wangxueli1993 / CG-MPC-ECDSA-1

Multi-Party ECDSA from Class Group

CG-MPC-ECDSA

This project aims to implement two-party and multi-party ECDSA protocols based on class group with Rust. It currently includes schemes described in [DMZ+21] (published in Asiacrypt 2021) and [XAX+21] (published in CCS 2021).

• Descriptions of the protocols are as follows:

Protocol	Introduction
[DMZ+21]	This paper proposes efficient two-party and multi-party threshold ECDSA protocols from CL encryptions based on class groups. This protocol avoids the low order assumption, which is a strong and non-standard assumption, and reduces the communication cost in keygen.
[XAX+21]	This paper proposes a framework of two-party ECDSA protocols. It seperates the signing part into online and offline phases. The online phase is non-interactive and somehow optimal, and the offline phase only needs a single call of MtA.

• We adopt CL-based MtA in [CCL+19] when implementing [XAX+21].
• We implement the refresh function. This function allows key shares to be refreshed while keeping the whole secret key (then the public key) unchanged.
• Class group library used in this project supports multi-threaded execution.

How to use

$ cargo run --bin mpc-ecdsa

USAGE:
    mpc-ecdsa <SUBCOMMAND>

FLAGS:
    -h, --help       Prints help information
    -V, --version    Prints version information

SUBCOMMANDS:
    dmz-multi-keygen    
    dmz-multi-sign      
    dmz-party-one       
    dmz-party-two       
    help                Prints this message or the help of the given subcommand(s)
    key-refresh         
    xax-party-one       
    xax-party-two

Details in: cli/README.md

Performance

Running with Intel® Core™ i7-10510U CPU @ 1.80GHz × 8.

P2P network

• Two-Party ECDSA

Protocols	KeyGen	Sign-Offline	Sign-Online
[DMZ+21]	1276ms	384ms	169ms
[XAX+21]	12ms	1698ms	1.5ms

• Multi-Party ECDSA

(t, n)	KeyGen	Sign-Offline	Sign-Online
(1,3)	371ms	1593ms	6.1ms
(2, 4)	426ms	4318ms	14ms
(3, 5)	510ms	5065ms	19ms

Local

• Two-Party ECDSA

Protocols	KeyGen	Sign-Offline	Sign-Online
[DMZ+21]	1260 ms	357ms	142ms
[XAX+21]	11 ms	1797ms	0.1ms

• Multi-Party ECDSA

(t, n)	KeyGen	Sign-Offline	Sign-Online
(1,3)	289ms	1503ms	0.8ms
(2, 4)	345ms	3590ms	1.2ms
(3, 5)	382ms	4681ms	1.6ms

References

[DMZ+21] https://eprint.iacr.org/2022/297

[XAX+21] https://eprint.iacr.org/2022/318

[CCL+19] https://eprint.iacr.org/2019/503