Abstract
Most of the cryptographic constructions deployed in practical systems today, in particular digital signatures and key-establishment schemes, are vulnerable to attacks using quantum computers. Post-quantum cryptography (PQC) deals with the design and implementation of cryptographic algorithms that are resistant to these attacks. In this paper, we evaluate the NIST’s PQC competition candidates with respect to their suitability for the implementation on special hardware platforms. In particular, we focus on the implementability on constrained platforms (e.g., smart cards, small single-board computers) on one side and on the performance on very fast hardware-accelerated platforms (i.e., field-programmable gate arrays - FPGAs) on the other side. Besides the analysis of the candidates’ design features affecting the performance on these devices and security aspects, we present also the practical results from the existing implementation on contemporary hardware.
Keywords
This work is supported by the National Sustainability Program under grant LO1401 and Ministry of Interior under grant VI20192022126.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
NIST - Computer Security Resource Center (CSRC). https://csrc.nist.gov/Projects/Post-Quantum-Cryptography/round-2-submissions
Albrecht, M.R., Hanser, C., Hoeller, A., Pöppelmann, T., Virdia, F., Wallner, A.: Implementing RLWE-based schemes using an RSA co-processor. IACR Trans. Cryptograph. Hardware Embedded Syst. 2019(1), 169–208 (2019)
Alkim, E., Ducas, L., Pöppelmann, T., Schwabe, P.: Post-quantum key exchange-a new hope. In: USENIX Security Symposium, vol. 2016 (2016)
Basu, K., Soni, D., Nabeel, M., Karri, R.: NIST post-quantum cryptography-a hardware evaluation study. IACR Cryptol. ePrint Archive 2019, 47 (2019)
Bernstein, D.J.: Post-quantum cryptography. In: van Tilborg, H.C.A., Jajodia, S. (eds.) Encyclopedia of Cryptography and Security, pp. 949–950. Springer, Heidelberg (2011). https://doi.org/10.1007/978-1-4419-5906-5
Bertoni, G., Daemen, J., Hoffert, S., Peeters, M., Van Assche, G., Van Keer, R.: Extended keccak code package. https://github.com/XKCP/XKCP
Boorghany, A., Jalili, R.: Implementation and comparison of lattice-based identification protocols on smart cards and microcontrollers. IACR Cryptol. ePrint Archive 2014, 78 (2014)
Boorghany, A., Sarmadi, S.B., Jalili, R.: On constrained implementation of lattice-based cryptographic primitives and schemes on smart cards. ACM Trans. Embedded Comput. Syst. (TECS) 14(3), 42 (2015)
Bos, J., et al.: Frodo: take off the ring! practical, quantum-secure key exchange from LWE. In: Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, pp. 1006–1018. ACM (2016)
Bos, J., et al.: CRYSTALS-kyber: a CCA-secure module-lattice-based KEM. In: 2018 IEEE European Symposium on Security and Privacy (EuroS&P). IEEE (2018)
Chen, J.-M., Yang, B.-Y.: A more secure and efficacious TTS signature scheme. In: Lim, J.-I., Lee, D.-H. (eds.) ICISC 2003. LNCS, vol. 2971, pp. 320–338. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24691-6_24
Daemen, J., Rijmen, V.: The Design of Rijndael: AES-the Advanced Encryption Standard. Springer, Berlin (2013)
Ding, J., Schmidt, D.: Rainbow, a new multivariable polynomial signature scheme. In: Ioannidis, J., Keromytis, A., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 164–175. Springer, Heidelberg (2005). https://doi.org/10.1007/11496137_12
Ebrahimi, S., Bayat-Sarmadi, S., Mosanaei-Boorani, H.: Post-quantum cryptoprocessors optimized for edge and resource-constrained devices in IoT. IEEE IoT J. 6, 5500–5507 (2019)
Ferozpuri, A., Gaj, K.: High-speed FPGA implementation of the NIST round 1 rainbow signature scheme. In: 2018 International Conference on ReConFigurable Computing and FPGAs (ReConFig), pp. 1–8. IEEE (2018)
OpenSSL Foundation: OpenSSL cryptography and SSL/TLS toolkit. https://www.openssl.org/
Granlund, T.: The GNU multiple precision arithmetic library. https://gmplib.org/
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). https://doi.org/10.1007/BFb0054868
Howe, J., Rafferty, C., Khalid, A., O’Neill, M.: Compact and provably secure lattice-based signatures in hardware. In: 2017 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–4. IEEE (2017)
Jao, D., De Feo, L.: Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies. In: Yang, B.-Y. (ed.) PQCrypto 2011. LNCS, vol. 7071, pp. 19–34. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25405-5_2
Kipnis, A., Patarin, J., Goubin, L.: Unbalanced oil and vinegar signature schemes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 206–222. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48910-X_15
Koziel, B., Azarderakhsh, R., Kermani, M.M., Jao, D.: Post-quantum cryptography on FPGA based on isogenies on elliptic curves. IEEE Trans. Circuits Syst. I Regul. Pap. 64(1), 86–99 (2016)
Kuo, P.C., et al.: Post-quantum key exchange on FPGAs. IACR Cryptol. ePrint Archive 2017, 690 (2017)
Lamport, L.: Constructing digital signatures from a one-way function. Technical report, Technical Report CSL-98, SRI International Palo Alto (1979)
Martín-López, E., Laing, A., Lawson, T., Alvarez, R., Zhou, X.Q., O’brien, J.L.: Experimental realization of Shor’s quantum factoring algorithm using qubit recycling. Nat. Photonics 6(11), 773 (2012)
Mceliece, R.J.: A public-key cryptosystem based on algebraic. Coding Thv 4244, 114–116 (1978)
Merkle, R.C.: A certified digital signature. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 218–238. Springer, New York (1990). https://doi.org/10.1007/0-387-34805-0_21
Moses, T.: Quantum computing and cryptography. Entrust Inc., January 2009
Nejatollahi, H., Dutt, N., Ray, S., Regazzoni, F., Banerjee, I., Cammarota, R.: Software and hardware implementation of lattice-cased cryptography schemes (2017)
Nejatollahi, H., Dutt, N., Ray, S., Regazzoni, F., Banerjee, I., Cammarota, R.: Post-quantum lattice-based cryptography implementations: a survey. ACM Comput. Surv. 51(6), 129:1–129:41 (2019). https://doi.org/10.1145/3292548. http://doi.acm.org.ezproxy.lib.vutbr.cz/10.1145/3292548
Niederreiter, H.: Knapsack-type cryptosystems and algebraic coding theory. Prob. Control Inf. Theory 15(2), 159–166 (1986)
Oder, T., Güneysu, T.: Implementing the newhope-simple key exchange on low-cost FPGAs. In: Lange, T., Dunkelman, O. (eds.) LATINCRYPT 2017. LNCS, vol. 11368, pp. 128–142. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-25283-0_7
Patarin, J.: Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): two new families of asymmetric algorithms. In: Maurer, U. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 33–48. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-68339-9_4
Pöppelmann, T.: Efficient implementation of ideal lattice-based cryptography. IT-Inf. Technol. 59(6), 305–309 (2017)
Saarinen, M.J.O.: Ring-LWE ciphertext compression and error correction: tools for lightweight post-quantum cryptography. In: Proceedings of the 3rd ACM International Workshop on IoT Privacy, Trust, and Security, pp. 15–22. ACM (2017)
Shoup, V.: NTL: a library for doing number theory. https://shoup.net/ntl/
Soni, D., Basu, K., Nabeel, M., Karri, R.: A hardware evaluation study of NIST post-quantum cryptographic signature schemes (2020)
Strenzke, F.: A smart card implementation of the McEliece PKC. In: Samarati, P., Tunstall, M., Posegga, J., Markantonakis, K., Sauveron, D. (eds.) WISTP 2010. LNCS, vol. 6033, pp. 47–59. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-12368-9_4
Wang, W., Szefer, J., Niederhagen, R.: FPGA-based niederreiter cryptosystem using binary goppa codes. In: Lange, T., Steinwandt, R. (eds.) PQCrypto 2018. LNCS, vol. 10786, pp. 77–98. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-79063-3_4
Yuan, Y., Fukushima, K., Kiyomoto, S., Takagi, T.: Memory-constrained implementation of lattice-based encryption scheme on standard Java card. In: 2017 IEEE International Symposium on Hardware Oriented Security and Trust (HOST), pp. 47–50. IEEE (2017)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
A Post Quantum Cryptography Size Requirements
A Post Quantum Cryptography Size Requirements
This section discusses the current size requirements of the 2nd round NIST competitors. Our overview on current PQC schemes deals with implementations on devises which have limited memory capacity. Therefore, the suitability of a PQC scheme depends at first on its memory requirements. If the scheme is too demanding, it can not be directly implemented. Table 6 shows key pair, signature and ciphertext sizes of 2nd round NIST schemes. Regarding signature schemes, Dilithium and Falcon are the proposals which require less storage. Note that both the schemes belong to LBC group.
In case of KEM schemes, ROLLO-I and Round5 are the most promising ones. Therefore, the less demanding schemes between LBC and CBC groups have comparable memory requirements for KEM. Observe that NewHope also demands small memory capacity.
It is important to notice that memory capacity is only one of the component which have to be taken in consideration when schemes are compared.
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Malina, L., Ricci, S., Dzurenda, P., Smekal, D., Hajny, J., Gerlich, T. (2020). Towards Practical Deployment of Post-quantum Cryptography on Constrained Platforms and Hardware-Accelerated Platforms. In: Simion, E., Géraud-Stewart, R. (eds) Innovative Security Solutions for Information Technology and Communications. SecITC 2019. Lecture Notes in Computer Science(), vol 12001. Springer, Cham. https://doi.org/10.1007/978-3-030-41025-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-41025-4_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-41024-7
Online ISBN: 978-3-030-41025-4
eBook Packages: Computer ScienceComputer Science (R0)