Short Lattice Signature Scheme with Tighter Reduction under Ring-SIS Assumption

Kaisei KAJITA; Go OHTAKE; Kazuto OGAWA; Koji NUIDA; Tsuyoshi TAKAGI

doi:10.1587/transfun.2022CIP0017

Short Lattice Signature Scheme with Tighter Reduction under Ring-SIS Assumption

Kaisei KAJITA, Go OHTAKE, Kazuto OGAWA, Koji NUIDA, Tsuyoshi TAKAGI

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Summary :

We propose a short signature scheme under the ring-SIS assumption in the standard model. Specifically, by revisiting an existing construction [Ducas and Micciancio, CRYPTO 2014], we demonstrate lattice-based signatures with improved reduction loss. As far as we know, there are no ways to use multiple tags in the signature simulation of security proof in the lattice tag-based signatures. We address the tag-collision possibility in the lattice setting, which improves reduction loss. Our scheme generates tags from messages by constructing a scheme under a mild security condition that is existentially unforgeable against random message attack with auxiliary information. Thus our scheme can reduce the signature size since it does not need to send tags with the signatures. Our scheme has short signature sizes of O(1) and achieves tighter reduction loss than that of Ducas et al.'s scheme. Our proposed scheme has two variants. Our scheme with one property has tighter reduction and the same verification key size of O(log n) as that of Ducas et al.'s scheme, where n is the security parameter. Our scheme with the other property achieves much tighter reduction loss of O(Q/n) and verification key size of O(n), where Q is the number of signing queries.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E106-A No.3 pp.228-240

Publication Date: 2023/03/01

Publicized: 2022/09/08

Online ISSN: 1745-1337

DOI: 10.1587/transfun.2022CIP0017

Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)

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Authors

Kaisei KAJITA
  Japan Broadcasting Corporation
Go OHTAKE
  Japan Broadcasting Corporation
Kazuto OGAWA
  Japan Broadcasting Corporation
Koji NUIDA
  Kyushu University
Tsuyoshi TAKAGI
  The University of Tokyo

Keyword

digital signatures, ring-SIS assumption, security reduction, trapdoor commitment

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Kaisei KAJITA, Go OHTAKE, Kazuto OGAWA, Koji NUIDA, Tsuyoshi TAKAGI, "Short Lattice Signature Scheme with Tighter Reduction under Ring-SIS Assumption" in IEICE TRANSACTIONS on Fundamentals, vol. E106-A, no. 3, pp. 228-240, March 2023, doi: 10.1587/transfun.2022CIP0017.
Abstract: We propose a short signature scheme under the ring-SIS assumption in the standard model. Specifically, by revisiting an existing construction [Ducas and Micciancio, CRYPTO 2014], we demonstrate lattice-based signatures with improved reduction loss. As far as we know, there are no ways to use multiple tags in the signature simulation of security proof in the lattice tag-based signatures. We address the tag-collision possibility in the lattice setting, which improves reduction loss. Our scheme generates tags from messages by constructing a scheme under a mild security condition that is existentially unforgeable against random message attack with auxiliary information. Thus our scheme can reduce the signature size since it does not need to send tags with the signatures. Our scheme has short signature sizes of O(1) and achieves tighter reduction loss than that of Ducas et al.'s scheme. Our proposed scheme has two variants. Our scheme with one property has tighter reduction and the same verification key size of O(log n) as that of Ducas et al.'s scheme, where n is the security parameter. Our scheme with the other property achieves much tighter reduction loss of O(Q/n) and verification key size of O(n), where Q is the number of signing queries.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2022CIP0017/_p

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@ARTICLE{e106-a_3_228,
author={Kaisei KAJITA, Go OHTAKE, Kazuto OGAWA, Koji NUIDA, Tsuyoshi TAKAGI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Short Lattice Signature Scheme with Tighter Reduction under Ring-SIS Assumption},
year={2023},
volume={E106-A},
number={3},
pages={228-240},
abstract={We propose a short signature scheme under the ring-SIS assumption in the standard model. Specifically, by revisiting an existing construction [Ducas and Micciancio, CRYPTO 2014], we demonstrate lattice-based signatures with improved reduction loss. As far as we know, there are no ways to use multiple tags in the signature simulation of security proof in the lattice tag-based signatures. We address the tag-collision possibility in the lattice setting, which improves reduction loss. Our scheme generates tags from messages by constructing a scheme under a mild security condition that is existentially unforgeable against random message attack with auxiliary information. Thus our scheme can reduce the signature size since it does not need to send tags with the signatures. Our scheme has short signature sizes of O(1) and achieves tighter reduction loss than that of Ducas et al.'s scheme. Our proposed scheme has two variants. Our scheme with one property has tighter reduction and the same verification key size of O(log n) as that of Ducas et al.'s scheme, where n is the security parameter. Our scheme with the other property achieves much tighter reduction loss of O(Q/n) and verification key size of O(n), where Q is the number of signing queries.},
keywords={},
doi={10.1587/transfun.2022CIP0017},
ISSN={1745-1337},
month={March},}

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TY - JOUR
TI - Short Lattice Signature Scheme with Tighter Reduction under Ring-SIS Assumption
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 228
EP - 240
AU - Kaisei KAJITA
AU - Go OHTAKE
AU - Kazuto OGAWA
AU - Koji NUIDA
AU - Tsuyoshi TAKAGI
PY - 2023
DO - 10.1587/transfun.2022CIP0017
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E106-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 2023
AB - We propose a short signature scheme under the ring-SIS assumption in the standard model. Specifically, by revisiting an existing construction [Ducas and Micciancio, CRYPTO 2014], we demonstrate lattice-based signatures with improved reduction loss. As far as we know, there are no ways to use multiple tags in the signature simulation of security proof in the lattice tag-based signatures. We address the tag-collision possibility in the lattice setting, which improves reduction loss. Our scheme generates tags from messages by constructing a scheme under a mild security condition that is existentially unforgeable against random message attack with auxiliary information. Thus our scheme can reduce the signature size since it does not need to send tags with the signatures. Our scheme has short signature sizes of O(1) and achieves tighter reduction loss than that of Ducas et al.'s scheme. Our proposed scheme has two variants. Our scheme with one property has tighter reduction and the same verification key size of O(log n) as that of Ducas et al.'s scheme, where n is the security parameter. Our scheme with the other property achieves much tighter reduction loss of O(Q/n) and verification key size of O(n), where Q is the number of signing queries.
ER -