Elligator Squared module

This adds a module with an implementation of the Elligator Squared
algorithm for encoding/decoding public keys in uniformly random
byte arrays.

Author: sipa

Makefile.am

@@ -173,3 +173,7 @@ endif
 if ENABLE_MODULE_SCHNORRSIG
 include src/modules/schnorrsig/Makefile.am.include
 endif
+
+if ENABLE_MODULE_ELLSQ
+include src/modules/ellsq/Makefile.am.include
+endif

configure.ac

@@ -161,6 +161,11 @@ AC_ARG_ENABLE(module_schnorrsig,
     [enable_module_schnorrsig=$enableval],
     [enable_module_schnorrsig=no])
 
+AC_ARG_ENABLE(module_ellsq,
+    AS_HELP_STRING([--enable-module-ellsq],[enable Elligator^2 module (experimental)]),
+    [enable_module_ellsq=$enableval],
+    [enable_module_ellsq=no])
+
 AC_ARG_ENABLE(external_default_callbacks,
     AS_HELP_STRING([--enable-external-default-callbacks],[enable external default callback functions [default=no]]),
     [use_external_default_callbacks=$enableval],
@@ -456,6 +461,10 @@ if test x"$enable_module_extrakeys" = x"yes"; then
   AC_DEFINE(ENABLE_MODULE_EXTRAKEYS, 1, [Define this symbol to enable the extrakeys module])
 fi
 
+if test x"$enable_module_ellsq" = x"yes"; then
+  AC_DEFINE(ENABLE_MODULE_ELLSQ, 1, [Define this symbol to enable the Elligator^2 module])
+fi
+
 if test x"$use_external_default_callbacks" = x"yes"; then
   AC_DEFINE(USE_EXTERNAL_DEFAULT_CALLBACKS, 1, [Define this symbol if an external implementation of the default callbacks is used])
 fi
@@ -470,6 +479,7 @@ if test x"$enable_experimental" = x"yes"; then
   AC_MSG_NOTICE([Experimental features do not have stable APIs or properties, and may not be safe for production use.])
   AC_MSG_NOTICE([Building extrakeys module: $enable_module_extrakeys])
   AC_MSG_NOTICE([Building schnorrsig module: $enable_module_schnorrsig])
+  AC_MSG_NOTICE([Building Elligator^2 module: $enable_module_ellsq])
   AC_MSG_NOTICE([******])
 else
   if test x"$enable_module_extrakeys" = x"yes"; then
@@ -478,6 +488,9 @@ else
   if test x"$enable_module_schnorrsig" = x"yes"; then
     AC_MSG_ERROR([schnorrsig module is experimental. Use --enable-experimental to allow.])
   fi
+  if test x"$enable_module_ellsq" = x"yes"; then
+    AC_MSG_ERROR([Elligator^2 module is experimental. Use --enable-experimental to allow.])
+  fi
   if test x"$set_asm" = x"arm"; then
     AC_MSG_ERROR([ARM assembly optimization is experimental. Use --enable-experimental to allow.])
   fi
@@ -503,6 +516,7 @@ AM_CONDITIONAL([ENABLE_MODULE_ECDH], [test x"$enable_module_ecdh" = x"yes"])
 AM_CONDITIONAL([ENABLE_MODULE_RECOVERY], [test x"$enable_module_recovery" = x"yes"])
 AM_CONDITIONAL([ENABLE_MODULE_EXTRAKEYS], [test x"$enable_module_extrakeys" = x"yes"])
 AM_CONDITIONAL([ENABLE_MODULE_SCHNORRSIG], [test x"$enable_module_schnorrsig" = x"yes"])
+AM_CONDITIONAL([ENABLE_MODULE_ELLSQ], [test x"$enable_module_ellsq" = x"yes"])
 AM_CONDITIONAL([USE_EXTERNAL_ASM], [test x"$use_external_asm" = x"yes"])
 AM_CONDITIONAL([USE_ASM_ARM], [test x"$set_asm" = x"arm"])
 
@@ -525,6 +539,7 @@ echo "  module ecdh             = $enable_module_ecdh"
 echo "  module recovery         = $enable_module_recovery"
 echo "  module extrakeys        = $enable_module_extrakeys"
 echo "  module schnorrsig       = $enable_module_schnorrsig"
+echo "  module ellsq            = $enable_module_ellsq"
 echo
 echo "  asm                     = $set_asm"
 echo "  ecmult window size      = $set_ecmult_window"

include/secp256k1_ellsq.h

@@ -0,0 +1,78 @@
+#ifndef SECP256K1_ELLSQ_H
+#define SECP256K1_ELLSQ_H
+
+#include "secp256k1.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* This module provides an implementation of the Elligator Squared encoding
+ * for secp256k1 public keys. Given a uniformly random public key, this
+ * produces a 64-byte encoding that is indistinguishable from uniformly
+ * random bytes.
+ *
+ * Elligator Squared is described in https://eprint.iacr.org/2014/043.pdf by
+ * Mehdi Tibouchi. The mapping function used is described in
+ * https://www.di.ens.fr/~fouque/pub/latincrypt12.pdf by Fouque and Tibouchi.
+ *
+ * Let f be the function from field elements to curve points, defined as
+ * follows:
+ * f(t):
+ * - Let c = 0xa2d2ba93507f1df233770c2a797962cc61f6d15da14ecd47d8d27ae1cd5f852
+ * - Let x1 = (c - 1)/2 - c*t^2 / (t^2 + 8) (mod p)
+ * - Let x2 = (-c - 1)/2 + c*t^2 / (t^2 + 8) (mod p)
+ * - Let x3 = 1 - (t^2 + 8)^2 / (3*t^2) (mod p)
+ * - Let x be the first of [x1,x2,x3] that is an X coordinate on the curve
+ *   (at least one of them is, for any field element t).
+ * - Let y be the the corresponding Y coordinate to x, with the same parity
+ *   as t (even if t is even, odd if t is odd).
+ * - Return the curve point with coordinates (x, y).
+ *
+ * Then an Elligator Squared encoding of P consists of the 32-byte big-endian
+ * encodings of field elements u1 and u2 concatenated, where f(u1)+f(u2) = P.
+ * The encoding algorithm is described in the paper, and effectively picks a
+ * uniformly random pair (u1,u2) among those which encode P.
+ *
+ * To make the encoding able to deal with all inputs, if f(u1)+f(u2) is the
+ * point at infinity, the decoding is defined to be f(0) instead.
+ */
+
+/* Construct a 64-byte Elligator Squared encoding of a given pubkey.
+ *
+ *  Returns: 1 when pubkey is valid.
+ *  Args:    ctx:        pointer to a context object
+ *  Out:     ell64:      pointer to a 64-byte array to be filled
+ *  In:      rnd32:      pointer to 32 bytes of entropy (must be unpredictable)
+ *           pubkey:     a pointer to a secp256k1_pubkey containing an
+ *                       initialized public key
+ *
+ * This function runs in variable time.
+ */
+SECP256K1_API int secp256k1_ellsq_encode(
+    const secp256k1_context* ctx,
+    unsigned char *ell64,
+    const unsigned char *rnd32,
+    const secp256k1_pubkey *pubkey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Decode a 64-bytes Elligator Squared encoded public key.
+ *
+ *  Returns: always 1
+ *  Args:    ctx:        pointer to a context object
+ *  Out:     pubkey:     pointer to a secp256k1_pubkey that will be filled
+ *  In:      ell64:      pointer to a 64-byte array to decode
+ *
+ * This function runs in variable time.
+ */
+SECP256K1_API int secp256k1_ellsq_decode(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *pubkey,
+    const unsigned char *ell64
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* SECP256K1_ELLSQ_H */

src/bench_ellsq.c

@@ -0,0 +1,70 @@
+/***********************************************************************
+ * Copyright (c) 2021 Pieter Wuille                                    *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#include <string.h>
+
+#include "../include/secp256k1.h"
+#include "../include/secp256k1_ellsq.h"
+#include "util.h"
+#include "bench.h"
+
+typedef struct {
+    secp256k1_context *ctx;
+    secp256k1_pubkey point;
+    unsigned char rnd64[64];
+} bench_ellsq_data;
+
+static void bench_ellsq_setup(void* arg) {
+    bench_ellsq_data *data = (bench_ellsq_data*)arg;
+    const unsigned char point[] = {
+        0x03,
+        0x54, 0x94, 0xc1, 0x5d, 0x32, 0x09, 0x97, 0x06,
+        0xc2, 0x37, 0x5f, 0x94, 0x34, 0x87, 0x45, 0xfd,
+        0x75, 0x7c, 0xe3, 0x0e, 0x4e, 0x8c, 0x90, 0xfb,
+        0xa2, 0xba, 0xd1, 0x84, 0xf8, 0x83, 0xc6, 0x9f
+    };
+    CHECK(secp256k1_ec_pubkey_parse(data->ctx, &data->point, point, sizeof(point)) == 1);
+}
+
+static void bench_ellsq_encode(void* arg, int iters) {
+    int i;
+    bench_ellsq_data *data = (bench_ellsq_data*)arg;
+
+    for (i = 0; i < iters; i++) {
+        data->rnd64[29] ^= 145;
+        CHECK(secp256k1_ellsq_encode(data->ctx, data->rnd64, data->rnd64 + 16, &data->point) == 1);
+    }
+}
+
+static void bench_ellsq_decode(void* arg, int iters) {
+    int i;
+    secp256k1_pubkey out;
+    bench_ellsq_data *data = (bench_ellsq_data*)arg;
+
+    for (i = 0; i < iters; i++) {
+        data->rnd64[13] ^= 247;
+        data->rnd64[47] ^= 113;
+        CHECK(secp256k1_ellsq_decode(data->ctx, &out, data->rnd64) == 1);
+        memcpy(data->rnd64, &out.data, 64);
+    }
+}
+
+int main(void) {
+    bench_ellsq_data data;
+
+    int iters = get_iters(10000);
+
+    /* create a context with no capabilities */
+    data.ctx = secp256k1_context_create(SECP256K1_FLAGS_TYPE_CONTEXT);
+    memset(data.rnd64, 11, sizeof(data.rnd64));
+
+    run_benchmark("ellsq_encode", bench_ellsq_encode, bench_ellsq_setup, NULL, &data, 10, iters);
+    run_benchmark("ellsq_decode", bench_ellsq_decode, bench_ellsq_setup, NULL, &data, 10, iters);
+
+    secp256k1_context_destroy(data.ctx);
+
+    return 0;
+}

src/modules/ellsq/Makefile.am.include

@@ -0,0 +1,8 @@
+include_HEADERS += include/secp256k1_ellsq.h
+noinst_HEADERS += src/modules/ellsq/main_impl.h
+noinst_HEADERS += src/modules/ellsq/tests_impl.h
+if USE_BENCHMARK
+noinst_PROGRAMS += bench_ellsq
+bench_ellsq_SOURCES = src/bench_ellsq.c
+bench_ellsq_LDADD = libsecp256k1.la $(SECP_LIBS) $(COMMON_LIB)
+endif