Abstract
Selection of a proper elliptic curve is the most important aspect of Elliptic Curve Cryptography (ECC). Security of ECC is based on the Elliptic Curve Discrete Logarithm Problem which is believed to be unsolvable. Some of the well-known elliptic curve standards are NIST FIPS 186-2, Brainpool, and ANSI X9.62. Among these, NIST-recommended curves are a popular choice for industrial applications, in particular, for Internet security as a part of TLS/SSL, and even in real-time media encryption which uses Voice over IP (VoIP) technology. Specifically, NIST P-256 curve is widely used in these applications. Some NIST curves have disadvantages related to security issues, and therefore it is important to search for secure alternatives. In our work, we propose a new secure short Weierstrass curve \(EW_{256357}\) at the 128-bit security level and compare it with the NIST P-256 curve. Our proposed curve is compatible with NIST P-256 curve but features better security. Based on the performance analysis of related curves in our previous and present works in terms of delay and jitter, we say that our proposed curve is suitable for the real-time media encryption.
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References
Digital Signature Standard (DSS). Federal Information Processing Standards Publication 186–4. https://nvlpubs.nist.gov/nistpubs/fips/nist.fips.186-4.pdf
ECC Brainpool. ECC Brainpool Standard Curves and Curve Generation. https://www.teletrust.de/fileadmin/files/oid/oid_ECC-Brainpool-Standard-curves-V1.pdf
IEEE 1363–2000: Standard specifications for public key cryptography. https://standards.ieee.org/standard/1363-2000.html
ITU-T, Series G: Transmission Systems and Media, Digital Systems and Networks. https://www.itu.int/rec/T-REC-G.114-200305-I
Report and Recommendations of the Visiting Committee on Advanced Technology of the National Institute of Standards and Technology. https://www.nist.gov/sites/default/files/documents/2017/05/09/VCAT-Report-on-NIST-Cryptographic-Standards-and-Guidelines-Process.pdf
Rabin, M.O.: Probabilistic algorithm for testing primality. J. Number Theory 12, 128–138 (1980)
Lynn, B.: Elliptic Curves - The MOV attack. https://crypto.stanford.edu/pbc/notes/elliptic/movattack.html
Hales, C.: The NSA Back Door to NIST. Not. AMS 61(2), 190–192
Hankerson, D., Menezes, A., Vanstone, S.: Guide to Elliptic Curve Cryptography. Springer, Heidelberg (2004). https://doi.org/10.1007/b97644
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., Lange, T.: Failures in NIST’s ECC standards. https://cr.yp.to/newelliptic/nistecc-20160106.pdf
Bernstein, D.J., Lange, T.: SafeCurves: choosing safe curves for elliptic-curve cryptography. https://safecurves.cr.yp.to. Accessed 20 June 2020
Bernstein, D.J., Lange, T.: Security dangers of the NIST curves. https://cr.yp.to/talks/2013.05.31/slides-dan+tanja-20130531-4x3.pdf
Bernstein, D.J., Hamburg, M., Krasnova, A., Lange, T.: Elligator: elliptic-curve points indistinguishable from uniform random strings. In: ACM Conference on Computer and Communications Security
Biehl, I., Meyer, B., Muller, V.: Differential fault attacks on elliptic curve cryptosystems. In: Annual International Cryptology Conference, pp. 131–146 (2000)
Faugère, J.-C., Perret, L., Petit, C., Renault, G.: Improving the complexity of index calculus algorithms in elliptic curves over binary fields. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 27–44. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_4
Bos, J.W., Costello, C., Longa, P., Naehrig, M.: Specification of curve selection and supported curve parameters in MSR ECCLib. https://www.researchgate.net/publication/281897794_Specification_of_Curve_Selection_and_Supported_Curve_Parameters_in_MSR_ECCLib
Bos, J.W., Costello, C., Longa, P., Naehrig, M.: Selecting elliptic curves for cryptography: an efficiency and security analysis. J. Cryptographic Eng. 6(4), 259–286 (2016)
Bos, J.W., Halderman, J.A., Heninger, N., Moore, J., Naehrig, M., Wustrow, E.: Elliptic curve cryptography in practice. https://eprint.iacr.org/2013/734.pdf
Caswell, M.: OpenSSL Wins the Levchin Prize. https://www.openssl.org/blog/blog/2018/01/10/levchin/
Hamburg, M.: Ed448-Goldilocks, a new elliptic curve. Cryptology ePrint Archive, Report 2015/625 (2015)
Lochter, M., Wiemers, A.: Twist Insecurity, International Association for Cryptologic Research. https://pdfs.semanticscholar.org/3428/3663d6d5bfa60c6dfeafadbf50d69e9b9b40.pdf
Scott, M.: Backdoors in NIST elliptic curves. https://www.miracl.com/press/backdoors-in-nist-elliptic-curves
Koblitz, N.: Elliptic curve cryptosystems. Math. Comput. 48(177), 203–209 (1987)
Perlroth, N.: The New York Times, Government announces steps to restore confidence on encryption standards. http://bits.blogs.nytimes.com/2013/09/10/government-announces-steps-to-restore-confidence-on-encryption-standards
Sen, N., Dantu, R., Jagannath, V., Thompson, M.: Performance Analysis of Elliptic Curves for Real-time Video Encryption, pp. 64–71. National Cyber Summit, USA (2018)
Schoof, R.: Counting points on elliptic curves over finite fields. J. Theory Numbers Bordeaux 7, 219–254 (1995)
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
Shoup, V.: A Proposal for an ISO Standard for Public Key Encryption. https://www.shoup.net/papers/iso-2_1.pdf. Accessed 15 July 2019
Acknowledgement
This research is based upon work supported by the National Science Foundation under awards 1241768 and 1637291.
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Sen, N., Dantu, R., Morozov, K. (2020). \(EW_{256357}\): A New Secure NIST P-256 Compatible Elliptic Curve for VoIP Applications’ Security. In: Park, N., Sun, K., Foresti, S., Butler, K., Saxena, N. (eds) Security and Privacy in Communication Networks. SecureComm 2020. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 336. Springer, Cham. https://doi.org/10.1007/978-3-030-63095-9_19
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