Computer implemented method and system for knowledge proof in blockchain transactions
A method of enabling knowledge proof in a blockchain transaction is disclosed. The method comprises sending, from a verifier to a prover, a blockchain transaction redeemable by means of data including (i) first data (y) based on a combination of an ephemeral key (r), second data (c) and a private key of a public-private key pair of a cryptography system, wherein the public key (v) is based on an integer generator raised to a first power, wherein the first power is based on the private key, and wherein knowledge of the private key is required in order to determine the ephemeral key from the first data, and (ii) third data (x) based on the integer generator raised to a second power, wherein the second power is based on the ephemeral key.
1. A method of enabling knowledge proof in a blockchain transaction, the method comprising:
generating, at a verifier computing system, a first blockchain transaction comprising a locking script, the locking script comprising:
(i) fourth data based on a public key of a public-private key pair of a cryptography system,
(ii) second data, and
(iii) a prime number shared between the verifier computing system and a prover computing system that are outside of a blockchain network, and wherein the prime number is used in computation of intermediate results to validate the first blockchain transaction;
wherein the first blockchain transaction is redeemable by means of a second blockchain transaction comprising an unlocking script, the unlocking script including:
(i) first data based on a combination of an ephemeral key, the second data and a private key of the public-private key pair of the cryptography system, wherein the public key of the public-private key pair of the cryptography system is based on an integer generator raised to a first power, wherein the first power is based on the private key, and
(ii) third data based on the integer generator raised to a second power that is different than the first power, wherein the second power is based on the ephemeral key;
transmitting, by the verifier computing system, the first blockchain transaction to the blockchain network for validation; and
responsive to receiving an indication of a success validation of the first blockchain transaction by the blockchain network, generating the second blockchain transaction to enable redemption of the first blockchain transaction on the blockchain network, the second blockchain transaction being generated by the prover computing system and the redemption of the first blockchain transaction is performed on the blockchain network based on modular arithmetic operations,
wherein execution of the locking and unlocking scripts on the blockchain network functions as a proof of knowledge that the prover computing system possesses the private key of the public-private key pair, and
wherein the public key, components of the first data, the fourth data, and the intermediate results are pre-computed off-chain.
2. The method according to claim 1 , wherein the integer generator is 2.
3. The method according to claim 1 , wherein the second data is provided by the verifier computing system.
4. The method according to claim 1 , further comprising:
sending, at the verifier computing system, the second data to the prover computing system separately from the first blockchain transaction.
5. The method according to claim 1 , wherein the first data is of the form:
y=r+s·c mod q,
where y is the first data, r is the ephemeral key, s the private key, c is the second data and q is prime.
6. The method according to claim 1 , wherein the second data is provided based on a message.
7. The method according to claim 6 , wherein the message includes data for implementing a smart contract.
8. The method according to claim 6 , wherein the second data is of the form:
c=H ( x∥m )mod q
where c is the second data, x is the third data, m is the message, q is prime and H is a hash function.
9. The method according to claim 6 , further comprising:
receiving, at the verifier computing system, the message.
10. The method according to claim 1 , wherein the ephemeral key is shared between the verifier and the prover computing systems.
11. The method according to claim 1 , further comprising:
receiving, by the verifier computing system, said public key.
12. The method according to claim 1 , further comprising:
receiving, by the verifier computing system, said first data and said second data.