Towards a triple mode common operator FFT for Software Radio systems

International audienceA scenario to design a Triple Mode FFT is addressed. Based on a Dual Mode FFT structure, we present a methodology to reach a triple mode FFT operator (TMFFT) able to operate over three different fields: complex number domain C, Galois Fields GF(Ft) and GF(2m). We propose a reconfigurable Triple mode Multiplier that constitutes the core of the Butterflybased FFT. A scalable and flexible unit for the polynomial reduction needed in the GF(2m) multiplication is also proposed. An FPGA implementation of the proposed multiplier is given and the measures show a gain of 18%in terms of performance-to-cost ratio compared to a "Velcro" approach where two self-contained operators are implemented separately

Hardware/Software Co-design Applied to Reed-Solomon Decoding for the DMB Standard

This paper addresses the implementation of Reed- Solomon decoding for battery-powered wireless devices. The scope of this paper is constrained by the Digital Media Broadcasting (DMB). The most critical element of the Reed-Solomon algorithm is implemented on two different reconfigurable hardware architectures: an FPGA and a coarse-grained architecture: the Montium, The remaining parts are executed on an ARM processor. The results of this research show that a co-design of the ARM together with an FPGA or a Montium leads to a substantial decrease in energy consumption. The energy consumption of syndrome calculation of the Reed- Solomon decoding algorithm is estimated for an FPGA and a Montium by means of simulations. The Montium proves to be more efficient

Hardware Obfuscation for Finite Field Algorithms

With the rise of computing devices, the security robustness of the devices has become of utmost importance. Companies invest huge sums of money, time and effort in security analysis and vulnerability testing of their software products. Bug bounty programs are held which incentivize security researchers for finding security holes in software. Once holes are found, software firms release security patches for their products. The semiconductor industry has flourished with accelerated innovation. Fabless manufacturing has reduced the time-to-market and lowered the cost of production of devices. Fabless paradigm has introduced trust issues among the hardware designers and manufacturers. Increasing dependence on computing devices in personal applications as well as in critical infrastructure has given a rise to hardware attacks on the devices in the last decade. Reverse engineering and IP theft are major challenges that have emerged for the electronics industry. Integrated circuit design companies experience a loss of billions of dollars because of malicious acts by untrustworthy parties involved in the design and fabrication process, and because of attacks by adversaries on the electronic devices in which the chips are embedded. To counter these attacks, researchers have been working extensively towards finding strong countermeasures. Hardware obfuscation techniques make the reverse engineering of device design and functionality difficult for the adversary. The goal is to conceal or lock the underlying intellectual property of the integrated circuit. Obfuscation in hardware circuits can be implemented to hide the gate-level design, layout and the IP cores. Our work presents a novel hardware obfuscation design through reconfigurable finite field arithmetic units, which can be employed in various error correction and cryptographic algorithms. The effectiveness and efficiency of the proposed methods are verified by an obfuscated Reformulated Inversion-less Berlekamp-Massey (RiBM) architecture based Reed-Solomon decoder. Our experimental results show the hardware implementation of RiBM based Reed-Solomon decoder built using reconfigurable field multiplier designs. The proposed design provides only very low overhead with improved security by obfuscating the functionality and the outputs. The design proposed in our work can also be implemented in hardware designs of other algorithms that are based on finite field arithmetic. However, our main motivation was to target encryption and decryption circuits which store and process sensitive data and are used in critical applications

Customisable arithmetic hardware designs

Imperial Users onl

A common operator for FFT and FEC decoding

International audienceIn the Software Radio context, the parametrization is becoming an important topic especially when it comes to multistandard designs. This paper capitalizes on the Common Operator technique to present new common structures for the FFT and FEC decoding algorithms. A key benefit of exhibiting common operators is the regular architecture it brings when implemented in a Common Operator Bank (COB). This regularity makes the architecture open to future function mapping and adapted to accommodated silicon technology variability through dependable design

A VLSI synthesis of a Reed-Solomon processor for digital communication systems

The Reed-Solomon codes have been widely used in digital communication systems such as computer networks, satellites, VCRs, mobile communications and high- definition television (HDTV), in order to protect digital data against erasures, random and burst errors during transmission. Since the encoding and decoding algorithms for such codes are computationally intensive, special purpose hardware implementations are often required to meet the real time requirements. -- One motivation for this thesis is to investigate and introduce reconfigurable Galois field arithmetic structures which exploit the symmetric properties of available architectures. Another is to design and implement an RS encoder/decoder ASIC which can support a wide family of RS codes. -- An m-programmable Galois field multiplier which uses the standard basis representation of the elements is first introduced. It is then demonstrated that the exponentiator can be used to implement a fast inverter which outperforms the available inverters in GF(2m). Using these basic structures, an ASIC design and synthesis of a reconfigurable Reed-Solomon encoder/decoder processor which implements a large family of RS codes is proposed. The design is parameterized in terms of the block length n, Galois field symbol size m, and error correction capability t for the various RS codes. The design has been captured using the VHDL hardware description language and mapped onto CMOS standard cells available in the 0.8-µm BiCMOS design kits for Cadence and Synopsys tools. The experimental chip contains 218,206 logic gates and supports values of the Galois field symbol size m = 3,4,5,6,7,8 and error correction capability t = 1,2,3, ..., 16. Thus, the block length n is variable from 7 to 255. Error correction t and Galois field symbol size m are pin-selectable. -- Since low design complexity and high throughput are desired in the VLSI chip, the algebraic decoding technique has been investigated instead of the time or transform domain. The encoder uses a self-reciprocal generator polynomial which structures the codewords in a systematic form. At the beginning of the decoding process, received words are initially stored in the first-in-first-out (FIFO) buffer as they enter the syndrome module. The Berlekemp-Massey algorithm is used to determine both the error locator and error evaluator polynomials. The Chien Search and Forney's algorithms operate sequentially to solve for the error locations and error values respectively. The error values are exclusive or-ed with the buffered messages in order to correct the errors, as the processed data leave the chip

Implementaciones hardware de circuitos aritméticos sobre cuerpos finitos (Hardwareimolementations of arithmetic circuits over finite field)

La aritmética sobre cuerpos finitos ha recibido mucho interés debido a su importancia en criptografía, control de errores de codificación y procesado de señales digitales. Una gran parte del tiempo de las rutinas criptográficas se dedica al cálculo de operaciones aritméticas sobre cuerpos finitos. Los sistemas que usan esta aritmética deben ser rápidos debido a los rendimientos requeridos en los sistemas de comunicación actuales. La suma en GF(2^m) es una operación XOR binaria independiente, puede ser realizada de forma rápida y sin retardo. Sin embargo otras operaciones son mucho más complejas y con mayor retardo. La eficiencia de las implementaciones hardware se mide en términos del número de puertas (XOR y AND) y del retardo total debido a esas puertas del circuito. El objetivo de este documento es hacer un estudio comparativo de diferentes circuitos aritméticos sobre GF(2^m), se utilizarán los cuerpos recomendados por el NIST y el SECG. Por su importancia, se han estudiado diferentes implementaciones para los algoritmos de multiplicación, tanto multiplicación serie como paralela junto con multiplicación dígito serie. Para el estudio de toras operaciones aritméticas, también se estudian algoritmos para obtener el cuadrado y el inverso de elementos pertencientes a GF(2^m). Para realizar este trabajo se implentarán los algoritmos mencionados en VHDL para FPGAs estudiando el consumo de área y tiempo de las operaciones comparando los resultados entre sí y con los obtenidos por otros autores. [ABSTRACT]Finite field arithmetic has received much attention due to its importance in cryptography, error control coding and digital signal processing. A large portion of time from the routines of the cryptographies algorithms is used in the calculation of arithmetic operations on finite fields. Systems using this arithmetic must be faster because of performance required in current communication systems. Addition in GF(2^m) is bit independent XOR operation, it can be implemented in fast and inexpensive ways. Nevertheless other operations are much more complex and expensive. The efficiency of the hardware implementations is measured in terms of the numbers of gates (XOR and AND) and of the total gate delay of the circuit. The aim of this document is to make a comparative study of different arithmetic circuits over GF(2^m), NIST and SECG recommended fields will be used. Due to multiplication is one of the most complex and important operation in finite field arithmetic, different implementations will be treated, parallel and serial along with digit-serial algorithms. To perform other operations, also inversion and square algorithms over GF(2^m) have been discussed. VHDL implementations of these algorithms for FPGAs have been realized to study time and area consumption and to compare the result each other and with other authors'results

Efficient implementation of elliptic curve cryptography.

Elliptic Curve Cryptosystems (ECC) were introduced in 1985 by Neal Koblitz and Victor Miller. Small key size made elliptic curve attractive for public key cryptosystem implementation. This thesis introduces solutions of efficient implementation of ECC in algorithmic level and in computation level. In algorithmic level, a fast parallel elliptic curve scalar multiplication algorithm based on a dual-processor hardware system is developed. The method has an average computation time of n3 Elliptic Curve Point Addition on an n-bit scalar. The improvement is n Elliptic Curve Point Doubling compared to conventional methods. When a proper coordinate system and binary representation for the scalar k is used the average execution time will be as low as n Elliptic Curve Point Doubling, which makes this method about two times faster than conventional single processor multipliers using the same coordinate system. In computation level, a high performance elliptic curve processor (ECP) architecture is presented. The processor uses parallelism in finite field calculation to achieve high speed execution of scalar multiplication algorithm. The architecture relies on compile-time detection rather than of run-time detection of parallelism which results in less hardware. Implemented on FPGA, the proposed processor operates at 66MHz in GF(2 167) and performs scalar multiplication in 100muSec, which is considerably faster than recent implementations.Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .A57. Source: Masters Abstracts International, Volume: 44-03, page: 1446. Thesis (M.A.Sc.)--University of Windsor (Canada), 2005

Private and Public-Key Side-Channel Threats Against Hardware Accelerated Cryptosystems

Modern side-channel attacks (SCA) have the ability to reveal sensitive data from non-protected hardware implementations of cryptographic accelerators whether they be private or public-key systems. These protocols include but are not limited to symmetric, private-key encryption using AES-128, 192, 256, or public-key cryptosystems using elliptic curve cryptography (ECC). Traditionally, scalar point (SP) operations are compelled to be high-speed at any cost to reduce point multiplication latency. The majority of high-speed architectures of contemporary elliptic curve protocols rely on non-secure SP algorithms. This thesis delivers a novel design, analysis, and successful results from a custom differential power analysis attack on AES-128. The resulting SCA can break any 16-byte master key the sophisticated cipher uses and it\u27s direct applications towards public-key cryptosystems will become clear. Further, the architecture of a SCA resistant scalar point algorithm accompanied by an implementation of an optimized serial multiplier will be constructed. The optimized hardware design of the multiplier is highly modular and can use either NIST approved 233 & 283-bit Kobliz curves utilizing a polynomial basis. The proposed architecture will be implemented on Kintex-7 FPGA to later be integrated with the ARM Cortex-A9 processor on the Zynq-7000 AP SoC (XC7Z045) for seamless data transfer and analysis of the vulnerabilities SCAs can exploit