High Speed Unified Field Crypto processor for Security Applications using Verilog

Traditional cryptographic algorithms are developed on a software platform and provides information security schemes. Also, some processors have performed one of the crypto algorithms (either prime field or binary extension field) on chip level with optimal performance. The objective is to design and implement both symmetric key and public key algorithms of a cryptographic on chip level and make better architecture with pleasing performance. Crypto-processor design, have been designed with unified field instructions to make different processor architecture and improve system performance. The proposed high speed Montgomery modular multiplication and high radix Montgomery multiplication algorithms for pairing computation supports the public key algorithm. This design has been developed using Verilog HDL’s and verified using ModelSim-Altera 6.4a, and it has synthesized with Xilinx 9.1 Integrated Synthesis Environment (ISE) tool

High-speed VLSI implementation of Digit-serial Gaussian normal basis Multiplication over GF(2m)

In this paper, by employing the logical effort technique an efficient and high-speed VLSI implementation of the digit-serial Gaussian normal basis multiplier is presented. It is constructed by using AND, XOR and XOR tree components. To have a low-cost implementation with low number of transistors, the block of AND gates are implemented by using NAND gates based on the property of the XOR gates in the XOR tree. To optimally decrease the delay and increase the drive ability of the circuit the logical effort method as an efficient method for sizing the transistors is employed. By using this method and also a 4-input XOR gate structure, the circuit is designed for minimum delay. The digit-serial Gaussian normal basis multiplier is implemented over two binary finite fields GF(2163) and GF(2233) in 0.18μm CMOS technology for three different digit sizes. The results show that the proposed structures, compared to previous structures, have been improved in terms of delay and area parameters

A Chinese Remainder Theorem Approach to Bit-Parallel GF(2^n) Polynomial Basis Multipliers for Irreducible Trinomials

We show that the step “modulo the degree-n field generating irreducible polynomial” in the classical definition of the GF(2^n) multiplication operation can be avoided. This leads to an alternative representation of the finite field multiplication operation. Combining this representation and the Chinese Remainder Theorem, we design bit-parallel GF(2^n) multipliers for irreducible trinomials u^n + u^k + 1 on GF(2) where 1 < k &#8804; n=2. For some values of n, our architectures have the same time complexity as the fastest bit-parallel multipliers – the quadratic multipliers, but their space complexities are reduced. Take the special irreducible trinomial u^(2k) + u^k + 1 for example, the space complexity of the proposed design is reduced by about 1=8, while the time complexity matches the best result. Our experimental results show that among the 539 values of n such that 4 < n < 1000 and x^n+x^k+1 is irreducible over GF(2) for some k in the range 1 < k &#8804; n=2, the proposed multipliers beat the current fastest parallel multipliers for 290 values of n when (n &#8722; 1)=3 &#8804; k &#8804; n=2: they have the same time complexity, but the space complexities are reduced by 8.4% on average

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

Low Complexity MDS Matrices Using GF(2n)GF(2^n) SPB or GPB

While $GF(2^n)$ polynomial bases are widely used in symmetric-key components, e.g. MDS matrices, we show that even low time/space complexities can be achieved by using $GF(2^n)$ shifted polynomial bases (SPB) or generalized polynomial bases (GPB)

A Multiple Bit Parity Fault Detection Scheme for The Advanced Encryption Standard Galois/Counter Mode

The Advanced Encryption Standard (AES) is a symmetric-key block cipher for electronic data announced by the U.S. National Institute of Standards and Technology (NIST) in 2001. The encryption process is based on symmetric key (using the same key for both encryption and decryption) for block encryption of 128, 192, and 256 bits in size. AES and its standardized authentication Galois/Counter Mode (GCM) have been adopted in numerous security-based applications. GCM is a mode of operation for AES symmetric key cryptographic block ciphers, which has been selected for its high throughput rates in high speed communication channels. The GCM is an algorithm for authenticated encryption to provide both data authenticity and confidentiality that can be achieved with reasonable hardware resources. The hardware implementation of the AES-GCM demands tremendous amount of logic blocks and gates. Due to natural faults or intrusion attacks, faulty outputs in different logic blocks of the AES-GCM module results in erroneous output. There exist plenty of specific literature on methods of fault detection in the AES section of the AES-GCM. In this thesis, we consider a novel fault detection of the GCM section using parity prediction. For the purpose of fault detection in GCM, two independent methods are proposed. First, a new technique of fault detection using parity prediction for the entire GCM loop is presented. Then, matrix based CRC multiple-bit parity prediction schemes are developed and implemented. As a result, we achieve the fault coverage of about 99% with the longest path delay and area overhead of 23% and 10.9% respectively. The false alarm is 0.12% which can be ignored based on the number of injected faults

Efficient Bit-parallel Multiplication with Subquadratic Space Complexity in Binary Extension Field

Bit-parallel multiplication in GF(2^n) with subquadratic space complexity has been explored in recent years due to its lower area cost compared with traditional parallel multiplications. Based on \u27divide and conquer\u27 technique, several algorithms have been proposed to build subquadratic space complexity multipliers. Among them, Karatsuba algorithm and its generalizations are most often used to construct multiplication architectures with significantly improved efficiency. However, recursively using one type of Karatsuba formula may not result in an optimal structure for many finite fields. It has been shown that improvements on multiplier complexity can be achieved by using a combination of several methods. After completion of a detailed study of existing subquadratic multipliers, this thesis has proposed a new algorithm to find the best combination of selected methods through comprehensive search for constructing polynomial multiplication over GF(2^n). Using this algorithm, ameliorated architectures with shortened critical path or reduced gates cost will be obtained for the given value of n, where n is in the range of [126, 600] reflecting the key size for current cryptographic applications. With different input constraints the proposed algorithm can also yield subquadratic space multiplier architectures optimized for trade-offs between space and time. Optimized multiplication architectures over NIST recommended fields generated from the proposed algorithm are presented and analyzed in detail. Compared with existing works with subquadratic space complexity, the proposed architectures are highly modular and have improved efficiency on space or time complexity. Finally generalization of the proposed algorithm to be suitable for much larger size of fields discussed

ENERGY-EFFICIENT AND SECURE HARDWARE FOR INTERNET OF THINGS (IoT) DEVICES

Internet of Things (IoT) is a network of devices that are connected through the Internet to exchange the data for intelligent applications. Though IoT devices provide several advantages to improve the quality of life, they also present challenges related to security. The security issues related to IoT devices include leakage of information through Differential Power Analysis (DPA) based side channel attacks, authentication, piracy, etc. DPA is a type of side-channel attack where the attacker monitors the power consumption of the device to guess the secret key stored in it. There are several countermeasures to overcome DPA attacks. However, most of the existing countermeasures consume high power which makes them not suitable to implement in power constraint devices. IoT devices are battery operated, hence it is important to investigate the methods to design energy-efficient and secure IoT devices not susceptible to DPA attacks. In this research, we have explored the usefulness of a novel computing platform called adiabatic logic, low-leakage FinFET devices and Magnetic Tunnel Junction (MTJ) Logic-in-Memory (LiM) architecture to design energy-efficient and DPA secure hardware. Further, we have also explored the usefulness of adiabatic logic in the design of energy-efficient and reliable Physically Unclonable Function (PUF) circuits to overcome the authentication and piracy issues in IoT devices. Adiabatic logic is a low-power circuit design technique to design energy-efficient hardware. Adiabatic logic has reduced dynamic switching energy loss due to the recycling of charge to the power clock. As the first contribution of this dissertation, we have proposed a novel DPA-resistant adiabatic logic family called Energy-Efficient Secure Positive Feedback Adiabatic Logic (EE-SPFAL). EE-SPFAL based circuits are energy-efficient compared to the conventional CMOS based design because of recycling the charge after every clock cycle. Further, EE-SPFAL based circuits consume uniform power irrespective of input data transition which makes them resilience against DPA attacks. Scaling of CMOS transistors have served the industry for more than 50 years in providing integrated circuits that are denser, and cheaper along with its high performance, and low power. However, scaling of the transistors leads to increase in leakage current. Increase in leakage current reduces the energy-efficiency of the computing circuits,and increases their vulnerability to DPA attack. Hence, it is important to investigate the crypto circuits in low leakage devices such as FinFET to make them energy-efficient and DPA resistant. In this dissertation, we have proposed a novel FinFET based Secure Adiabatic Logic (FinSAL) family. FinSAL based designs utilize the low-leakage FinFET device along with adiabatic logic principles to improve energy-efficiency along with its resistance against DPA attack. Recently, Magnetic Tunnel Junction (MTJ)/CMOS based Logic-in-Memory (LiM) circuits have been explored to design low-power non-volatile hardware. Some of the advantages of MTJ device include non-volatility, near-zero leakage power, high integration density and easy compatibility with CMOS devices. However, the differences in power consumption between the switching of MTJ devices increase the vulnerability of Differential Power Analysis (DPA) based side-channel attack. Further, the MTJ/CMOS hybrid logic circuits which require frequent switching of MTJs are not very energy-efficient due to the significant energy required to switch the MTJ devices. In the third contribution of this dissertation, we have investigated a novel approach of building cryptographic hardware in MTJ/CMOS circuits using Look-Up Table (LUT) based method where the data stored in MTJs are constant during the entire encryption/decryption operation. Currently, high supply voltage is required in both writing and sensing operations of hybrid MTJ/CMOS based LiM circuits which consumes a considerable amount of energy. In order to meet the power budget in low-power devices, it is important to investigate the novel design techniques to design ultra-low-power MTJ/CMOS circuits. In the fourth contribution of this dissertation, we have proposed a novel energy-efficient Secure MTJ/CMOS Logic (SMCL) family. The proposed SMCL logic family consumes uniform power irrespective of data transition in MTJ and more energy-efficient compared to the state-of-art MTJ/ CMOS designs by using charge sharing technique. The other important contribution of this dissertation is the design of reliable Physical Unclonable Function (PUF). Physically Unclonable Function (PUF) are circuits which are used to generate secret keys to avoid the piracy and device authentication problems. However, existing PUFs consume high power and they suffer from the problem of generating unreliable bits. This dissertation have addressed this issue in PUFs by designing a novel adiabatic logic based PUF. The time ramp voltages in adiabatic PUF is utilized to improve the reliability of the PUF along with its energy-efficiency. Reliability of the adiabatic logic based PUF proposed in this dissertation is tested through simulation based temperature variations and supply voltage variations