To prove the graph relations such as the connectivity and isolation for a certified graph, a system of a graph signature and proofs has been proposed. In this system, an issuer generates a signature certifying the topology of an undirected graph, and issues the signature to a prover. The prover can prove the knowledge of the signature and the graph in the zero-knowledge, i.e., the signature and the signed graph are hidden. In addition, the prover can prove relations on the certified graph such as the connectivity and isolation between two vertexes. In the previous system, using integer commitments on RSA modulus, the graph relations are proved. However, the RSA modulus needs a longer size for each element. Furthermore, the proof size and verification cost depend on the total numbers of vertexes and edges. In this paper, we propose a graph signature and proof system, where these are computed on bilinear groups without the RSA modulus. Moreover, using a bilinear map accumulator, the prover can prove the connectivity and isolation on a graph, where the proof size and verification cost become independent from the total numbers of vertexes and edges.
Toru NAKANISHI
Hiroshima University
Hiromi YOSHINO
Hiroshima University
Tomoki MURAKAMI
Hiroshima University
Guru-Vamsi POLICHARLA
Indian Institute of Technology
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Toru NAKANISHI, Hiromi YOSHINO, Tomoki MURAKAMI, Guru-Vamsi POLICHARLA, "Efficient Zero-Knowledge Proofs of Graph Signature for Connectivity and Isolation Using Bilinear-Map Accumulator" in IEICE TRANSACTIONS on Fundamentals,
vol. E105-A, no. 3, pp. 389-403, March 2022, doi: 10.1587/transfun.2021TAP0003.
Abstract: To prove the graph relations such as the connectivity and isolation for a certified graph, a system of a graph signature and proofs has been proposed. In this system, an issuer generates a signature certifying the topology of an undirected graph, and issues the signature to a prover. The prover can prove the knowledge of the signature and the graph in the zero-knowledge, i.e., the signature and the signed graph are hidden. In addition, the prover can prove relations on the certified graph such as the connectivity and isolation between two vertexes. In the previous system, using integer commitments on RSA modulus, the graph relations are proved. However, the RSA modulus needs a longer size for each element. Furthermore, the proof size and verification cost depend on the total numbers of vertexes and edges. In this paper, we propose a graph signature and proof system, where these are computed on bilinear groups without the RSA modulus. Moreover, using a bilinear map accumulator, the prover can prove the connectivity and isolation on a graph, where the proof size and verification cost become independent from the total numbers of vertexes and edges.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021TAP0003/_p
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@ARTICLE{e105-a_3_389,
author={Toru NAKANISHI, Hiromi YOSHINO, Tomoki MURAKAMI, Guru-Vamsi POLICHARLA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Efficient Zero-Knowledge Proofs of Graph Signature for Connectivity and Isolation Using Bilinear-Map Accumulator},
year={2022},
volume={E105-A},
number={3},
pages={389-403},
abstract={To prove the graph relations such as the connectivity and isolation for a certified graph, a system of a graph signature and proofs has been proposed. In this system, an issuer generates a signature certifying the topology of an undirected graph, and issues the signature to a prover. The prover can prove the knowledge of the signature and the graph in the zero-knowledge, i.e., the signature and the signed graph are hidden. In addition, the prover can prove relations on the certified graph such as the connectivity and isolation between two vertexes. In the previous system, using integer commitments on RSA modulus, the graph relations are proved. However, the RSA modulus needs a longer size for each element. Furthermore, the proof size and verification cost depend on the total numbers of vertexes and edges. In this paper, we propose a graph signature and proof system, where these are computed on bilinear groups without the RSA modulus. Moreover, using a bilinear map accumulator, the prover can prove the connectivity and isolation on a graph, where the proof size and verification cost become independent from the total numbers of vertexes and edges.},
keywords={},
doi={10.1587/transfun.2021TAP0003},
ISSN={1745-1337},
month={March},}
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TY - JOUR
TI - Efficient Zero-Knowledge Proofs of Graph Signature for Connectivity and Isolation Using Bilinear-Map Accumulator
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 389
EP - 403
AU - Toru NAKANISHI
AU - Hiromi YOSHINO
AU - Tomoki MURAKAMI
AU - Guru-Vamsi POLICHARLA
PY - 2022
DO - 10.1587/transfun.2021TAP0003
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E105-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 2022
AB - To prove the graph relations such as the connectivity and isolation for a certified graph, a system of a graph signature and proofs has been proposed. In this system, an issuer generates a signature certifying the topology of an undirected graph, and issues the signature to a prover. The prover can prove the knowledge of the signature and the graph in the zero-knowledge, i.e., the signature and the signed graph are hidden. In addition, the prover can prove relations on the certified graph such as the connectivity and isolation between two vertexes. In the previous system, using integer commitments on RSA modulus, the graph relations are proved. However, the RSA modulus needs a longer size for each element. Furthermore, the proof size and verification cost depend on the total numbers of vertexes and edges. In this paper, we propose a graph signature and proof system, where these are computed on bilinear groups without the RSA modulus. Moreover, using a bilinear map accumulator, the prover can prove the connectivity and isolation on a graph, where the proof size and verification cost become independent from the total numbers of vertexes and edges.
ER -