TORTL DKG: Two-Round Trustless Distributed Key Generation

"Preview Talk" (by team Kelvin Zero) @ TCPT3, in reply to the NIST Threshold Call

Abstract: In this presentation, we describe two members of the Two-Round Trustless Distributed Key Generation (TORTL DKG) family: TORTL Elliptic Curve (TORTL-EC) and TORTL Module Lattice (TORTL-ML) DKG.  TORTL DKG leverages functional verification to minimize the size of data exchanged over the network at the end of each round. We build on top of standard secret sharing schemes and Chaum-Pedersen-type Zero Knowledge Proofs (ZKP) to construct a two-round DKG with exact interpolation and verifiable correctness and soundness. TORTL DKG's functional verifications validate whether the resulting secret sharing implements the threshold access structure for the expected threshold T and number of parties N. While this technique does not permit identifiable aborts, the protocol can only succeed if each party contributed to the secret sharing, removing the need for trust in the other parties. TORTL-EC results in a Shamir secret sharing of a joint-random elliptic curve key for P256, which is compatible with thresholdized Diffie-Hellman-based schemes. TORTL-ML results in a replicated secret sharing of a joint-random small-norm module lattice key, efficient for small T and N (single-digit parameters). The resulting secret sharing is compatible with thresholdized ML-based schemes.

Joint work: Maxime Godon, Florian Le Mouël, Nadège Pulgar-Vidal, Thierry St-Jacques-Gagnon.

Suggested readings

• Preview Writeup (PDF): TORTL DKG: Two-Round Trustless Distributed Key Generation
• Trustless Distributed Symmetric-key Encryption (arxiv:2408.16137)
• Practical post-quantum few-time verifiable random function with applications to Algorand (ia.cr/2020/1222)