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Journal of Cryptology
Erschienen in: Journal of Cryptology 2/2022

01.04.2022 | Research Article

Two-Round n-out-of-n and Multi-Signatures and Trapdoor Commitment from Lattices

verfasst von: Ivan Damgård, Claudio Orlandi, Akira Takahashi, Mehdi Tibouchi

Erschienen in: Journal of Cryptology | Ausgabe 2/2022

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Abstract

Although they have been studied for a long time, distributed signature protocols have garnered renewed interest in recent years in view of novel applications to topics like blockchains. Most recent works have focused on distributed versions of ECDSA or variants of Schnorr signatures; however, and in particular, little attention has been given to constructions based on post-quantum secure assumptions like the hardness of lattice problems. A few lattice-based threshold signature and multi-signature schemes have been proposed in the literature, but they either rely on hash-and-sign lattice signatures (which tend to be comparatively inefficient), use expensive generic transformations, or only come with incomplete security proofs. In this paper, we construct several lattice-based distributed signing protocols with low round complexity following the Fiat–Shamir with Aborts (FSwA) paradigm of Lyubashevsky (Asiacrypt 2009). Our protocols can be seen as distributed variants of the fast Dilithium-G signature scheme and the full security proof can be made assuming the hardness of module SIS and LWE problems. A key step to achieving security (unexplained in some earlier papers) is to prevent the leakage that can occur when parties abort after their first message—which can inevitably happen in the Fiat–Shamir with Aborts setting. We manage to do so using homomorphic commitments. Exploiting the similarities between FSwA and Schnorr-style signatures, our approach makes the most of observations from recent advancements in the discrete log setting, such as Drijvers et al.’s seminal work on two-round multi-signatures (S&P 2019). In particular, we observe that the use of commitment not only resolves the subtle issue with aborts, but also makes it possible to realize secure two-round n-out-of-n distributed signing and multi-signature in the plain public key model, by equipping the commitment with a trapdoor feature. The construction of suitable trapdoor commitment from lattices is a side contribution of this paper.
Vorheriger Artikel TinyKeys: A New Approach to Efficient Multi-Party Computation

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Fußnoten
1
It is still an open question whether the aborts issue can instead be resolved by careful parameter choice, allowing to simulate the rejected transcripts without any additional assumptions. But we are aware of on-going work in this direction. If the question is answered in the affirmative our three-round protocol could be proven secure even without a commitment. However, the use of homomorphic commitment is crucial for constructing our new two-round protocols, which is our main contribution.
 
2
We include this for completeness since, while the three-round protocol itself is not novel, to the best of our knowledge there has been no publicly available complete security proof solely relying on Module-LWE.
 
3
We remark that the “commitments” generated by \({\mathsf {H}}_1\) and \({\mathsf {H}}_2\) in Fig. 6 are not randomized, and therefore they are not hiding. In our protocol, however, all committed values have high min-entropy and this is indeed sufficient for the security proof to hold. Alternatively, one could cheaply turn them into full-fledged secure and extractable commitments by additionally hashing random strings that are to be sent out during the opening phase [80].
 
4
To be more precise, since the verification bound scales as \(n^{3/2}\), one should also increase q by the same bound to avoid arithmetic overflow. This makes the \(\mathsf {MSIS}_{}\) problem harder, but the \(\mathsf {MLWE}_{}\) easier if the dimension is kept unchanged. To keep the same security level, one should therefore also increase N by a factor of \(1+O(\frac{\log n}{\log q_0})\) where \(q_0\) is the value of q in the single-user setting. Therefore, one could in principle argue that signature size actually scales as \(O(\log ^2 n)\). However, one typically chooses \(q_0 > 2^{20}\), and therefore even in settings with billions of parties, \(\frac{\log n}{\log q_0} < 2\). Thus, one can effectively regard N as independent of n.
 
5
This condition could be actually relaxed somewhat by applying the result due to Nguyen [76]
 
Literatur
1.
H.K. Alper, J. Burdges, Two-round trip schnorr multi-signatures via delinearized witnesses. in CRYPTO 2021, Part I, vol. 12825 of LNCS, Virtual Event, (Springer, Heidelberg, 2021), pp. 157–188
2.
M. Abe, S. Fehr, Adaptively secure feldman VSS and applications to universally-composable threshold cryptography. in CRYPTO 2004, vol. 3152 of LNCS, (Springer, Heidelberg, 2004), pp. 317–334
3.
M. Abdalla, P.-A. Fouque, V. Lyubashevsky, M. Tibouchi, Tightly secure signatures from lossy identification schemes. Journal of Cryptology, 29(3), 597–631, (2016)MathSciNetCrossRef
4.
5.
G. Barthe, S. Belaïd, T. Espitau, P.-A. Fouque, B. Grégoire, M. Rossi, M. Tibouchi, Masking the GLP lattice-based signature scheme at any order. in EUROCRYPT 2018, Part II, vol. 10821 of LNCS, (Springer, Heidelberg, 2018), pp. 354–384
6.
G. Barthe, S. Belaïd, T. Espitau, P.-A. Fouque, M. Rossi, and M. Tibouchi, GALACTICS: Gaussian sampling for lattice-based constant- time implementation of cryptographic signatures, revisited. in ACM CCS 2019, (ACM Press, 2019), pp. 2147–2164
7.
A. Bagherzandi, J.H. Cheon, S. Jarecki, Multisignatures secure under the discrete logarithm assumption and a generalized forking lemma. in ACM CCS 2008, (ACM Press, 2008), pp. 449–458
8.
F. Benhamouda, J. Camenisch, S. Krenn, V. Lyubashevsky, G. Neven, Better zero-knowledge proofs for lattice encryption and their application to group signatures. in ASIACRYPT 2014, Part I, vol. 8873 of LNCS, (Springer, Heidelberg, 2014), pp. 551–572
9.
M. Bellare, W. Dai, Chain reductions for multi-signatures and the HBMS scheme. in Advances in Cryptology - ASIACRYPT 2021 - 27th International Conference on the Theory and Application of Cryptology and Information Security, Singapore, December 6-10, 2021, Proceedings, Part IV, vol. 13093 of Lecture Notes in Computer Science, (Springer, 2021), pp. 650–678
10.
M. Bellare, H. Davis, F. Günther. Separate your domains: NIST PQC KEMs, oracle cloning and read-only indifferentiability. in EUROCRYPT 2020, Part II, vol. 12106 of LNCS, (Springer, Heidelberg, 2020), pp. 3–32
11.
C. Baum, I. Damgård, V. Lyubashevsky, S. Oechsner, C. Peikert, More efficient commitments from structured lattice assumptions. in SCN 18, vol. 11035 of LNCS, (Springer, Heidelberg, 2018), pp. 368–385
12.
D. Boneh, R. Gennaro, S. Goldfeder, A. Jain, S. Kim, P. M. R. Rasmussen, A. Sahai, Threshold cryptosystems from threshold fully homomorphic encryption. in CRYPTO 2018, Part I, vol. 10991 of LNCS, (Springer, Heidelberg, 2018), pp. 565–596
13.
F. Benhamouda, S. Krenn, V. Lyubashevsky, K. Pietrzak, Efficient zero-knowledge proofs for commitments from learning with errors over rings. In ESORICS 2015, Part I, vol. 9326 of LNCS, (Springer, Heidelberg, 2015), pp. 305–325
14.
R. Bendlin, S. Krehbiel, C. Peikert, How to share a lattice trapdoor: Threshold protocols for signatures and (H)IBE. in ACNS 13, vol. 7954 of LNCS, (Springer, Heidelberg, 2013), pp. 218–236
15.
J. Bootle, V. Lyubashevsky, G. Seiler, Algebraic techniques for short(er) exact lattice-based zero-knowledge proofs. in CRYPTO 2019, Part I, vol. 11692 of LNCS, (Springer, Heidelberg, 2019), pp. 176–202
16.
M. Bellare, G. Neven, Multi-signatures in the plain public-key model and a general forking lemma. in ACM CCS 2006, (ACM Press, 2006), pp. 390–399
17.
K. Boudgoust, A. Roux-Langlois, Compressed linear aggregate signatures based on module lattices. IACR Cryptol. ePrint Arch., p. 263, 2021
18.
S. Bettaieb, J. Schrek, Improved lattice-based threshold ring signature scheme. in Post-Quantum Cryptography - 5th International Workshop, PQCrypto 2013, (Springer, Heidelberg, 2013), pp. 34–51
19.
G. Castagnos, D. Catalano, F. Laguillaumie, F. Savasta, I. Tucker. Two-party ECDSA from hash proof systems and efficient instantiations. in CRYPTO 2019, Part III, vol. 11694 of LNCS, (Springer, Heidelberg, 2019), pp. 191–221
20.
G. Castagnos, D. Catalano, F. Laguillaumie, F. Savasta, I. Tucker. Bandwidth-efficient threshold EC-DSA. in PKC 2020, Part II, vol. 12111 of LNCS, (Springer, Heidelberg, 2020), pp. 266–296
21.
R. Canetti, R. Gennaro, S. Goldfeder, N. Makriyannis, U. Peled, UC non-interactive, proactive, threshold ECDSA with identifiable aborts. In ACM CCS 2020, (ACM Press, 2020), pp. 1769–1787
22.
D. Cash, D. Hofheinz, E. Kiltz, C. Peikert, Bonsai trees, or how to delegate a lattice basis. in EUROCRYPT 2010, vol. 6110 of LNCS, (Springer, Heidelberg, 2010), pp. 523–552
23.
R. Choi, K. Kim, Lattice-based multi-signature with linear homomorphism. in 2016 Symposium on Cryptography and Information Security (SCIS 2016), 2016
24.
P. Cayrel, R. Lindner, M. Rückert, R. Silva, A lattice-based threshold ring signature scheme. in LATINCRYPT 2010, vol. 6212 of LNCS, (Springer, 2010), pp. 255–272
25.
M. Ciampi, R. Ostrovsky, L. Siniscalchi, I. Visconti, Delayed-input non-malleable zero knowledge and multi-party coin tossing in four rounds. in TCC 2017, Part I, vol. 10677 of LNCS, (Springer, Heidelberg, 2017), pp. 711–742
26.
M. Ciampi, R. Ostrovsky, L. Siniscalchi, I. Visconti, Four-round concurrent non-malleable commitments from one-way functions. in CRYPTO 2017, Part II, vol. 10402 of LNCS, (Springer, Heidelberg, 2017), pp. 127–157
27.
M. Ciampi, G. Persiano, A. Scafuro, L. Siniscalchi, I. Visconti, Improved OR-composition of sigma-protocols. in TCC 2016-A, Part II, vol. 9563 of LNCS, (Springer, Heidelberg, 2016), pp. 112–141
28.
D. Cozzo, N. P. Smart, Sharing the LUOV: Threshold post-quantum signatures. in 17th IMA International Conference on Cryptography and Coding, vol. 11929 of LNCS, (Springer, Heidelberg, 2019), pp. 128–153
29.
I. Damgård, Efficient concurrent zero-knowledge in the auxiliary string model. in EUROCRYPT 2000, vol. 1807 of LNCS, (Springer, Heidelberg, 2000), pp. 418–430
30.
L. Ducas, A. Durmus, T. Lepoint, V. Lyubashevsky, Lattice signatures and bimodal Gaussians. in CRYPTO 2013, Part I, vol. 8042 of LNCS, (Springer, Heidelberg, 2013), pp. 40–56
31.
M. Drijvers, K. Edalatnejad, B. Ford, E. Kiltz, J. Loss, G. Neven, I. Stepanovs. On the security of two-round multi-signatures. in 2019 IEEE Symposium on Security and Privacy, (IEEE Computer Society Press, 2019), pp. 1084–1101
32.
33.
I. Damgård, T.P. Jakobsen, J.B. Nielsen, J.I. Pagter, M.B. Østergaard, Fast threshold ECDSA with honest majority. In SCN 20, vol. 12238 of LNCS, (Springer, Heidelberg, 2020), pp. 382–400
34.
J. Doerner, Y. Kondi, E. Lee, a. shelat. Secure two-party threshold ECDSA from ECDSA assumptions. in 2018 IEEE Symposium on Security and Privacy, (IEEE Computer Society Press, 2018), pp. 980–997
35.
J. Doerner, Y. Kondi, E. Lee, a. shelat, Threshold ECDSA from ECDSA assumptions: The multiparty case. in 2019 IEEE Symposium on Security and Privacy, (IEEE Computer Society Press, 2019), pp. 1051–1066
36.
37.
R. del Pino, V. Lyubashevsky, G. Seiler. Lattice-based group signatures and zero-knowledge proofs of automorphism stability. In ACM CCS 2018, (ACM Press, 2018), pp. 574–591
38.
L. Ducas, D. Micciancio, Improved short lattice signatures in the standard model. in CRYPTO 2014, Part I, vol. 8616 of LNCS, (Springer, Heidelberg, 2014), pp. 335–352
39.
A.P.K. Dalskov, C. Orlandi, M. Keller, K. Shrishak, H. Shulman, Securing DNSSEC keys via threshold ECDSA from generic MPC. in ESORICS 2020, Part II, vol. 12309 of LNCS, (Springer, Heidelberg, 2020), pp. 654–673
40.
M.F. Esgin, O. Ersoy, Z. Erkin, Post-quantum adaptor signatures and payment channel networks. in ESORICS 2020, Part II, vol. 12309 of LNCS, (Springer, Heidelberg, 2020), pp. 378–397
41.
R. El Bansarkhani, J. Sturm, An efficient lattice-based multisignature scheme with applications to bitcoins. in CANS 16, vol. 10052 of LNCS, (Springer, Heidelberg, 2016), pp. 140–155
42.
M.F. Esgin, R. Steinfeld, J.K. Liu, D. Liu, Lattice-based zero-knowledge proofs: New techniques for shorter and faster constructions and applications. in CRYPTO 2019, Part I, vol. 11692 of LNCS, (Springer, Heidelberg, 2019), pp. 115–146
43.
M. F. Esgin, R. Steinfeld, A. Sakzad, J. K. Liu, D. Liu, Short lattice-based one-out-of-many proofs and applications to ring signatures. In ACNS 19, vol. 11464 of LNCS, (Springer, Heidelberg, 2019), pp. 67–88
44.
M. Fukumitsu, S. Hasegawa. A tightly-secure lattice-based multisignature. in APKC@AsiaCCS 2019, (ACM, 2019), pp. 3–11
45.
M. Fukumitsu, S. Hasegawa, A lattice-based provably secure multisignature scheme in quantum random oracle model. in ProvSec 2020, vol. 12505 of LNCS, (Springer, Heidelberg, 2020), pp. 45–64
46.
R. Gennaro, S. Goldfeder, Fast multiparty threshold ECDSA with fast trustless setup. in ACM CCS 2018, (ACM Press, 2018), pp. 1179–1194
47.
48.
R. Gennaro, S. Goldfeder, A. Narayanan, Threshold-optimal DSA/ECDSA signatures and an application to bitcoin wallet security. in ACNS 16, vol. 9696 of LNCS, (Springer, Heidelberg, 2016), pp. 156–174
49.
R. Gennaro, S. Jarecki, H. Krawczyk, T. Rabin, Secure distributed key generation for discrete-log based cryptosystems. Journal of Cryptology, 20(1), 51–83, (2007).MathSciNetCrossRef
50.
51.
T. Güneysu, V. Lyubashevsky, T. Pöppelmann, Practical lattice-based cryptography: A signature scheme for embedded systems. in CHES 2012, vol. 7428 of LNCS, (Springer, Heidelberg, 2012), pp. 530–547
52.
N. Genise, D. Micciancio, Faster Gaussian sampling for trapdoor lattices with arbitrary modulus. in EUROCRYPT 2018, Part I, vol. 10820 of LNCS, (Springer, Heidelberg, 2018), pp. 174–203
53.
C. Gentry, C. Peikert, V. Vaikuntanathan, Trapdoors for hard lattices and new cryptographic constructions. in 40th ACM STOC, (ACM Press, 2008), pp. 197–206
54.
C. Gentry, A. Sahai, B. Waters, Homomorphic encryption from learning with errors: Conceptually-simpler, asymptotically-faster, attribute-based. in CRYPTO 2013, Part I, vol. 8042 of LNCS, (Springer, Heidelberg, 2013), pp. 75–92
55.
S. Gorbunov, V. Vaikuntanathan, D. Wichs, Leveled fully homomorphic signatures from standard lattices. in 47th ACM STOC, (ACM Press, 2015), pp. 469–477
56.
N. Howgrave-Graham, A. Joux, New generic algorithms for hard knapsacks. in EUROCRYPT 2010, vol. 6110 of LNCS, (Springer, Heidelberg, 2010), pp. 235–256
57.
M. Kansal, R. Dutta, Round optimal secure multisignature schemes from lattice with public key aggregation and signature compression. In AFRICACRYPT 20, vol. 12174 of LNCS, (Springer, Heidelberg, 2020), pp. 281–300
58.
C. Komlo, I. Goldberg, FROST: flexible round-optimized schnorr threshold signatures. in Selected Areas in Cryptography - SAC 2020 - 27th International Conference, Halifax, NS, Canada (Virtual Event), October 21-23, 2020, Revised Selected Papers, vol. 12804 of Lecture Notes in Computer Science, (Springer, 2020), pp. 34–65
59.
E. Kiltz, V. Lyubashevsky, C. Schaffner, A concrete treatment of Fiat-Shamir signatures in the quantum random-oracle model. in EUROCRYPT 2018, Part III, vol. 10822 of LNCS, (Springer, Heidelberg, 2018), pp. 552–586
60.
61.
Y. Lindell, Fast secure two-party ECDSA signing. in CRYPTO 2017, Part II, vol. 10402 of LNCS, (Springer, Heidelberg, 2017), pp. 613–644
62.
Y. Lindell, A. Nof, Fast secure multiparty ECDSA with practical distributed key generation and applications to cryptocurrency custody. in ACM CCS 2018, (ACM Press, 2018), pp. 1837–1854
63.
B. Libert, K. Nguyen, B.H.M. Tan, H. Wang, Zero-knowledge elementary databases with more expressive queries. in PKC 2019, Part I, vol. 11442 of LNCS, (Springer, Heidelberg, 2019), pp. 255–285
64.
V. Lyubashevsky, C. Peikert, O. Regev, A toolkit for ring-LWE cryptography. in EUROCRYPT 2013, vol. 7881 of LNCS, (Springer, Heidelberg, 2013), pp. 35–54
65.
V. Lyubashevsky, G. Seiler, Short, invertible elements in partially splitting cyclotomic rings and applications to lattice-based zero-knowledge proofs. in EUROCRYPT 2018, Part I, vol. 10820 of LNCS, (Springer, Heidelberg, 2018), pp. 204–224
66.
67.
V. Lyubashevsky, Fiat-Shamir with aborts: Applications to lattice and factoring-based signatures. in ASIACRYPT 2009, vol. 5912 of LNCS, (Springer, Heidelberg, 2009), pp. 598–616
68.
V. Lyubashevsky, Lattice signatures without trapdoors. in EUROCRYPT 2012, vol. 7237 of LNCS, (Springer, Heidelberg, 2012), pp. 738–755
69.
70.
C. Ma, M. Jiang, Practical lattice-based multisignature schemes for blockchains. IEEE Access, 7, 179765–179778, (2019)CrossRef
71.
S. Micali, K. Ohta, L. Reyzin, Accountable-subgroup multisignatures: Extended abstract. in ACM CCS 2001, (ACM Press, 2001), pp. 245–254
72.
D. Micciancio, C. Peikert, Trapdoors for lattices: Simpler, tighter, faster, smaller. in EUROCRYPT 2012, vol. 7237 of LNCS, (Springer, Heidelberg, 2012), pp. 700–718
73.
D. Micciancio, C. Peikert, Hardness of SIS and LWE with small parameters. in CRYPTO 2013, Part I, vol. 8042 of LNCS, (Springer, Heidelberg, 2013), pp. 21–39
74.
G. Maxwell, A. Poelstra, Y. Seurin, P. Wuille, Simple schnorr multi-signatures with applications to bitcoin. Des. Codes Cryptogr., 87(9), 2139–2164, (2019)MathSciNetCrossRef
75.
C. Ma, J. Weng, Y. Li, R.H. Deng, Efficient discrete logarithm based multi-signature scheme in the plain public key model. Des. Codes Cryptogr., 54(2), 121–133, (2010)MathSciNetCrossRef
76.
N.K. Nguyen, On the non-existence of short vectors in random module lattices. in ASIACRYPT 2019, Part II, vol. 11922 of LNCS, (Springer, Heidelberg, 2019), pp. 121–150
77.
A. Nicolosi, M.N. Krohn, Y. Dodis, D. Mazières, Proactive two-party signatures for user authentication. in NDSS 2003. (The Internet Society, 2003)
78.
J. Nick, T. Ruffing, Y. Seurin, MuSig2: Simple two-round Schnorr multi-signatures. in CRYPTO 2021, Part I, vol. 12825 of LNCS, (Virtual Event, 2021. Springer, Heidelberg), pp. 189–221
79.
J. Nick, T. Ruffing, Y. Seurin, P. Wuille, MuSig-DN: Schnorr multi-signatures with verifiably deterministic nonces. in ACM CCS 2020, (ACM Press, 2020), pp. 1717–1731
80.
R. Pass, On deniability in the common reference string and random oracle model. in CRYPTO 2003, vol. 2729 of LNCS, (Springer, Heidelberg, 2003), pp. 316–337
81.
T.P. Pedersen, Non-interactive and information-theoretic secure verifiable secret sharing. in CRYPTO’91, vol. 576 of LNCS, (Springer, Heidelberg, 1992), pp. 129–140
82.
C. Peikert, An efficient and parallel Gaussian sampler for lattices. in CRYPTO 2010, vol. 6223 of LNCS, (Springer, Heidelberg, 2010), pp. 80–97
83.
D. Pointcheval, J. Stern, Security arguments for digital signatures and blind signatures. Journal of Cryptology, 13(3), 361–396, (2000)CrossRef
84.
C.-P. Schnorr, Efficient identification and signatures for smart cards. in CRYPTO’89, vol. 435 of LNCS, (Springer, Heidelberg, 1990), pp. 239–252
85.
D.R. Stinson, R. Strobl, Provably secure distributed Schnorr signatures and a \((t, n)\) threshold scheme for implicit certificates. in ACISP 01, vol. 2119 of LNCS, (Springer, Heidelberg, 2001), pp. 417–434
86.
E. Syta, I. Tamas, D. Visher, D.I. Wolinsky, P. Jovanovic, L. Gasser, N. Gailly, I. Khoffi, B. Ford, Keeping authorities “honest or bust” with decentralized witness cosigning. in 2016 IEEE Symposium on Security and Privacy, (IEEE Computer Society Press, 2016), pp. 526–545
87.
88.
R. Tso, Z. Liu, Y. Tseng, Identity-based blind multisignature from lattices. IEEE Access, 7, 182916–182923, (2019)CrossRef
89.
W.A. Torres, R. Steinfeld, A. Sakzad, V. Kuchta, Post-quantum linkable ring signature enabling distributed authorised ring confidential transactions in blockchain. Cryptology ePrint Archive, Report 2020/1121, 2020. https://​eprint.​iacr.​org/​2020/​1121
90.
D. Wagner, A generalized birthday problem. in CRYPTO 2002, vol. 2442 of LNCS, (Springer, Heidelberg, 2002), pp. 288–303
91.
R. Yang, M. H. Au, Z. Zhang, Q. Xu, Z. Yu, W. Whyte, Efficient lattice-based zero-knowledge arguments with standard soundness: Construction and applications. in CRYPTO 2019, Part I, vol. 11692 of LNCS, (Springer, Heidelberg, 2019), pp. 147–175
Metadaten
Titel
Two-Round n-out-of-n and Multi-Signatures and Trapdoor Commitment from Lattices
verfasst von
Ivan Damgård
Claudio Orlandi
Akira Takahashi
Mehdi Tibouchi
Publikationsdatum
01.04.2022
Verlag
Springer US
Erschienen in
Journal of Cryptology / Ausgabe 2/2022
Print ISSN: 0933-2790
Elektronische ISSN: 1432-1378
DOI
https://doi.org/10.1007/s00145-022-09425-3

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