Abstract
We propose a rank metric codes based encryption based on the hard problem of rank syndrome decoding problem. We distort the matrix used for our encryption by adding a random distortion matrix over \(\mathbb {F}_{q^m}\). We show that IND-CPA security is achievable for our encryption under assumption of Decisional Rank Syndrome Decoding problem. Our proposal allows the choice of the error terms with rank up to r/2, where r is the error-correcting capability of a code. Our encryption based on Gabidulin codes has public key size of 13.68 KB, which is 82 times smaller than the public key size of McEliece Cryptosystem based on Goppa codes. For similar post-quantum security level of \(2^{140}\) bits, our encryption scheme has smaller public key size than key size suggested by LOI17 Encryption [7].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aragon, N., Gaborit, P., Hauteville, A., Tillich, J.P.: Improvement of Generic Attacks on the Rank Syndrome Decoding Problem (2017). \(<\)hal-01618464\(>\)
Gabidulin, E.M., Paramonov, A.V., Tretjakov, O.V.: Ideals over a non-commutative ring and their application in cryptology. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 482–489. Springer, Heidelberg (1991). https://doi.org/10.1007/3-540-46416-6_41
Gaborit, P., Hauteville, A., Phan, D.H., Tillich, J.-P.: Identity-based encryption from codes with rank metric. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10403, pp. 194–224. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63697-9_7
Gaborit, P., Ruatta, O., Schrek, J.: On the complexity of the rank syndrome decoding problem. IEEE Trans. Inf. Theory 62(2), 1006–1019 (2016)
Gaborit, P., Zémor, G.: On the hardness of the decoding and the minimum distance problems for rank codes. IEEE Trans. Inf. Theory 62(12), 7245–7252 (2016)
Horlemann-Trautmann, A., Marshall, K., Rosenthal, J.: Extension of Overbeck’s Attack for Gabidulin Based Cryptosystems. CoRR, abs/1511.01549 (2015)
Loidreau, P.: A new rank metric codes based encryption scheme. In: Lange, T., Takagi, T. (eds.) PQCrypto 2017. LNCS, vol. 10346, pp. 3–17. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59879-6_1
McEliece, R.J.: A public-key cryptosystem based on algebraic coding theory. The Deep Space Network Progress Report 42–44, Jet Propulsion Laboratory, Pasedena, pp. 114–116 (1978)
Otmani, A., Kalachi, H.T., Ndjeya, S.: Improved Cryptanalysis of Rank Metric Schemes Based on Gabidulin Codes. CoRR abs/1602.08549 (2016)
Ourivski, A.V., Johansson, T.: New technique for decoding codes in the rank metric and its cryptography applications. Probl. Inf. Trans. 38(3), 237–246 (2002)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Lau, T.S.C., Tan, C.H. (2018). A New Encryption Scheme Based on Rank Metric Codes. In: Susilo, W., Yang, G. (eds) Information Security and Privacy. ACISP 2018. Lecture Notes in Computer Science(), vol 10946. Springer, Cham. https://doi.org/10.1007/978-3-319-93638-3_43
Download citation
DOI: https://doi.org/10.1007/978-3-319-93638-3_43
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-93637-6
Online ISBN: 978-3-319-93638-3
eBook Packages: Computer ScienceComputer Science (R0)