[en] A Dining Cryptographers network (DCnet for short) allows anonymous communication with sender and receiver untraceability even if an adversary has unlimited access to the connection metadata of the network. Originally introduced by David Chaum in the 1980s, DCnets were for a long time considered not practical for real-world applications because of the tremendous communication and computation overhead they introduce. However, technological innovations such as 5G networks and extremely powerful 64-bit processors make a good case to reassess the practicality of DCnets. In addition, recent advances in elliptic-curve based commitment schemes and Zero-Knowledge Proofs (ZKPs) provide a great opportunity to reduce the computational cost of modern DCnets that are able to detect malicious behavior of communicating parties. In this paper we introduce X64ECC, a self-contained library for Elliptic Curve Cryptography (ECC) developed from scratch to support all the public-key operations needed by modern DCnets: key exchange, digital signatures, Pedersen commitments, and ZKPs. X64ECC is written in C and uses compiler intrinsics to speed up performance-critical arithmetic operations. It is highly scalable and works with Montgomery curves and twisted Edwards curves of different cryptographic strength. Despite its high scalability and portability, X64ECC is able to compute a fixed-base scalar multiplication on a twisted Edwards curve over a 255-bit prime field in about 145,000 clock cycles on a modern Intel X64 processor. All cryptosystems can be adapted on-the-fly (i.e. without recompilation) to implement DCnets with arbitrary message sizes, and tradeoffs between the cryptographic strength and throughput of a DCnet are possible.
Disciplines :
Computer science
Author, co-author :
Dupont, Elona ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > CVI2
Franck, Christian ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS)
Groszschädl, Johann ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS)
External co-authors :
no
Language :
English
Title :
Fast and Flexible Elliptic Curve Cryptography for Dining Cryptographers Networks
Publication date :
October 2020
Event name :
6th International Conference on Mobile, Secure, and Programmable Networking (MSPN 2020)
Event place :
Paris, France
Event date :
from 28-10-2020 to 29-10-2020
Audience :
International
Main work title :
Mobile, Secure, and Programmable Networking, 6th International Conference, MSPN 2020, Paris, France, October 28–29, 2020, Revised Selected Papers
Bernstein, D.J.: Curve25519: new Diffie-Hellman speed records. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T. (eds.) PKC 2006. LNCS, vol. 3958, pp. 207– 228. Springer, Heidelberg (2006). https://doi.org/10.1007/11745853 14
Bernstein, D.J., Birkner, P., Joye, M., Lange, T., Peters, C.: Twisted Edwards curves. In: Vaudenay, S. (ed.) AFRICACRYPT 2008. LNCS, vol. 5023, pp. 389– 405. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-68164-9 26
Bernstein, D.J., Lange, T.: Montgomery curves and the montgomery ladder. Cryp-tology ePrint Archive, Report 2017/293 (2017). https://eprint.iacr.org/2017/293
Bernstein, D.J., Lange, T., Schwabe, P.: The security impact of a new cryptographic library. In: Hevia, A., Neven, G. (eds.) LATINCRYPT 2012. LNCS, vol. 7533, pp. 159–176. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33481-8 9
Bos, J., den Boer, B.: Detection of disrupters in the DC protocol. In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol. 434, pp. 320–327. Springer, Heidelberg (1990). https://doi.org/10.1007/3-540-46885-4 33
Camenisch, J., Stadler, M.: Proof systems for general statements about discrete logarithms. Technical report/ETH Zurich, Department of Computer Science 260 (1997)
Chaum, D.: The dining cryptographers problem: unconditional sender and recipient untraceability. J. Cryptol. 1(1), 65–75 (1988)
Corrigan-Gibbs, H., Ford, B.: Dissent: accountable anonymous group messaging. In: Proceedings of the 17th ACM Conference on Computer and Communications Security, pp. 340–350 (2010)
Diffie, W., Hellman, M.: New directions in cryptography. IEEE Trans. Inf. Theory 22(6), 644–654 (1976)
Düll, M., Haase, B., Hinterwälder, G., Hutter, M., Paar, C., Sánchez, A.H., Schwabe, P.: High-speed Curve25519 on 8-bit, 16-bit and 32-bit microcontrollers. Des. Codes Crypt. 77(2–3), 493–514 (2015)
Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987). https://doi.org/10.1007/3-540-47721-7 12
Franck, C.: New directions for dining cryptographers. Master’s thesis, University of Luxembourg, 2008 (2008)
Franck, C.: Dining cryptographers with 0.924 verifiable collision resolution. Ann. UMCS Informatica 14(1), 49–59 (2014). https://doi.org/10.2478/umcsinfo-2014-0007
Franck, C., van de Graaf, J.: Dining cryptographers are practical (2014)
Franck, C., Großschädl, J.: Efficient implementation of Pedersen commitments using twisted Edwards curves. In: Bouzefrane, S., Banerjee, S., Sailhan, F., Boumerdassi, S., Renault, E. (eds.) MSPN 2017. LNCS, vol. 10566, pp. 1–17. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-67807-8 1
Ghatpande, S., Großschädl, J., Liu, Z.: A family of lightweight twisted Edwards curves for the internet of things. In: Blazy, O., Yeun, C.Y. (eds.) WISTP 2018. LNCS, vol. 11469, pp. 193–206. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-20074-9 14
Intel Corporation: Intel Core i7–9750H Processor (12M Cache, up to 4.50 GHz) Product Specifications. https://ark.intel.com/content/www/us/en/ark/products/191045/intel-core-i7-9750h-processor-12m-cache-up-to-4-50-ghz.html
Josefsson, S., Liusvaara, I.: Edwards-Curve Digital Signature Algorithm (EdDSA). Internet Research Task Force, Crypto Forum Research Group, RFC 8032, January 2017
Krasnova, A., Neikes, M., Schwabe, P.: Footprint scheduling for dining-cryptographer networks. In: Grossklags, J., Preneel, B. (eds.) FC 2016. LNCS, vol. 9603, pp. 385–402. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54970-4 23
Langley, A., Hamburg, M., Turner, S.: Elliptic Curves for Security. RFC 7748, January 2016. https://doi.org/10.17487/RFC7748. https://rfc-editor.org/rfc/rfc7748. txt
Miller, V.S.: Use of elliptic curves in cryptography. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 417–426. Springer, Heidelberg (1986). https://doi.org/10.1007/3-540-39799-X 31
Montgomery, P.L.: Speeding the Pollard and elliptic curve methods of factorization. Math. Comput. 48(177), 243–264 (1987)
Öztürk, E., Guilford, J., Gopal, V.: Large integer squaring on intel architecture processors (2013). Intel white paper, available for download at http://www.intel. com/content/dam/www/public/us/en/documents/white-papers/large-integer-squaring-ia-paper.pdf
Öztürk, E., Guilford, J., Gopal, V., Feghali, W.: New instructions supporting large integer arithmetic on intel architecture processors (2012). Intel white paper, available for download at http://www.intel.com/content/dam/www/public/us/en/documents/white-papers/ia-large-integer-arithmetic-paper.pdf
De la Cadena, W., Kaiser, D., Mitseva, A., Panchenko, A., Engel, T.: Analysis of multi-path onion routing-based anonymization networks. In: Foley, S.N. (ed.) DBSec 2019. LNCS, vol. 11559, pp. 240–258. Springer, Cham (2019). https://doi. org/10.1007/978-3-030-22479-0 13
Pedersen, T.P.: Non-interactive and information-theoretic secure verifiable secret sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-46766-1 9
Pfitzmann, A.: Diensteintegrierende Kommunikationsnetze mit teil-nehmerüberprüfbarem Datenschutz. Springer, Heidelberg (1990)
Ruffing, T., Moreno-Sanchez, P., Kate, A.: CoinShuffle: practical decentralized coin mixing for bitcoin. In: Kuty̷lowski, M., Vaidya, J. (eds.) ESORICS 2014. LNCS, vol. 8713, pp. 345–364. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11212-1 20
Samsung: 6G-the next hyper-connected experience for all. Technical report, Samsung Research (2020)
Schnorr, C.P.: Efficient identification and signatures for smart cards. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 239–252. Springer, New York (1990). https://doi.org/10.1007/0-387-34805-0 22
Waidner, M.: Unconditional sender and recipient untraceability in spite of active attacks. In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol. 434, pp. 302–319. Springer, Heidelberg (1990). https://doi.org/10.1007/3-540-46885-4 32
Waidner, M., Pfitzmann, B.: The dining cryptographers in the disco: unconditional sender and recipient untraceability with computationally secure serviceability. In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol. 434, p. 690. Springer, Heidelberg (1990). https://doi.org/10.1007/3-540-46885-4 69
Wu, H., Wang, F.: A survey of noninteractive zero knowledge proof system and its applications. Sci. World J. 2014 (2014)
