Abstract
Constructing secure and effective code-based signature schemes has been an open problem. In this paper, we efficiently reduce the key size of the Durandal signature scheme introduced by Aragon et al. (EUROCRYPT 2019). We prove that the improved scheme is EUF-CMA secure by reducing its security to the advanced product spaces subspaces indistinguishability (PSSI+) problem, the decisional rank syndrome decoding (DRSD) problem, and the affine rank syndrome decoding (ARSD) problem under the random oracle model. Furthermore, our signature scheme is more secure than the Durandal scheme because recovering key attacks are equivalent to solving the rank syndrome decoding (RSD) problem, instead of the rank support learning (RSL) problem in the original Durandal scheme. Our signature scheme takes less time to generate a signature owing to the fact that our signature scheme enjoys smaller security parameters in comparison to the Duradual scheme. We compare the new scheme with existing code-based signature schemes and find that our signature scheme has advantages in terms of the public key size.
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References
Shor P W. Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, Santa Fe, 1994. 124–134
Dou Z, Xu G, Chen X-B, et al. A secure rational quantum state sharing protocol. Sci China Inf Sci, 2018, 61: 022501
Yang L, Wu C M, Xie H Q. Mutual authenticated quantum no-key encryption scheme over private quantum channel. Sci China Inf Sci, 2018, 61: 022502
Dong X Y, Wang X Y. Quantum key-recovery attack on Feistel structures. Sci China Inf Sci, 2018, 61: 102501
Wang Y, Tian C X, Su Q, et al. Measurement-device-independent quantum secret sharing and quantum conference based on Gaussian cluster state. Sci China Inf Sci, 2019, 62: 072501
Mceliece R J. A Public-key Cryptosystem Based on Algebraic Coding Theory. Technical Report DSN Progress Report, 1978, 4244: 114–116
Niederreiter H. Knapsack-type cryptosystems and algebraic coding thoery. Prob Control Inf Theory, 1986, 15: 159-166
Berlekamp E, McEliece R, van Tilborg H. On the inherent intractability of certain coding problems. IEEE Trans Inform Theor, 1978, 24: 384–386
Courtois N, Finiasz M, Sendrier N. How to achieve a McEliece-based digital signature scheme. In: Proceedings of ASIACRYPT, Gold Coast, 2001. 157–174
Baldi M, Bianchi M, Chiaraluce F, et al. Using LDGM codes and sparse syndromes to achieve digital signatures. In: Proceedings of PQCrypto, Limoges, 2013. 1–15
Londahl C, Johansson T. A new version of McEliece PKC based on convolutional codes. In: Proceedings of the 14th International Conference on Information and Communications Security, Hong Kong, 2012. 461–470
Phesso A, Tillich J P. An efficient attack on a code-based signature scheme. In: Proceedings of PQCrypto, Fukuoka, 2016. 86–103
Landais G, Tillich J P. An efficient attack of a McEliece cryptosystem variant based on convolutional codes. In: Proceedings of PQCrypto, Limoges, 2013. 102–117
Gaborit P, Ruatta O, Schrek J, et al. RankSign: an efficient signature algorithm based on the rank metric. In: Proceedings of PQCrypto, Waterloo, 2014. 88–107
Gaborit P, Ruatta O, Schrek J, et al. New results for rank-based cryptography. In: Proceedings of AFRICACRYPT, Marrakesh, 2014. 1–12
Gaborit P, Murat G, Ruatta O, et al. Low rank parity check codes and their application to cryptography. In: Proceedings of the Workshop on Coding and Cryptography, Bergen, 2013. 167–179
Aragon N, Gaborit P, Hauteville A, et al. RankSign-a signature proposal for the NIST’s call. First Round Submission to the NIST Post-Quantum Cryptography Call, 2017. https://csrc.nist.gov/Projects/post-quantum-cryptography/Round-1-Submissions
Debris-Alazard T, Tillich J P. Two attacks on rank metric code-based schemes: RankSign and an IBE scheme. In: Proceedings of ASIACRYPT, Brisbane, 2018. 62–92
Fiat A, Shamir A. How to prove yourself: practical solutions to identification and signature problems. In: Proceedings of CRYPTO, Santa Barbara, 1986. 186–194
Stern J. A new identification scheme based on syndrome decoding. In: Proceedings of CRYPTO, Santa Barbara, 1993. 13–21
Cayrel P, Veron P, Alaoui S M E Y. A zero-knowledge identification scheme based on the q-ary syndrome decoding problem. In: Proceedings of Selected Areas in Cryptography, Waterloo, 2010. 171–186
Aragon N, Blazy O, Gaborit P, et al. Durandal: a rank metric based signature scheme. In: Proceedings of EURO-CRYPT, Darmstadt, 2019. 728–758
Persichetti E. Improving the efficiency of code-based cryptography. Dissertation for Ph.D. Degree. Auckland: University of Auckland, 2012. 111–115
Persichetti E. Efficient one-time signatures from quasi-cyclic codes: a full treatment. Cryptography, 2018, 2: 30
Fukushima K, Roy P S, Xu R, et al. Random code-based signature scheme (RaCoSS). First Round Submission to the NIST Post-quantum Cryptography Call. 2017. https://csrc.nist.gov/projects/post-quantum-cryptography/round-1-submissions
Roy P S, Morozov K, Fukushima K, et al. Code-based Signature Scheme Without Trapdoors. IEICE Technical Report, 2018, 118: 17–22
Lyubashevsky V. Lattice signatures without trapdoors. In: Proceedings of EUROCRYPT, Cambridge, 2012. 738–755
Melchor C A, Aragon N, Bettaieb S, et al. Rank quasi-cyclic (RQC). Second Round Submission to the NIST Postquantum Cryptography Call, 2019. https://pqc-rqc.org/doc/rqc-specification_2019-04-10.pdf
Loidreau P. Properties of codes in rank metric. 2006. arXiv: cs/0610057
Gaborit P. Shorter keys for code based cryptography. In: Proceedings of the Workshop on Coding and Cryptography, Bergen, 2005. 81–91
Hauteville A, Tillich J P. New algorithms for decoding in the rank metric and an attack on the LRPC cryptosystem. In: Proceedings of International Symposium on Information Theory, Hong Kong, 2015. 2747–2751
Gabidulin E M, Paramonov A V, Tretjakov O V. Ideals over a non-commutative ring and thier applications in cryptology. In: Proceedings of EUROCRYPT, Brighton, 1991. 482–489
Gaborit P, Zemor G. On the hardness of the decoding and the minimum distance problems for rank codes. IEEE Trans Inform Theor, 2016, 62: 7245–7252
Bartz H. Algebraic decoding of subspace and rank-metric codes. Dissertation for Ph.D. Degree. Germany: Technical University Munich, 2017. 1–184
Gaborit P, Ruatta O, Schrek J. On the complexity of the rank syndrome decoding problem. IEEE Trans Inform Theor, 2016, 62: 1006–1019
Aragon N, Gaborit P, Hauteville A, et al. A new algorithm for solving the rank syndrome decoding problem. In: Proceedings of International Symposium on Information Theory, Vail, 2018. 2421–2425
Guo Q, Johansson T, Londahl C. A new algorithm for solving ring-LPN with a reducible polynomial. IEEE Trans Inform Theor, 2015, 61: 6204–6212
Londahl C, Johansson T, Shooshtari M K, et al. Squaring attacks on McEliece public-key cryptosystems using quasicyclic codes of even dimension. Des Codes Cryptogr, 2016, 80: 359–377
Sendrier N. Decoding one out of many. In: Proceedings of PQCrypto, Taipei, 2011. 51–67
Faugere J C, Levy-dit-Vehel F, Perret L. Cryptanalysis of MinRank. In: Proceedings of CRYPTO, Santa Barbara, 2008. 280–296
Faugere J C, Din M S E, Spaenlehauer P J. Computing loci of rank defects of linear matrices using Grobner bases and applications to cryptology. In: Proceedings of Symbolic and Algebraic Computation, International Symposium, Munich, 2010. 257–264
Debris-Alazard T, Sendrier N, Tillich J P. Wave: a new code-based signature scheme. 2018. arXiv: 1810.07554
Kabatianskii G, Krouk E, Smeets B. A digital signature scheme based on random error-correcting codes. In: Proceedings of the 6th IMA International Conference on Cryptography and Coding, Cirencester, 1997. 161–167
Cayrel P L, Otmani A, Vergnaud D. On Kabatianskii-Krouk-Smeets signatures. In: Proceedings ofthe 1st International Workshop on Arithmetic of Finite Fields, Madrid, 2007. 237–251
Gaborit P, Girault M. Lightweight code-based identification and signature. In: Proceedings of International Symposium on Information Theory, Nice, 2007. 191–195
Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant Nos. 61822202, 61872087, 61841701, 61902070) and GuangDong Natural Science Foundation (Grant No. 2019B010137002).
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Song, Y., Huang, X., Mu, Y. et al. An improved Durandal signature scheme. Sci. China Inf. Sci. 63, 132103 (2020). https://doi.org/10.1007/s11432-019-2670-7
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DOI: https://doi.org/10.1007/s11432-019-2670-7