An improved Durandal signature scheme

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.

[1]  Mohammad Reza Aref,et al.  Squaring attacks on McEliece public-key cryptosystems using quasi-cyclic codes of even dimension , 2016, Des. Codes Cryptogr..

[2]  Gang Xu,et al.  A secure rational quantum state sharing protocol , 2016, Science China Information Sciences.

[3]  Vadim Lyubashevsky,et al.  Lattice Signatures Without Trapdoors , 2012, IACR Cryptol. ePrint Arch..

[4]  Jean-Pierre Tillich,et al.  Wave: A New Code-Based Signature Scheme , 2018, IACR Cryptol. ePrint Arch..

[5]  Gilles Zémor,et al.  New Results for Rank-Based Cryptography , 2014, AFRICACRYPT.

[6]  Adrien Hauteville,et al.  Durandal: a rank metric based signature scheme , 2019, IACR Cryptol. ePrint Arch..

[7]  Pierre-Louis Cayrel,et al.  On Kabatianskii-Krouk-Smeets Signatures , 2007, WAIFI.

[8]  Hannes Bartz Algebraic Decoding of Subspace and Rank-Metric Codes , 2017 .

[9]  中口 俊哉,et al.  投影型拡張現実感技術を用いた可搬型医療支援システム (イメージ・メディア・クオリティ) , 2014 .

[10]  Jean-Pierre Tillich,et al.  Two Attacks on Rank Metric Code-Based Schemes: RankSign and an IBE Scheme , 2018, ASIACRYPT.

[11]  Gilles Zémor,et al.  On the Hardness of the Decoding and the Minimum Distance Problems for Rank Codes , 2016, IEEE Transactions on Information Theory.

[12]  Ernst M. Gabidulin,et al.  Ideals over a Non-Commutative Ring and thier Applications in Cryptology , 1991, EUROCRYPT.

[13]  Edoardo Persichetti,et al.  Efficient One-Time Signatures from Quasi-Cyclic Codes: A Full Treatment , 2018, Cryptogr..

[14]  Matthieu Finiasz,et al.  How to Achieve a McEliece-Based Digital Signature Scheme , 2001, ASIACRYPT.

[15]  Olivier Blazy,et al.  Rank Quasi-Cyclic (RQC) , 2017 .

[16]  Sidi Mohamed El Yousfi Alaoui,et al.  A Zero-Knowledge Identification Scheme Based on the q-ary Syndrome Decoding Problem , 2010, Selected Areas in Cryptography.

[17]  Thomas Johansson,et al.  A New Version of McEliece PKC Based on Convolutional Codes , 2012, ICICS.

[18]  Jean-Charles Faugère,et al.  Computing loci of rank defects of linear matrices using Gröbner bases and applications to cryptology , 2010, ISSAC.

[19]  Adrien Hauteville,et al.  A New Algorithm for Solving the Rank Syndrome Decoding Problem , 2018, 2018 IEEE International Symposium on Information Theory (ISIT).

[20]  Joachim Rosenthal,et al.  Using LDGM Codes and Sparse Syndromes to Achieve Digital Signatures , 2013, PQCrypto.

[21]  Jean-Pierre Tillich,et al.  An Efficient Attack on a Code-Based Signature Scheme , 2016, PQCrypto.

[22]  Thomas Johansson,et al.  A New Algorithm for Solving Ring-LPN With a Reducible Polynomial , 2015, IEEE Transactions on Information Theory.

[23]  Pierre Loidreau,et al.  Properties of codes in rank metric , 2006, ArXiv.

[24]  Meihong Wang,et al.  Measurement-device-independent quantum secret sharing and quantum conference based on Gaussian cluster state , 2019, Science China Information Sciences.

[25]  Nicolas Sendrier,et al.  Decoding One Out of Many , 2011, PQCrypto.

[26]  Chenmiao Wu,et al.  Mutual authenticated quantum no-key encryption scheme over private quantum channel , 2017, Science China Information Sciences.

[27]  Gilles Zémor,et al.  Low Rank Parity Check codes and their application to cryptography , 2013 .

[28]  Gilles Zémor,et al.  RankSign: An Efficient Signature Algorithm Based on the Rank Metric , 2014, PQCrypto.

[29]  Adrien Hauteville,et al.  New algorithms for decoding in the rank metric and an attack on the LRPC cryptosystem , 2015, 2015 IEEE International Symposium on Information Theory (ISIT).

[30]  Amos Fiat,et al.  How to Prove Yourself: Practical Solutions to Identification and Signature Problems , 1986, CRYPTO.

[31]  Chunhua Su,et al.  A New Identification Scheme based on Syndrome Decoding Problem with Provable Security against Quantum Adversaries , 2019, J. Univers. Comput. Sci..

[32]  Gregory A. Kabatiansky,et al.  A Digital Signature Scheme Based on Random Error-Correcting Codes , 1997, IMACC.

[33]  Robert J. McEliece,et al.  A public key cryptosystem based on algebraic coding theory , 1978 .

[34]  Kiyomoto Shinsaku,et al.  Code-Based Signature Scheme without Trapdoors , 2018 .

[35]  Philippe Gaborit,et al.  On the Complexity of the Rank Syndrome Decoding Problem , 2013, IEEE Transactions on Information Theory.

[36]  Philippe Gaborit,et al.  Shorter keys for code-based cryptography , 2005 .

[37]  Edoardo Persichetti,et al.  Improving the Efficiency of Code-Based Cryptography , 2012 .

[38]  Ludovic Perret,et al.  Cryptanalysis of MinRank , 2008, CRYPTO.

[39]  Elwyn R. Berlekamp,et al.  On the inherent intractability of certain coding problems (Corresp.) , 1978, IEEE Trans. Inf. Theory.

[40]  Xiaoyun Wang,et al.  Quantum key-recovery attack on Feistel structures , 2018, Science China Information Sciences.

[41]  Jean-Pierre Tillich,et al.  An Efficient Attack of a McEliece Cryptosystem Variant Based on Convolutional Codes , 2013, PQCrypto.

[42]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[43]  Marc Girault,et al.  Lightweight code-based identification and signature , 2007, 2007 IEEE International Symposium on Information Theory.