secp256k1-zkp/src/modules/rangeproof/pedersen.h

/**********************************************************************
 * Copyright (c) 2014, 2015 Gregory Maxwell                          *
 * Distributed under the MIT software license, see the accompanying   *
 * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
 **********************************************************************/

#ifndef _SECP256K1_PEDERSEN_H_
#define _SECP256K1_PEDERSEN_H_

#include "group.h"
#include "scalar.h"

#include <stdint.h>

/** Multiply a small number with the generator: r = gn*G2 */
static void secp256k1_pedersen_ecmult_small(secp256k1_gej *r, uint64_t gn);

/* sec * G + value * G2. */
static void secp256k1_pedersen_ecmult(const secp256k1_ecmult_gen_context *ecmult_gen_ctx, secp256k1_gej *rj, const secp256k1_scalar *sec, uint64_t value);

#endif
Pedersen commitments, borromean ring signatures, and ZK range proofs. This commit adds three new cryptosystems to libsecp256k1: Pedersen commitments are a system for making blinded commitments to a value. Functionally they work like: commit_b,v = H(blind_b \|\| value_v), except they are additively homorphic, e.g. C(b1, v1) - C(b2, v2) = C(b1 - b2, v1 - v2) and C(b1, v1) - C(b1, v1) = 0, etc. The commitments themselves are EC points, serialized as 33 bytes. In addition to the commit function this implementation includes utility functions for verifying that a set of commitments sums to zero, and for picking blinding factors that sum to zero. If the blinding factors are uniformly random, pedersen commitments have information theoretic privacy. Borromean ring signatures are a novel efficient ring signature construction for AND/OR admissions policies (the code here implements an AND of ORs, each of any size). This construction requires 32 bytes of signature per pubkey used plus 32 bytes of constant overhead. With these you can construct signatures like "Given pubkeys A B C D E F G, the signer knows the discrete logs satisifying (A \|\| B) & (C \|\| D \|\| E) & (F \|\| G)". ZK range proofs allow someone to prove a pedersen commitment is in a particular range (e.g. [0..2^64)) without revealing the specific value. The construction here is based on the above borromean ring signature and uses a radix-4 encoding and other optimizations to maximize efficiency. It also supports encoding proofs with a non-private base-10 exponent and minimum-value to allow trading off secrecy for size and speed (or just avoiding wasting space keeping data private that was already public due to external constraints). A proof for a 32-bit mantissa takes 2564 bytes, but 2048 bytes of this can be used to communicate a private message to a receiver who shares a secret random seed with the prover. Also: get rid of precomputed H tables (Pieter Wuille) 2015-08-05 19:04:14 +02:00			`/**********************************************************************`
			`* Copyright (c) 2014, 2015 Gregory Maxwell *`
			`* Distributed under the MIT software license, see the accompanying *`
			`* file COPYING or http://www.opensource.org/licenses/mit-license.php.*`
			`**********************************************************************/`

			`#ifndef _SECP256K1_PEDERSEN_H_`
			`#define _SECP256K1_PEDERSEN_H_`

			`#include "group.h"`
			`#include "scalar.h"`

			`#include <stdint.h>`

			`/** Multiply a small number with the generator: r = gnG2 /`
			`static void secp256k1_pedersen_ecmult_small(secp256k1_gej *r, uint64_t gn);`

			`/* sec * G + value * G2. */`
			`static void secp256k1_pedersen_ecmult(const secp256k1_ecmult_gen_context ecmult_gen_ctx, secp256k1_gej rj, const secp256k1_scalar *sec, uint64_t value);`

			`#endif`