Aggregated Set Membership Proofs: Aggregated Signature-Based Set Membership Proofs and implementation in Client and Server Verifiable Additive Homomorphic Secret Sharing
Examensarbete för masterexamen
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|Type: ||Examensarbete för masterexamen|
|Title: ||Aggregated Set Membership Proofs: Aggregated Signature-Based Set Membership Proofs and implementation in Client and Server Verifiable Additive Homomorphic Secret Sharing|
|Authors: ||Ek, Hanna|
|Abstract: ||This thesis addresses the issue of inflated computational complexity for the verification
of multiple zero-knowledge proofs. More precisely, verification of numerous
zero-knowledge set membership proofs performed by a single verifier is considered.
To reduce the computations required by such a verifier Aggregated Set Membership
Proofs are introduced.
Aggregated set membership proofs unifies multiple set membership proofs into one
aggregated proof, such that the validity of the aggregated proof implies the validity
of all individual proofs. Completeness, soundness and zero-knowledge requirements
are established for zero-knowledge aggregated set membership proofs.
A concrete construction of aggregated set membership proofs is presented and proved
to satisfy the completeness, soundness and zero-knowledge requirements. The construction
is a partial aggregation of signature-based set membership proofs, , and
is referred to as aggregated signature-based set membership proofs.
A general technique to verify clients in verifiable additive homomorphic secret sharing
is derived. The clients are verified by computing zero-knowledge proofs, derived
from Pedersen commitments, of some given statement and then the proofs are validated
by a verifier. If the proved statement is that the shared secrets belong to a
discrete set, clients construct set membership proofs. Usually, several clients participate
in verifiable additive homomorphic secret sharing protocols resulting in that
the verification of clients is computationally expensive.
A prototype implementation considering 100 clients showed that the runtime for verification
of clients was reduced by 13% when verifying an aggregated signature-based
set membership proof compared to verifying the same proofs without performing the
|Keywords: ||Aggregated Set Membership Proofs;Zero-knowledge proofs;VAHSS;cryptography|
|Issue Date: ||2021|
|Publisher: ||Chalmers tekniska högskola / Institutionen för data och informationsteknik|
|Collection:||Examensarbeten för masterexamen // Master Theses|
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