Furkan Turan
Abstract
This article describes a field-programmable gate array (FPGA) cryptographic architecture, which combines the elliptic curve--based Ed25519 digital signature algorithm and the X25519 key establishment scheme in a single module. Cryptographically, these are high-security elliptic curve cryptography algorithms with short key sizes and impressive execution times in software. Our goal is to provide a lightweight FPGA module that enables them on resource-constrained devices, specifically for Internet of Things (IoT) applications. In addition, we aim at extensibility with customisable countermeasures against timing and differential power analysis side-channel attacks and fault-injection attacks. For the former, we offer a choice between time-optimised versus constant-time execution, with or without Z-coordinate randomisation and base-point blinding; and for the latter, we offer enabling or disabling default-case statements in the Finite State Machine (FSM) descriptions. To obtain compactness and at the same time fast execution times, we make maximum use of the Digital Signal Processing (DSP) slices on the FPGA. We designed a single arithmetic unit that is flexible to support operations with two moduli and non-modulus arithmetic. In addition, our design benefits in-place memory management and the local storage of inputs into DSP slices’ pipeline registers and takes advantage of distributed memory. These eliminate a memory access bottleneck. The flexibility is offered by a micro-code supported instruction-set architecture. Our design targets 7-Series Xilinx FPGAs and is prototyped on a Zynq System-on-Chip (SoC). The base design combining Ed25519 and X25519 in a single module, and its implementation requires only around 11.1K Lookup Tables (LUTs), 2.6K registers, and 16 DSP slices. Also, it achieves performance of 1.6ms for a signature generation and 3.6ms for a signature verification for a 1024-bit message with an 82MHz clock. Moreover, the design can be optimised only for X25519, which gives the most compact FPGA implementation compared to previously published X25519 implementations.
- 2017. Estimated Value of the North American Smart Home Market From 2012 to 2021 (in Billion U.S. Dollars). Retrieved from https://www.statista.com/statistics/296113/north-america-smart-home-market-revenue/.Google Scholar
- Daniel J. Bernstein. 2006. Curve25519: New Diffie-Hellman speed records. In International Workshop on Public Key Cryptography. Springer, 207--228. Google ScholarDigital Library
- Daniel J. Bernstein, Niels Duif, Tanja Lange, Peter Schwabe, and Bo-Yin Yang. 2012. High-speed high-security signatures. J. Cryptographic Eng. 2, 2 (2012), 77--89.Google ScholarCross Ref
- Daniel J. Bernstein, Bernard Van Gastel, Wesley Janssen, Tanja Lange, Peter Schwabe, and Sjaak Smetsers. 2014. TweetNaCl: A crypto library in 100 tweets. In International Conference on Cryptology and Information Security in Latin America. Springer, 64--83.Google Scholar
- Billy Bob Brumley and Nicola Tuveri. 2011. Remote timing attacks are still practical. In Computer Security—ESORICS 2011, Vijay Atluri and Claudia Diaz (Eds.). Springer, Berlin, Germany, 355--371. Google ScholarDigital Library
- Jean-Sébastien Coron. 1999. Resistance against differential power analysis for elliptic curve cryptosystems. In Cryptographic Hardware and Embedded Systems. Springer, 725--725. Google ScholarDigital Library
- Darrel Hankerson, Alfred J. Menezes, and Scott Vanstone. 2005. Guide to elliptic curve cryptography. Computing Reviews 46, 1 (2005), 13.Google ScholarDigital Library
- Hüseyin Hisil, Kenneth Koon-Ho Wong, Gary Carter, and Edward Dawson. 2008. Twisted Edwards curves revisited. In Asiacrypt, Vol. 5350. Springer, 326--343. Google ScholarDigital Library
- Mei-Chen Hsueh, Timothy K. Tsai, and Ravishankar K. Iyer. 1997. Fault injection techniques and tools. Comput. 30, 4 (1997), 75--82. Google ScholarDigital Library
- Simon Josefsson and Ilari Liusvaara. 2017. Edwards-curve Digital Signature Algorithm (eddsa). Technical Report RFC 8032.Google Scholar
- Paul Kocher, Joshua Jaffe, and Benjamin Jun. 1998. Introduction to differential power analysis and related attacks.Google Scholar
- Philipp Koppermann, Fabrizio De Santis, Johann Heyszl, and Georg Sigl. 2016. X25519 hardware implementation for low-latency applications. In 2016 Euromicro Conference on Digital System Design (DSD), 2016 Euromicro Conference on. IEEE, 99--106.Google ScholarCross Ref
- Philipp Koppermann, Fabrizio De Santis, Johann Heyszl, and Georg Sigl. 2017. Low-latency X25519 hardware implementation: Breaking the 100 microseconds barrier. Microprocess. Microsyst. 52 (2017), 491--497. Google ScholarDigital Library
- Peter L. Montgomery. 1987. Speeding the Pollard and elliptic curve methods of factorization. Math. Comput. 48, 177 (1987), 243--264.Google ScholarCross Ref
- Joost Renes and Benjamin Smith. 2017. qDSA: Small and secure digital signatures with curve-based Diffie-Hellman key pairs. In International Conference on the Theory and Application of Cryptology and Information Security. Springer, 273--302.Google ScholarCross Ref
- Yolan Romailler and Sylvain Pelissier. 2017. Practical fault attack against the Ed25519 and EdDSA signature schemes. In 2017 Workshop on Fault Diagnosis and Tolerance in Cryptography (FDTC). IEEE, 17--24.Google ScholarCross Ref
- Vladimir Rozic, Bohan Yang, Wim Dehaene, and Ingrid Verbauwhede. 2015. Highly efficient entropy extraction for true random number generators on FPGAs. In 52nd ACM/EDAC/IEEE Design Automation Conference (DAC). IEEE, 1--6. Google ScholarDigital Library
- Pascal Sasdrich and Tim Güneysu. 2014. Efficient elliptic-curve cryptography using curve25519 on reconfigurable devices. ARC 8405 (2014), 25--36.Google Scholar
- Pascal Sasdrich and Tim Güneysu. 2015. Implementing curve25519 for side-channel--protected elliptic curve cryptography. ACM Trans. Reconfigurable Technol. Syst. (TRETS) 9, 1 (2015), 3. Google ScholarDigital Library
- Furkan Turan, Ruan De Clercq, Pieter Maene, Oscar Reparaz, and Ingrid Verbauwhede. 2016. Hardware acceleration of a software-based VPN. In 26th International Conference on Field Programmable Logic and Applications (FPL). IEEE, 1--9.Google ScholarCross Ref
- Xilinx. 2012. Vivado Design Suite User Guide: Synthesis. Xilinx. v2012.2.Google Scholar
- Xilinx. 2014. 7 Series DSP48E1 Slice. Xilinx. v1.8.Google Scholar
- Xilinx. 2015. Zynq-7000 All Programmable SoC Technical Reference Manual. Xilinx v1.10.Google Scholar
Index Terms
- Compact and Flexible FPGA Implementation of Ed25519 and X25519
Recommendations
Implementing Curve25519 for Side-Channel--Protected Elliptic Curve Cryptography
Special Section on the 2014 International Symposium on Applied Reconfigurable ComputingFor security-critical embedded applications Elliptic Curve Cryptography (ECC) has become the predominant cryptographic system for efficient key agreement and digital signatures. However, ECC still involves complex modular arithmetic that is a particular ...
Low-latency X25519 hardware implementation
In the past few years, there has been a growing interest in Curve25519 due to its elegant design aimed at both high-security and high-performance, making it one of the most promising candidates to secure IoT applications. Until now Curve25519 hardware ...
Comments