0)