Abstract
CFS is the first practical code-based signature scheme. In the present paper, we present the initial scheme and its evolutions, the attacks it had to face and the countermeasures applied. We compare the different algorithmic choices involved during the implementation of the scheme and aim to provide guidelines to this task. We will show that all things considered the system remains practical. Finally, we present a state-of-the-art software implementation of the signing primitive to prove our claim. For eighty bits of security our implementation produces a signature in 1.3 seconds on a single core of Intel Xeon W3670 at 3.20 GHz. Moreover the computation is easy to distribute and we can take full profit of multi-core processors reducing the signature time to a fraction of second in software.
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References
Courtois, N.T., Finiasz, M., Sendrier, N.: How to Achieve a McEliece-Based Digital Signature Scheme. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 157–174. Springer, Heidelberg (2001)
McEliece, R.: A public-key cryptosystem based on algebraic coding theory. DSN Prog. Rep., Jet Prop. Lab., California Inst. Technol., Pasadena, CA, 114–116 (January 1978)
Beuchat, J.L., Sendrier, N., Tisserand, A., Villard, G.: FPGA implementation of a recently published signature scheme. Rapport de recherche 5158, INRIA (2004)
Faugère, J.C., Gauthier, V., Otmani, A., Perret, L., Tillich, J.P.: A distinguisher for high rate McEliece cryptosystems. In: ITW 2011, Paraty, Brazil, pp. 282–286 (October 2011)
Finiasz, M.: Parallel-CFS: Strengthening the CFS McEliece-Based Signature Scheme. In: Biryukov, A., Gong, G., Stinson, D.R. (eds.) SAC 2010. LNCS, vol. 6544, pp. 159–170. Springer, Heidelberg (2011)
Berlekamp, E., McEliece, R., van Tilborg, H.: On the inherent intractability of certain coding problems. IEEE Transactions on Information Theory 24(3) (May 1978)
Prange, E.: The use of information sets in decoding cyclic codes. IRE Transactions IT-8, S5–S9 (1962)
Stern, J.: A Method for Finding Codewords of Small Weight. In: Cohen, G., Wolfmann, J. (eds.) Coding Theory 1988. LNCS, vol. 388, pp. 106–113. Springer, Heidelberg (1989)
Bernstein, D.J., Lange, T., Peters, C.: Smaller Decoding Exponents: Ball-Collision Decoding. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 743–760. Springer, Heidelberg (2011)
May, A., Meurer, A., Thomae, E.: Decoding Random Linear Codes in \(\tilde{\mathcal{O}}(2^{0.054n})\). In: Lee, D., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 107–124. Springer, Heidelberg (2011)
Wagner, D.: A Generalized Birthday Problem. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 288–303. Springer, Heidelberg (2002)
Camion, P., Patarin, J.: The Knapsack Hash Function Proposed at Crypto 1989 Can Be Broken. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 39–53. Springer, Heidelberg (1991)
Coron, J.S., Joux, A.: Cryptanalysis of a provably secure cryptographic hash function. Cryptology ePrint Archive, Report 2004/013 (2004), http://eprint.iacr.org/
Overbeck, R., Sendrier, N.: Code-based cryptography. In: Bernstein, D., Buchmann, J., Dahmen, E. (eds.) Post-Quantum Cryptography, pp. 95–145. Springer (2009)
Johansson, T., Jönsson, F.: On the complexity of some cryptographic problems based on the general decoding problem. IEEE-IT 48(10), 2669–2678 (2002)
Sendrier, N.: Decoding One Out of Many. In: Yang, B.-Y. (ed.) PQCrypto 2011. LNCS, vol. 7071, pp. 51–67. Springer, Heidelberg (2011)
Dumer, I.: On minimum distance decoding of linear codes. In: Proc. 5th Joint Soviet-Swedish Int. Workshop Inform. Theory, Moscow, pp. 50–52 (1991)
Finiasz, M., Sendrier, N.: Security Bounds for the Design of Code-Based Cryptosystems. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 88–105. Springer, Heidelberg (2009)
Becker, A., Joux, A., May, A., Meurer, A.: Decoding Random Binary Linear Codes in 2n/20: How 1 + 1 = 0 Improves Information Set Decoding. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 520–536. Springer, Heidelberg (2012)
Patterson, N.: The algebraic decoding of Goppa codes. IEEE Transactions on Information Theory 21(2), 203–207 (1975)
Massey, J.: Shift-register synthesis and BCH decoding. IEEE Transactions on Information Theory 15(1), 122–127 (1969)
Berlekamp, E.: Algebraic Coding Theory. Aegen Park Press (1968)
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Landais, G., Sendrier, N. (2012). Implementing CFS. In: Galbraith, S., Nandi, M. (eds) Progress in Cryptology - INDOCRYPT 2012. INDOCRYPT 2012. Lecture Notes in Computer Science, vol 7668. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34931-7_27
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DOI: https://doi.org/10.1007/978-3-642-34931-7_27
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