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2020 | OriginalPaper | Chapter

One-More Assumptions Do Not Help Fiat-Shamir-type Signature Schemes in NPROM

Authors : Masayuki Fukumitsu, Shingo Hasegawa

Published in: Topics in Cryptology – CT-RSA 2020

Publisher: Springer International Publishing

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Abstract

On the Fiat-Shamir-type signature schemes, there are several impossibility results concerning their provable security. Most of these impossibility results employ the non-programmable random oracle model (NPROM), and to the best of our knowledge, all impossibilities deal with the security reductions from the non-interactive cryptographic assumptions except for the result on the security of Schnorr signature scheme from the One-More DL (OM-DL) assumption in ProvSec2017.

In this paper, we extend the impossibility result above concerning Schnorr signature scheme and the OM-DL assumption to a wider class of the Fiat-Shamir-type signature schemes, and aim to find out the conditions so that such impossibility results hold. We show that a specific class of the Fiat-Shamir-type signature schemes, including Schnorr signature scheme, cannot be proven to be euf-cma secure in NPROM from the generalized One-More cryptographic assumptions. This is just a generalization of the impossibility concerning Schnorr signature scheme and the OM-DL assumption. Our result also suggests that for some Fiat-Shamir-type signature schemes, which is not covered by our impossibility (e.g. the RSA-based schemes), there may exist a successful security proof in NPROM from the interactive cryptographic assumption.

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Abdalla, M., An, J.H., Bellare, M., Namprempre, C.: From identification to signatures via the Fiat-Shamir transform: necessary and sufficient conditions for security and forward-security. IEEE Trans. Inf. Theory 54(8), 3631–3646 (2008). https://doi.org/10.1109/TIT.2008.926303CrossRefMathSciNetMATH

Abdalla, M., Fouque, P.A., Lyubashevsky, V., Tibouchi, M.: Tightly secure signatures from lossy identification schemes. J. Cryptol. 29(3), 597–631 (2016). https://doi.org/10.1007/s00145-015-9203-7CrossRefMathSciNetMATH

Bader, C., Jager, T., Li, Y., Schäge, S.: On the impossibility of tight cryptographic reductions. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 273–304. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_10CrossRef

Bellare, M., Neven, G.: Multi-signatures in the plain public-key model and a general forking lemma. In: Proceedings of the 13th ACM Conference on Computer and Communications Security, CCS 2006, pp. 390–399. ACM, New York (2006). https://doi.org/10.1145/1180405.1180453

Bellare, M., Palacio, A.: GQ and schnorr identification schemes: proofs of security against impersonation under active and concurrent attacks. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 162–177. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45708-9_11CrossRef

Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: Proceedings of the 1st ACM Conference on Computer and Communications Security, CCS 1993, pp. 62–73. ACM, New York (1993). https://doi.org/10.1145/168588.168596

Bellare, M., Rogaway, P.: The exact security of digital signatures-how to sign with RSA and rabin. In: Maurer, U. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 399–416. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-68339-9_34CrossRef

Bernstein, D.J., Duif, N., Lange, T., Schwabe, P., Yang, B.Y.: High-speed high-security signatures. J. Cryptogr. Eng. 2(2), 77–89 (2012). https://doi.org/10.1007/s13389-012-0027-1CrossRefMATH

Boneh, D., Venkatesan, R.: Breaking RSA may not be equivalent to factoring. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 59–71. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0054117CrossRef

10.

Coron, J.S.: Optimal security proofs for PSS and other signature schemes. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 272–287. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-46035-7_18CrossRef

11.

Cramer, R., Shoup, V.: Signature schemes based on the strong RSA assumption. ACM Trans. Inf. Syst. Secur. 3(3), 161–185 (2000). https://doi.org/10.1145/357830.357847CrossRef

12.

Dierks, T., Allen, C.: The TLS protocol version 1.0 (1999). https://tools.ietf.org/html/rfc2246

13.

Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987). https://doi.org/10.1007/3-540-47721-7_12CrossRef

14.

Fischlin, M., Fleischhacker, N.: Limitations of the meta-reduction technique: the case of Schnorr signatures. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 444–460. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38348-9_27CrossRef

15.

Fischlin, M., Lehmann, A., Ristenpart, T., Shrimpton, T., Stam, M., Tessaro, S.: Random oracles with(out) programmability. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 303–320. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_18CrossRef

16.

Fleischhacker, N., Jager, T., Schröder, D.: On tight security proofs for Schnorr signatures. J. Cryptol. 32(2), 566–599 (2019). https://doi.org/10.1007/s00145-019-09311-5CrossRefMathSciNetMATH

17.

Fukumitsu, M., Hasegawa, S.: Impossibility on the provable security of the Fiat-Shamir-type signatures in the non-programmable random oracle model. In: Bishop, M., Nascimento, A.C.A. (eds.) ISC 2016. LNCS, vol. 9866, pp. 389–407. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-45871-7_23CrossRefMATH

18.

Fukumitsu, M., Hasegawa, S.: Impossibility of the provable security of the Schnorr signature from the one-more DL assumption in the non-programmable random oracle model. In: Okamoto, T., Yu, Y., Au, M.H., Li, Y. (eds.) ProvSec 2017. LNCS, vol. 10592, pp. 201–218. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-68637-0_12CrossRefMATH

19.

Fukumitsu, M., Hasegawa, S.: Black-box separations on Fiat-Shamir-type signatures in the non-programmable random oracle model. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E101.A(1), 77–87 (2018). https://doi.org/10.1587/transfun.E101.A.77CrossRefMATH

20.

Goldwasser, S., Micali, S., Rivest, R.L.: A digital signature scheme secure against adaptive chosen-message attacks. SIAM J. Comput. 17(2), 281–308 (1988). https://doi.org/10.1137/0217017CrossRefMathSciNetMATH

21.

Guillou, L.C., Quisquater, J.J.: A practical zero-knowledge protocol fitted to security microprocessor minimizing both transmission and memory. In: Barstow, D., et al. (eds.) EUROCRYPT 1988. LNCS, vol. 330, pp. 123–128. Springer, Heidelberg (1988). https://doi.org/10.1007/3-540-45961-8_11CrossRef

22.

Hasegawa, S., Isobe, S.: A lossy identification scheme using the subgroup decision assumption. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E97.A(6), 1296–1306 (2014). https://doi.org/10.1587/transfun.E97.A.1296CrossRef

23.

Hasegawa, S., Isobe, S.: Lossy identification schemes from decisional RSA. Interdisc. Inf. Sci. (2019). https://doi.org/10.4036/iis.2019.R.01

24.

Hess, F.: Efficient identity based signature schemes based on pairings. In: Nyberg, K., Heys, H. (eds.) SAC 2002. LNCS, vol. 2595, pp. 310–324. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36492-7_20CrossRef

25.

Kakvi, S.A., Kiltz, E.: Optimal security proofs for full domain hash, revisited. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 537–553. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_32CrossRef

26.

Katz, J., Wang, N.: Efficiency improvements for signature schemes with tight security reductions. In: Proceedings of the 10th ACM Conference on Computer and Communications Security, CCS 2003, pp. 155–164. ACM, New York (2003). https://doi.org/10.1145/948109.948132

27.

Lv, X., Xu, F., Ping, P., Liu, X., Su, H.: Schnorr ring signature scheme with designated verifiability. In: 2015 14th International Symposium on Distributed Computing and Applications for Business Engineering and Science (DCABES), pp. 163–166, August 2015. https://doi.org/10.1109/DCABES.2015.48

28.

Lyubashevsky, V.: Lattice-based identification schemes secure under active attacks. In: Cramer, R. (ed.) PKC 2008. LNCS, vol. 4939, pp. 162–179. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78440-1_10CrossRef

29.

Morgan, A., Pass, R.: On the security loss of unique signatures. In: Beimel, A., Dziembowski, S. (eds.) TCC 2018. LNCS, vol. 11239, pp. 507–536. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03807-6_19CrossRefMATH

30.

Nakamoto, S., et al.: Bitcoin: a peer-to-peer electronic cash system (2008). https://bitcoin.org/bitcoin.pdf

31.

Ohta, K., Okamoto, T.: A digital multisignature scheme based on the Fiat-Shamir scheme. In: Imai, H., Rivest, R.L., Matsumoto, T. (eds.) ASIACRYPT 1991. LNCS, vol. 739, pp. 139–148. Springer, Heidelberg (1993). https://doi.org/10.1007/3-540-57332-1_11CrossRef

32.

Okamoto, T.: Provably secure and practical identification schemes and corresponding signature schemes. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 31–53. Springer, Heidelberg (1993). https://doi.org/10.1007/3-540-48071-4_3CrossRef

33.

Paillier, P., Vergnaud, D.: Discrete-log-based signatures may not be equivalent to discrete log. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 1–20. Springer, Heidelberg (2005). https://doi.org/10.1007/11593447_1CrossRef

34.

Pass, R.: Limits of provable security from standard assumptions. In: Proceedings of the Forty-third Annual ACM Symposium on Theory of Computing, STOC 2011, pp. 109–118. ACM, New York (2011). https://doi.org/10.1145/1993636.1993652

35.

Pointcheval, D., Stern, J.: Provably secure blind signature schemes. In: Kim, K., Matsumoto, T. (eds.) ASIACRYPT 1996. LNCS, vol. 1163, pp. 252–265. Springer, Heidelberg (1996). https://doi.org/10.1007/BFb0034852CrossRef

36.

Pointcheval, D., Stern, J.: Security arguments for digital signatures and blind signatures. J. Cryptol. 13(3), 361–396 (2000). https://doi.org/10.1007/s001450010003CrossRefMATH

37.

Schnorr, C.P.: Efficient signature generation by smart cards. J. Cryptol. 4(3), 161–174 (1991). https://doi.org/10.1007/BF00196725CrossRefMATH

38.

Shamir, A.: Identity-based cryptosystems and signature schemes. In: Blakley, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985). https://doi.org/10.1007/3-540-39568-7_5CrossRef

39.

Tor: Tor. https://www.torproject.org/

40.

Ylonen, T.: The secure shell (SSH) transport layer protocol (2006). https://tools.ietf.org/html/rfc4253

41.

Zhang, J., Zhang, Z., Chen, Y., Guo, Y., Zhang, Z.: Black-box separations for one-more (static) CDH and its generalization. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 366–385. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-45608-8_20CrossRef

42.

Zhang, Z., Chen, Y., Chow, S.S.M., Hanaoka, G., Cao, Z., Zhao, Y.: Black-box separations of hash-and-sign signatures in the non-programmable random oracle model. In: Au, M.-H., Miyaji, A. (eds.) ProvSec 2015. LNCS, vol. 9451, pp. 435–454. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-26059-4_24CrossRef

Title: One-More Assumptions Do Not Help Fiat-Shamir-type Signature Schemes in NPROM
Authors: Masayuki Fukumitsu
Shingo Hasegawa
Publisher: Springer International Publishing
Book: Topics in Cryptology – CT-RSA 2020
Print ISBN: 978-3-030-40185-6

Electronic ISBN: 978-3-030-40186-3

Copyright Year: 2020
DOI: https://doi.org/10.1007/978-3-030-40186-3_25

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