Side-Channel Vulnerabilities of Unified Point Addition on Binary Huff Curve and Its Countermeasure
Source abstract
Abstract
Unified point addition for computing elliptic curve point addition and doubling is considered to be resistant to simple power analysis. Recently, new side-channel attacks, such as recovery of secret exponent by triangular trace analysis and horizontal collision correlation analysis, have been successfully applied to elliptic curve methods to investigate their resistance to side-channel attacks. These attacks turn out to be very powerful since they only require leakage of a single power consumption trace. In this paper, using these side-channel attack analyses, we introduce two vulnerabilities of unified point addition on the binary Huff curve. Also, we propose a new unified point addition method for the binary Huff curve. Furthermore, to secure against these vulnerabilities, we apply an equivalence class to the side-channel atomic algorithm using the proposed unified point addition method.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Cryptography and Residue Arithmetic · Cryptographic Implementations and Security · Coding theory and cryptography
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Center for Information Security Technologies (CIST), Korea University, Seoul 02841, Korea
Department of Cyber Security, College of Science and Technology, Korea University, Sejong 30019, Korea
References (21)
Show source-provided references
1. Kocher, P., Jaffe, J., and Jun, B. (1999, January 15–19). Differential power analysis. Proceedings of the Annual International Cryptology Conference, Santa Barbara, CA, USA.10.1007/3-540-48405-1_25 ↗
2. Coron, J.S. (1999, January 12–13). Resistance against differential power analysis for elliptic curve cryptosystems. Proceedings of the International Workshop on Cryptographic Hardware and Embedded Systems, Worcester, MA, USA.10.1007/3-540-48059-5_25 ↗
3. Izu, T., and Takagi, T. (2002, January 12–14). A fast parallel elliptic curve multiplication resistant against side channel attacks. Proceedings of the International Workshop on Public Key Cryptography, Paris, France.10.1007/3-540-45664-3_20 ↗
4. Low-cost solutions for preventing simple side-channel analysis: Side-channel atomicity10.1109/TC.2004.13 ↗
5. Brier, E., and Joye, M. (2002, January 12–14). Weierstraß elliptic curves and side-channel attacks. Proceedings of the International Workshop on Public Key Cryptography, Paris, France.10.1007/3-540-45664-3_24 ↗
6. Horizontal collision correlation attack on elliptic curves10.1007/s12095-014-0111-8 ↗
7. Clavier, C., Feix, B., Gagnerot, G., Giraud, C., Roussellet, M., and Verneuil, V. (2012, January 9–12). ROSETTA for single trace analysis. Proceedings of the International Conference on Cryptology in India, Kolkata, India.10.1007/978-3-642-34931-7_9 ↗
8. Devigne, J., and Joye, M. (2011, January 14–18). Binary huff curves. Proceedings of the Cryptographers’ Track at the RSA Conference, San Francisco, CA, USA.10.1007/978-3-642-19074-2_22 ↗
9. Ghosh, S., Kumar, A., Das, A., and Verbauwhede, I. (2013, January 20–23). On the implementation of unified arithmetic on binary huff curves. Proceedings of the International Workshop on Cryptographic Hardware and Embedded Systems, Santa Barbara, CA, USA.10.1007/978-3-642-40349-1_20 ↗
10. Clavier, C., Feix, B., Gagnerot, G., Roussellet, M., and Verneuil, V. (2010, January 15–17). Horizontal correlation analysis on exponentiation. Proceedings of the International Conference on Information and Communications Security, Barcelona, Spain.10.1007/978-3-642-17650-0_5 ↗
11. Joye, M., Tibouchi, M., and Vergnaud, D. (2010, January 19–23). Huff’s model for elliptic curves. Proceedings of the International Algorithmic Number Theory Symposium, Nancy, France.10.1007/978-3-642-14518-6_20 ↗
12. O’Flynn, C., and Chen, Z.D. (2014, January 13–15). Chipwhisperer: An open-source platform for hardware embedded security research. Proceedings of the International Workshop on Constructive Side-Channel Analysis and Secure Design, Paris, France.10.1007/978-3-319-10175-0_17 ↗
13. Gierlichs, B., Lemke-Rust, K., and Paar, C. (2006, January 10–13). Templates vs. stochastic methods. Proceedings of the International Workshop on Cryptographic Hardware and Embedded Systems, Yokohama, Japan.10.1007/11894063_2 ↗
14. The generalization ofstudent’s’ problem when several different population variances are involved
15. Machine learning in side-channel analysis: a first study10.1007/s13389-011-0023-x ↗
16. Choudary, O., and Kuhn, M.G. (2013, January 27–29). Efficient template attacks. Proceedings of the International Conference on Smart Card Research and Advanced Applications, Berlin, Germany.10.1007/978-3-319-08302-5_17 ↗
17. Durvaux, F., and Standaert, F.X. (2016, January 8–12). From improved leakage detection to the detection of points of interests in leakage traces. Proceedings of the Annual International Conference on the Theory and Applications of Cryptographic Techniques, Vienna, Austria.10.1007/978-3-662-49890-3_10 ↗
18. Hankerson, D., Menezes, A.J., and Vanstone, S. (2006). Guide to Elliptic Curve Cryptography, Springer Science & Business Media.
19. Fan, J., Guo, X., De Mulder, E., Schaumont, P., Preneel, B., and Verbauwhede, I. (2010, January 13–14). State-of-the-art of secure ECC implementations: a survey on known side-channel attacks and countermeasures. Proceedings of the 2010 IEEE International Symposium on Hardware-Oriented Security and Trust (HOST), Anaheim, CA, USA.10.1109/HST.2010.5513110 ↗
20. Fips pub 186-3: Digital signature standard (dss)
21. Bernstein, D.J. (2018, October 22). Explicit-Formulas Database. Available online: http://www. hyperelliptic. org/EFD.