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

On Linear Product Codes and Their Duals Scientific Report No. 4

Tensor products of linear codes, and product codes with dual cyclic component code

Concurrent Error Detection in Finite Field Arithmetic Operations

With significant advances in wired and wireless technologies and also increased shrinking in the size of VLSI circuits, many devices have become very large because they need to contain several large units. This large number of gates and in turn large number of transistors causes the devices to be more prone to faults. These faults specially in sensitive and critical applications may cause serious failures and hence should be avoided. On the other hand, some critical applications such as cryptosystems may also be prone to deliberately injected faults by malicious attackers. Some of these faults can produce erroneous results that can reveal some important secret information of the cryptosystems. Furthermore, yield factor improvement is always an important issue in VLSI design and fabrication processes. Digital systems such as cryptosystems and digital signal processors usually contain finite field operations. Therefore, error detection and correction of such operations have become an important issue recently. In most of the work reported so far, error detection and correction are applied using redundancies in space (hardware), time, and/or information (coding theory). In this work, schemes based on these redundancies are presented to detect errors in important finite field arithmetic operations resulting from hardware faults. Finite fields are used in a number of practical cryptosystems and channel encoders/decoders. The schemes presented here can detect errors in arithmetic operations of finite fields represented in different bases, including polynomial, dual and/or normal basis, and implemented in various architectures, including bit-serial, bit-parallel and/or systolic arrays

Finding Significant Fourier Coefficients: Clarifications, Simplifications, Applications and Limitations

Ideas from Fourier analysis have been used in cryptography for the last three decades. Akavia, Goldwasser and Safra unified some of these ideas to give a complete algorithm that finds significant Fourier coefficients of functions on any finite abelian group. Their algorithm stimulated a lot of interest in the cryptography community, especially in the context of `bit security'. This manuscript attempts to be a friendly and comprehensive guide to the tools and results in this field. The intended readership is cryptographers who have heard about these tools and seek an understanding of their mechanics and their usefulness and limitations. A compact overview of the algorithm is presented with emphasis on the ideas behind it. We show how these ideas can be extended to a `modulus-switching' variant of the algorithm. We survey some applications of this algorithm, and explain that several results should be taken in the right context. In particular, we point out that some of the most important bit security problems are still open. Our original contributions include: a discussion of the limitations on the usefulness of these tools; an answer to an open question about the modular inversion hidden number problem

Reconfigurable architectures for the next generation of mobile device telecommunications systems

Mobile devices have become a dominant tool in our daily lives. Business and personal usage has escalated tremendously since the emergence of smartphones and tablets. The combination of powerful processing in mobile devices, such as smartphones and the Internet, have established a new era for communications systems. This has put further pressure on the performance and efficiency of telecommunications systems in delivering the aspirations of users. Mobile device users no longer want devices that merely perform phone calls and messaging. Rather, they look for further interactive applications such as video streaming, navigation and real time social interaction. Such applications require a new set of hardware and standards. The WiFi (IEEE 802.11) standard has been at the forefront of reliable and high-speed internet access telecommunications. This is due to its high signal quality (quality of service) and speed (throughput). However, its limited availability and short range highlights the need for further protocols, in particular when far away from access points or base stations. This led to the emergence of 3G followed by 4G and the upcoming 5G standard that, if fully realised, will provide another dimension in “anywhere, anytime internet connectivity.” On the other hand, the WiMAX (IEEE 802.16) standard promises to exceed the WiFi signal coverage range. The coverage range could be extended to kilometres at least with a better or similar WiFi signal level. This thesis considers a dynamically reconfigurable architecture that is capable of processing various modules within telecommunications systems. Forward error correction, coder and navigation modules are deployed in a unified low power communication platform. These modules have been selected since they are among those with the highest demand in terms of processing power, strict processing time or throughput. The modules are mainly realised within WiFi and WiMAX systems in addition to global positioning systems (GPS). The idea behind the selection of these modules is to investigate the possibility of designing an architecture capable of processing various systems and dynamically reconfiguring between them. The GPS system is a power-hungry application and, at the same time, it is not needed all of the time. Hence, one key idea presented in this thesis is to effectively exploit the dynamic reconfiguration capability so as to reconfigure the architecture (GPS) when it is not needed in order to process another needed application or function such as WiFi or WiMAX. This will allow lower energy consumption and the optimum usage of the hardware available on the device. This work investigates the major current coarse-grain reconfigurable architectures. A novel multi-rate convolution encoder is then designed and realised as a reconfigurable fabric. This demonstrates the ability to adapt the algorithms involved to meet various requirements. A throughput of between 200 and 800 Mbps has been achieved for the rates 1/2 to 7/8, which is a great achievement for the proposed novel architecture. A reconfigurable interleaver is designed as a standalone fabric and on a dynamically reconfigurable processor. High throughputs exceeding 90 Mbps are achieved for the various supported block sizes. The Reed Solomon coder is the next challenging system to be designed into a dynamically reconfigurable processor. A novel Galois Field multiplier is designed and integrated into the developed Reed Solomon reconfigurable processor. As a result of this work, throughputs of 200Mbps and 93Mbps respectively for RS encoding and decoding are achieved. A GPS correlation module is also investigated in this work. This is the main part of the GPS receiver responsible for continuously tracking GPS satellites and extracting messages from them. The challenging aspect of this part is its real-time nature and the associated critical time constraints. This work resulted in a novel dynamically reconfigurable multi-channel GPS correlator with up to 72 simultaneous channels. This work is a contribution towards a global unified processing platform that is capable of processing communication-related operations efficiently and dynamically with minimum energy consumption