Abstract
Nearly all of the currently used and well-tested signature schemes (e.g. RSA or DSA) are based either on the factoring assumption or the presumed intractability of the discrete logarithm problem. Further algorithmic advances on these problems may lead to the unpleasant situation that a large number of schemes have to be replaced with alternatives. In this work we present such an alternative – a signature scheme whose security is derived from the hardness of lattice problems. It is based on recent theoretical advances in lattice-based cryptography and is highly optimized for practicability and use in embedded systems. The public and secret keys are roughly 12000 and 2000 bits long, while the signature size is approximately 9000 bits for a security level of around 100 bits. The implementation results on reconfigurable hardware (Spartan/Virtex 6) are very promising and show that the scheme is scalable, has low area consumption, and even outperforms some classical schemes.
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Ansari, B., Hasan, M.: High performance architecture of elliptic curve scalar multiplication. CACR Research Report 1, 2006 (2006)
Arora, S., Ge, R.: New Algorithms for Learning in Presence of Errors. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part I. LNCS, vol. 6755, pp. 403–415. Springer, Heidelberg (2011)
Balasubramanian, S., Carter, H., Bogdanov, A., Rupp, A., Ding, J.: Fast multivariate signature generation in hardware: The case of rainbow. In: Application-Specific Systems, Architectures and Processors, ASAP 2008, pp. 25–30. IEEE (2008)
Beuchat, J., Sendrier, N., Tisserand, A., Villard, G., et al.: FPGA implementation of a recently published signature scheme. Rapport de Recherche RR LIP 2004-14 (2004)
Bogdanov, A., Eisenbarth, T., Rupp, A., Wolf, C.: Time-Area Optimized Public-Key Engines: \(\mathcal{MQ}\)-Cryptosystems as Replacement for Elliptic Curves? In: Oswald, E., Rohatgi, P. (eds.) CHES 2008. LNCS, vol. 5154, pp. 45–61. Springer, Heidelberg (2008)
Buchmann, J., Dahmen, E., Hülsing, A.: XMSS - A Practical Forward Secure Signature Scheme Based on Minimal Security Assumptions. In: Yang, B.-Y. (ed.) PQCrypto 2011. LNCS, vol. 7071, pp. 117–129. Springer, Heidelberg (2011)
Buchmann, J., May, A., Vollmer, U.: Perspectives for cryptographic long-term security. Commun. ACM 49, 50–55 (2006)
Chen, Y., Nguyen, P.Q.: BKZ 2.0: Better Lattice Security Estimates. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 1–20. Springer, Heidelberg (2011)
Comba, P.G.: Exponentiation cryptosystems on the IBM PC. IBM Syst. J. 29, 526–538 (1990)
Eisenbarth, T., Güneysu, T., Heyse, S., Paar, C.: MicroEliece: McEliece for Embedded Devices. In: Clavier, C., Gaj, K. (eds.) CHES 2009. LNCS, vol. 5747, pp. 49–64. Springer, Heidelberg (2009)
Fischer, J.-B., Stern, J.: An Efficient Pseudo-random Generator Provably as Secure as Syndrome Decoding. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 245–255. Springer, Heidelberg (1996)
Gama, N., Nguyen, P.Q.: Predicting Lattice Reduction. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 31–51. Springer, Heidelberg (2008)
Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: STOC, pp. 197–206 (2008)
Goldreich, O., Goldwasser, S., Halevi, S.: Public-Key Cryptosystems from Lattice Reduction Problems. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 112–131. Springer, Heidelberg (1997)
Güneysu, T., Paar, C.: Ultra High Performance ECC over NIST Primes on Commercial FPGAs. In: Oswald, E., Rohatgi, P. (eds.) CHES 2008. LNCS, vol. 5154, pp. 62–78. Springer, Heidelberg (2008)
Hoffstein, J., Howgrave-Graham, N., Pipher, J., Silverman, J.H., Whyte, W.: NTRUSign: Digital Signatures Using the NTRU Lattice. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 122–140. Springer, Heidelberg (2003)
Hoffstein, J., Pipher, J., Silverman, J.H.: NTRU: A Ring-Based Public Key Cryptosystem. In: Buhler, J.P. (ed.) ANTS 1998. LNCS, vol. 1423, pp. 267–288. Springer, Heidelberg (1998)
Hoffstein, J., Pipher, J., Silverman, J.H.: NSS: An NTRU Lattice-Based Signature Scheme. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 211–228. Springer, Heidelberg (2001)
Karatsuba, A., Ofman, Y.: Multiplication of multidigit numbers on automata. Soviet Physics Doklady 7, 595 (1963)
Lyubashevsky, V.: Fiat-Shamir with Aborts: Applications to Lattice and Factoring-Based Signatures. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 598–616. Springer, Heidelberg (2009)
Lyubashevsky, V.: Lattice Signatures without Trapdoors. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 738–755. Springer, Heidelberg (2012), Full version at http://eprint.iacr.org/2011/537
Lyubashevsky, V., Micciancio, D.: Generalized Compact Knapsacks Are Collision Resistant. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006, Part II. LNCS, vol. 4052, pp. 144–155. Springer, Heidelberg (2006)
Lyubashevsky, V., Micciancio, D.: Asymptotically Efficient Lattice-Based Digital Signatures. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 37–54. Springer, Heidelberg (2008)
Lyubashevsky, V., Micciancio, D., Peikert, C., Rosen, A.: SWIFFT: A Modest Proposal for FFT Hashing. In: Nyberg, K. (ed.) FSE 2008. LNCS, vol. 5086, pp. 54–72. Springer, Heidelberg (2008)
Lyubashevsky, V., Peikert, C., Regev, O.: On Ideal Lattices and Learning with Errors over Rings. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 1–23. Springer, Heidelberg (2010)
Micciancio, D.: Generalized compact knapsacks, cyclic lattices, and efficient one-way functions. Computational Complexity 16(4), 365–411 (2007)
Micciancio, D., Peikert, C.: Trapdoors for Lattices: Simpler, Tighter, Faster, Smaller. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 700–718. Springer, Heidelberg (2012), Full version at http://eprint.iacr.org/2011/501
Bernstein, D.J., Buchmann, J., Dahmen, E.: Post-Quantum Cryptography. Springer (2009) ISBN: 978-3-540-88701-0
Moenck, R.T.: Practical fast polynomial multiplication. In: Proceedings of the Third ACM Symposium on Symbolic and Algebraic Computation, SYMSAC 1976, pp. 136–148. ACM, New York (1976)
Nguyen, P., Regev, O.: Learning a parallelepiped: Cryptanalysis of GGH and NTRU signatures. Journal of Cryptology 22, 139–160 (2009)
Peikert, C., Rosen, A.: Efficient Collision-Resistant Hashing from Worst-Case Assumptions on Cyclic Lattices. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 145–166. Springer, Heidelberg (2006)
Petzoldt, A., Thomae, E., Bulygin, S., Wolf, C.: Small Public Keys and Fast Verification for \(\mathcal{M}\)ultivariate \(\mathcal{Q}\)uadratic Public Key Systems. In: Preneel, B., Takagi, T. (eds.) CHES 2011. LNCS, vol. 6917, pp. 475–490. Springer, Heidelberg (2011)
Pointcheval, D., Stern, J.: Security arguments for digital signatures and blind signatures. J. Cryptology 13(3), 361–396 (2000)
Shor, P.: Algorithms for quantum computation: discrete logarithms and factoring. In: 1994 Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pp. 124–134. IEEE (1994)
Shoufan, A., Wink, T., Molter, H., Huss, S., Kohnert, E.: A novel cryptoprocessor architecture for the McEliece public-key cryptosystem. IEEE Transactions on Computers 59(11), 1533–1546 (2010)
Solinas, J.: Generalized mersenne numbers. Faculty of Mathematics, University of Waterloo (1999)
Stehlé, D., Steinfeld, R., Tanaka, K., Xagawa, K.: Efficient Public Key Encryption Based on Ideal Lattices. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 617–635. Springer, Heidelberg (2009)
Suzuki, D.: How to Maximize the Potential of FPGA Resources for Modular Exponentiation. In: Paillier, P., Verbauwhede, I. (eds.) CHES 2007. LNCS, vol. 4727, pp. 272–288. Springer, Heidelberg (2007)
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Güneysu, T., Lyubashevsky, V., Pöppelmann, T. (2012). Practical Lattice-Based Cryptography: A Signature Scheme for Embedded Systems. In: Prouff, E., Schaumont, P. (eds) Cryptographic Hardware and Embedded Systems – CHES 2012. CHES 2012. Lecture Notes in Computer Science, vol 7428. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33027-8_31
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