Paper
2G2T: Constant-Size, Statistically Sound MSM Outsourcing
Authors
Majid Khabbazian
Abstract
Multi-scalar multiplication (MSM), defined as MSM(P, x) = sum_{i=1}^n x_i P_i, is a dominant computational kernel in discrete-logarithm-based cryptography and often becomes a bottleneck for verifiers and other resource-constrained clients. We present 2G2T, a simple protocol for verifiably outsourcing MSM to an untrusted server. After a one-time keyed setup for fixed bases P = (P1, ..., Pn) that produces a public merged-bases vector T and client secret state, the server answers each query x = (x1, ..., xn) with only two group elements: A claimed to equal MSM(P, x) and an auxiliary value B claimed to equal MSM(T, x). Verification requires a single length-n field inner product and a constant number of group operations (two scalar multiplications and one addition), while the server performs two MSMs. In our Ristretto255 implementation, verification is up to ~300x faster than computing the MSM locally using a highly optimized MSM routine for n up to 2^18, and the server-to-client response is constant-size (two compressed group elements, 64 bytes on Ristretto255). Despite its simplicity and efficiency, 2G2T achieves statistical soundness: for any (even computationally unbounded) adversarial server, the probability of accepting an incorrect result is at most 1/q per query, and at most e/q over e adaptive executions, in a prime-order group of size q.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2602.23464v1</id>\n <title>2G2T: Constant-Size, Statistically Sound MSM Outsourcing</title>\n <updated>2026-02-26T19:44:37Z</updated>\n <link href='https://arxiv.org/abs/2602.23464v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2602.23464v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>Multi-scalar multiplication (MSM), defined as MSM(P, x) = sum_{i=1}^n x_i P_i, is a dominant computational kernel in discrete-logarithm-based cryptography and often becomes a bottleneck for verifiers and other resource-constrained clients. We present 2G2T, a simple protocol for verifiably outsourcing MSM to an untrusted server. After a one-time keyed setup for fixed bases P = (P1, ..., Pn) that produces a public merged-bases vector T and client secret state, the server answers each query x = (x1, ..., xn) with only two group elements: A claimed to equal MSM(P, x) and an auxiliary value B claimed to equal MSM(T, x). Verification requires a single length-n field inner product and a constant number of group operations (two scalar multiplications and one addition), while the server performs two MSMs. In our Ristretto255 implementation, verification is up to ~300x faster than computing the MSM locally using a highly optimized MSM routine for n up to 2^18, and the server-to-client response is constant-size (two compressed group elements, 64 bytes on Ristretto255). Despite its simplicity and efficiency, 2G2T achieves statistical soundness: for any (even computationally unbounded) adversarial server, the probability of accepting an incorrect result is at most 1/q per query, and at most e/q over e adaptive executions, in a prime-order group of size q.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.CR'/>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.DC'/>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.DS'/>\n <published>2026-02-26T19:44:37Z</published>\n <arxiv:comment>18 pages, 1 figure</arxiv:comment>\n <arxiv:primary_category term='cs.CR'/>\n <author>\n <name>Majid Khabbazian</name>\n </author>\n </entry>"
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