Digital signing by utilizing multiple distinct signing keys, distributed between two parties
Described herein is a method and system for digital signing by utilizing Elliptic Curve Digital Signature Algorithm (ECDSA) with a group generator of an elliptic-curve group of order q, and an elliptic curve point Q. The method may be configured to receive a digital message and associated with a request from a third-party in order to sign the digital message. The system designed to sign such messages may comprise two parties denoted P 1 and P 2 configured to conduct a multiparty signing procedure by utilizing ECDSA. The digital signing procedure may follow preliminary steps configured to set the system with the necessary conditions for the multiparty signing procedure. Such preliminary steps may set the parties P 1 , and P 2 , in accordance with the configuration defined herein.
1. A method for digital signing by utilizing ECDSA with a group generator of an elliptic-curve group of order q, and an elliptic curve point Q, comprising: receiving a digital message and a request from a third-party to sign said digital message by two parties denoted P 1 and P 2 configured to perform digital signing by utilizing ECDSA, wherein:
(i) P 1 holds a first random share set to compute a first point on said elliptic curve, a public key and a private key of an additively homomorphic encryption scheme, the elliptic curve point Q,
(ii) P 2 holds a second random share, set to generate a second point on said elliptic curve, said public key, and a cipher text created by encrypting said first random share with said public key, the elliptic curve point Q,
creating a hash value of the digital message using a hash function applied by P 1 , and creating a hash value of the digital message with said hash function applied by P 2 ;
performing a digital signing procedure by P 1 and P 2 , wherein said digital signing procedure comprises:
using a random value K 1 chosen by P 1 to compute an elliptic curve point R 1 on said elliptic curve,
sending elliptic curve point R 1 from P 1 to P 2 ,
using a random value K 2 chosen by P 2 to compute an elliptic curve point R 2 ,
utilizing elliptic curve point R 1 and random value K 2 by P 2 to compute an elliptic curve point R,
using additive homomorphic scheme by P 2 to compute a value C, wherein said value C comprising: the hash value of the digital message, first random share, second random share, random value K 1 , random value K 2 and a random value chosen by P 2 , and wherein value C is encrypted with said public key,
sending value C from P 2 to P 1 ,
decrypting value C with the private key by P 1 , and utilizing the content in value C to produce a digital signature of the digital message;
sending the digital signature of the digital message and the hash value of the digital message to the third-party.
2. The method of claim 1 , wherein the digital message and the request from the third-party also comprise a session ID.
3. The method of claim 1 , wherein the first random share is not exposed to P 2 in a nonencrypted format during the signing process.
4. The method of claim 1 , wherein the second random share was not exposed to P 1 in a nonencrypted format during the signing process.
5. The method of claim 1 , wherein the hash value is created independently by P 1 with the one hash function.
6. The method of claim 1 , wherein the hash value is created independently by P 2 with the one hash function.
7. The method of claim 1 , wherein the digital signature of the digital message is sent by P 1 .
8. The method of claim 1 , wherein the additive homomorphic scheme is based on implementation of lattice-based scheme.
9. The method of claim 1 , wherein the additive homomorphic scheme is based on Paillier encryption scheme.