2G2T: Constant-Size, Statistically Sound MSM Outsourcing

Cryptographer Majid Khabbazian has introduced 2G2T, a groundbreaking protocol for verifiably outsourcing multi-scalar multiplication (MSM) operations to potentially untrusted servers. MSM calculations, defined as MSM(P, x) = sum_{i=1}^n x_i P_i, represent a fundamental bottleneck in discrete-logarithm-based cryptography, particularly for verifiers and resource-constrained clients in systems like zero-knowledge proofs and blockchain applications. The protocol's key innovation lies in its constant-size proofs and statistical soundness guarantees, allowing clients to securely delegate computationally intensive operations while maintaining cryptographic integrity.

The 2G2T protocol operates through a one-time keyed setup that produces a public merged-bases vector T and client secret state. For each query, the server returns just two group elements—a claimed result A and auxiliary value B—totaling only 64 bytes in Ristretto255 implementations. Verification requires merely a single length-n field inner product and constant group operations (two scalar multiplications and one addition), while the server performs two MSMs. This architecture enables verification speeds up to 300x faster than local computation for n up to 262,144, with statistical soundness ensuring error probability remains at most 1/q per query in prime-order groups. The protocol's efficiency breakthrough could revolutionize how lightweight devices participate in complex cryptographic ecosystems.