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Elliptic curve cryptography is a public key cryptosystem based on the elliptic curve discrete logarithm problem. The reason for the attractiveness of ECC is that there is no sub-exponential algorithm known to solve the elliptic curve discrete logarithm problem. This leads to lower memory requirements, lower computation requirements and higher security than other public key cryptosystems. This project...
The transport layer security (TLS) protocol is currently the predominant method of implementing Internet security. This paper proposes an FPGA-based embedded system integrating hardware that accelerates the cryptographic algorithms used in the SSL/TLS protocol. OpenSSL, an open source implementation of the SLL v3 and TLS v1 protocol, is deployed in the proposed embedded system powered with a Nios-2...
This paper outlines a FPGA implementation of an elliptic curve processor that utilises the GLV method. The GLV method has been shown to be able to speed up computationally expensive point multiplication operations. We also present an implementation of a Hiasat multiplier which can be used with special moduli to further speed up point multiplications. The Hiasat multiplier takes advantage of fast reduction...
Identity-based cryptography has been gradually accepted as a more effective way of implementing asymmetric cryptography. The calculation of cryptographically-suitable pairings is crucial for the performance of pairing based protocols. In this paper we present a comparative study of hardware implementation techniques for computing the ??T pairing over the finite field F3{su97|}. Our hardware-software...
The contribution in this paper describes a solution to implement a low cost-low area scalable elliptic curve cryptography (ECC) over binary finite fields GF(2m) using a hardware-software co-design approach. The proposed hardware-software co-design is hosted on a free-soft-core processor from Xilinx FPGA, namely PicoBlaze as a low-cost platform. The PicoBlaze is supported by two novel circuits to execute...
We describe a residue number system (RNS) implementation of the 192-bit elliptic curve digital signature algorithm over GF(p). It uses a Tensilica Xtensa LX2.1 microprocessor core with hardware extensions to improve the performance of RNS operations. The low power and small area of the enhanced Xtensa LX2.1 core make it suitable for smart cards. This implementation is the first to use the RNS for...
In this paper, a generic elliptic curve (EC) arithmetic unit with high flexibility and small chip covered area is proposed. This EC arithmetic unit is based on the one dimensional systolic architectural realization of a proposed modified multiplication - inversion algorithm that through appropriate initialization uses the algorithmic structure of inversion to also perform multiplication. The proposed...
The main contribution of this paper is to present a simple, scalable, and portable tiny processing system which can be implemented in various FPGAs. Our processing system includes a 16-bit processor, a cross assembler, and a cross compiler. The 16-bit processor runs in 89 MHz on the Xilinx Spartan-3A family FPGAXC3S700A using 336 out of 5888 slices (5.7%)and in 76 MHz on the Altera Cyclon III family...
This paper presents SPA (simple power analysis) attacks against public-key cryptosystems implemented on an FPGA platform. The SPA attack investigates a power waveform generated by a cryptographic module, and reveals a secret key in the module. We focus on chosen-message SPA attacks, which enhances the differences of operating waveforms between multiplication and squaring correlated to the secret key...
Algebraic torus-based cryptosystems are an alternative for Public-Key Cryptography (PKC). It maintains the security of a larger group while the actual computations are performed in a subgroup. Compared with RSA for the same security level, it allows faster exponentiation and much shorter bandwidth for the transmitted data. In this work we implement a torus-based cryptosystem, the so-called CEILIDH,...
This paper presents a high-radix elliptic curve cryptographic architecture that performs a scalar multiple of an elliptic curve point operations over GF(2m). The proposed architecture is based on a new algorithm, which is a modified version of the sliding window scalar multiplication algorithm. We speed-up the scalar multiplication by merging the point doubling and adding operations into a single...
Many important algorithms for public-key cryptography rely on computation-intensive arithmetic operations like modular exponentiation on very long integers, typically in the range of 512 and 2048 bits. Modular exponentiation is generally realized through a sequence of modular multiplications and spends the majority of execution time in simple inner loops. Speeding up these performance-critical inner...
This article presents efficient hardware implementations for the Gaussian normal basis multiplication over GF(2163). Hardware implementations of GF(2m) multiplication algorithms are suitable to design elliptic curve cryptoprocessors, which allow that elliptic curve based cryptosystems implemented in hardware provide more physical security and higher performance than software implementations. In this...
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