Revisiting LFSMs

Linear Finite State Machines (LFSMs) are particular primitives widely used in information theory, coding theory and cryptography. Among those linear automata, a particular case of study is Linear Feedback Shift Registers (LFSRs) used in many cryptographic applications such as design of stream ciphers or pseudo-random generation. LFSRs could be seen as particular LFSMs without inputs. In this paper, we first recall the description of LFSMs using traditional matrices representation. Then, we introduce a new matrices representation with polynomial fractional coefficients. This new representation leads to sparse representations and implementations. As direct applications, we focus our work on the Windmill LFSRs case, used for example in the E0 stream cipher and on other general applications that use this new representation. In a second part, a new design criterion called diffusion delay for LFSRs is introduced and well compared with existing related notions. This criterion represents the diffusion capacity of an LFSR. Thus, using the matrices representation, we present a new algorithm to randomly pick LFSRs with good properties (including the new one) and sparse descriptions dedicated to hardware and software designs. We present some examples of LFSRs generated using our algorithm to show the relevance of our approach.Comment: Submitted to IEEE-I

Automated Design Space Exploration and Datapath Synthesis for Finite Field Arithmetic with Applications to Lightweight Cryptography

Today, emerging technologies are reaching astronomical proportions. For example, the Internet of Things has numerous applications and consists of countless different devices using different technologies with different capabilities. But the one invariant is their connectivity. Consequently, secure communications, and cryptographic hardware as a means of providing them, are faced with new challenges. Cryptographic algorithms intended for hardware implementations must be designed with a good trade-off between implementation efficiency and sufficient cryptographic strength. Finite fields are widely used in cryptography. Examples of algorithm design choices related to finite field arithmetic are the field size, which arithmetic operations to use, how to represent the field elements, etc. As there are many parameters to be considered and analyzed, an automation framework is needed. This thesis proposes a framework for automated design, implementation and verification of finite field arithmetic hardware. The underlying motif throughout this work is “math meets hardware”. The automation framework is designed to bring the awareness of underlying mathematical structures to the hardware design flow. It is implemented in GAP, an open source computer algebra system that can work with finite fields and has symbolic computation capabilities. The framework is roughly divided into two phases, the architectural decisions and the automated design genera- tion. The architectural decisions phase supports parameter search and produces a list of candidates. The automated design generation phase is invoked for each candidate, and the generated VHDL files are passed on to conventional synthesis tools. The candidates and their implementation results form the design space, and the framework allows rapid design space exploration in a systematic way. In this thesis, design space exploration is focused on finite field arithmetic. Three distinctive features of the proposed framework are the structure of finite fields, tower field support, and on the fly submodule generation. Each finite field used in the design is represented as both a field and its corresponding vector space. It is easy for a designer to switch between fields and vector spaces, but strict distinction of the two is necessary for hierarchical designs. When an expression is defined over an extension field, the top-level module contains element signals and submodules for arithmetic operations on those signals. The submodules are generated with corresponding vector signals and the arithmetic operations are now performed on the coordinates. For tower fields, the submodules are generated for the subfield operations, and the design is generated in a top-down fashion. The binding of expressions to the appropriate finite fields or vector spaces and a set of customized methods allow the on the fly generation of expressions for implementation of arithmetic operations, and hence submodule generation. In the light of NIST Lightweight Cryptography Project (LWC), this work focuses mainly on small finite fields. The thesis illustrates the impact of hardware implementation results during the design process of WAGE, a Round 2 candidate in the NIST LWC standardization competition. WAGE is a hardware oriented authenticated encryption scheme. The parameter selection for WAGE was aimed at balancing the security and hardware implementation area, using hardware implementation results for many design decisions, for example field size, representation of field elements, etc. In the proposed framework, the components of WAGE are used as an example to illustrate different automation flows and demonstrate the design space exploration on a real-world algorithm

Area and Energy Optimizations in ASIC Implementations of AES and PRESENT Block Ciphers

When small, modern-day devices surface with neoteric features and promise benefits like streamlined business processes, cashierless stores, and autonomous driving, they are all too often accompanied by security risks due to a weak or absent security component. In particular, the lack of data privacy protection is a common concern that can be remedied by implementing encryption. This ensures that data remains undisclosed to unauthorized parties. While having a cryptographic module is often a goal, it is sometimes forfeited because a device's resources do not allow for the conventional cryptographic solutions. Thus, smaller, lower-energy security modules are in demand. Implementing a cipher in hardware as an application-specific integrated circuit (ASIC) will usually achieve better efficiency than alternatives like FPGAs or software, and can help towards goals such as extended battery life and smaller area footprint. The Advanced Encryption Standard (AES) is a block cipher established by the National Institute of Standards and Technology (NIST) in 2001. It has since become the most widely adopted block cipher and is applied in a variety of applications ranging from smartphones to passive RFID tags to high performance microprocessors. PRESENT, published in 2007, is a smaller lightweight block cipher designed for low-power applications. In this study, low-area and low-energy optimizations in ASICs are addressed for AES and PRESENT. In the low-area work, three existing AES encryption cores are implemented, analyzed, and benchmarked using a common fabrication technology (STM 65 nm). The analysis includes an examination of various implementations of internal AES operations and their suitability for different architectural choices. Using our taxonomy of design choices, we designed Quark-AES, a novel 8-bit AES architecture. At 1960 GE, it features a 13% improvement in area and 9% improvement in throughput/area² over the prior smallest design. To illustrate the extent of the variations due to the use of different ASIC libraries, Quark-AES and the three analyzed designs are also synthesized using three additional technologies. Even for the same transistor size, different ASIC libraries produce significantly different area results. To accommodate a variety of applications that seek different levels of tradeoffs in area and throughput, we extend all four designs to 16-bit and 32-bit datawidths. In the low-energy work, round unrolling and glitch filtering are applied together to achieve energy savings. Round unrolling, which applies multiple block cipher rounds in a combinational path, reduces the energy due to registers but increases the glitching energy. Glitch filtering complements round unrolling by reducing the amount of glitches and their associated energy consumption. For unrolled designs of PRESENT and AES, two glitch filtering schemes are assessed. One method uses AND-gates in between combinational rounds while the other used latches. Both methods work by allowing the propagation of signals only after they have stabilized. The experiments assess how energy consumption changes with respect to the degree of unrolling, the glitch filtering scheme, the degree of pipelining, the spacing between glitch filters, and the location of glitch filters when only a limited number of them can be applied due to area constraints. While in PRESENT, the optimal configuration depends on all the variables, in a larger cipher such as AES, the latch-based method consistently offers the most energy savings

Verification of Pipelined Ciphers

The purpose of this thesis is to explore the formal verification technique of completion functions and equivalence checking by verifying two pipelined cryptographic circuits, KASUMI and WG ciphers. Most of current methods of communications either involve a personal computer or a mobile phone. To ensure that the information is exchanged in a secure manner, encryption circuits are used to transform the information into an unintelligible form. To be highly secure, this type of circuits is generally designed such that it is hard to analyze. Due to this fact, it becomes hard to locate a design error in the verification of cryptographic circuits. Therefore, cryptographic circuits pose significant challenges in the area of formal verification. Formal verification use mathematics to formulate correctness criteria of designs, to develop mathematical models of designs, and to verify designs against their correctness criteria. The results of this work can extend the existing collection of verification methods as well as benefiting the area of cryptography. In this thesis, we implemented the KASUMI cipher in VHDL, and we applied the optimization technique of pipelining to create three additional implementations of KASUMI. We verified the three pipelined implementations of KASUMI with completion functions and equivalence checking. During the verification of KASUMI, we developed a methodology to handle the completion functions efficiently based on VHDL generic parameters. We implemented the WG cipher in VHDL, and we applied the optimization techniques of pipelining and hardware re-use to create an optimized implementation of WG. We verified the optimized implementation of WG with completion functions and equivalence checking. During the verification of WG, we developed the methodology of ``skipping" that can decrease the number of verification obligations required to verify the correctness of a circuit. During the verification of WG, we developed a way of applying the completion functions approach such that it can deal with a circuit that has been optimized with hardware re-use

Efficient Computation and FPGA implementation of Fully Homomorphic Encryption with Cloud Computing Significance

Homomorphic Encryption provides unique security solution for cloud computing. It ensures not only that data in cloud have confidentiality but also that data processing by cloud server does not compromise data privacy. The Fully Homomorphic Encryption (FHE) scheme proposed by Lopez-Alt, Tromer, and Vaikuntanathan (LTV), also known as NTRU(Nth degree truncated polynomial ring) based method, is considered one of the most important FHE methods suitable for practical implementation. In this thesis, an efficient algorithm and architecture for LTV Fully Homomorphic Encryption is proposed. Conventional linear feedback shift register (LFSR) structure is expanded and modified for performing the truncated polynomial ring multiplication in LTV scheme in parallel. Novel and efficient modular multiplier, modular adder and modular subtractor are proposed to support high speed processing of LFSR operations. In addition, a family of special moduli are selected for high speed computation of modular operations. Though the area keeps the complexity of O(Nn^2) with no advantage in circuit level. The proposed architecture effectively reduces the time complexity from O(N log N) to linear time, O(N), compared to the best existing works. An FPGA implementation of the proposed architecture for LTV FHE is achieved and demonstrated. An elaborate comparison of the existing methods and the proposed work is presented, which shows the proposed work gains significant speed up over existing works

A Hardware Security Solution against Scan-Based Attacks

Scan based Design for Test (DfT) schemes have been widely used to achieve high fault coverage for integrated circuits. The scan technique provides full access to the internal nodes of the device-under-test to control them or observe their response to input test vectors. While such comprehensive access is highly desirable for testing, it is not acceptable for secure chips as it is subject to exploitation by various attacks. In this work, new methods are presented to protect the security of critical information against scan-based attacks. In the proposed methods, access to the circuit containing secret information via the scan chain has been severely limited in order to reduce the risk of a security breach. To ensure the testability of the circuit, a built-in self-test which utilizes an LFSR as the test pattern generator (TPG) is proposed. The proposed schemes can be used as a countermeasure against side channel attacks with a low area overhead as compared to the existing solutions in literature

Contributions to Confidentiality and Integrity Algorithms for 5G

The confidentiality and integrity algorithms in cellular networks protect the transmission of user and signaling data over the air between users and the network, e.g., the base stations. There are three standardised cryptographic suites for confidentiality and integrity protection in 4G, which are based on the AES, SNOW 3G, and ZUC primitives, respectively. These primitives are used for providing a 128-bit security level and are usually implemented in hardware, e.g., using IP (intellectual property) cores, thus can be quite efficient. When we come to 5G, the innovative network architecture and high-performance demands pose new challenges to security. For the confidentiality and integrity protection, there are some new requirements on the underlying cryptographic algorithms. Specifically, these algorithms should: 1) provide 256 bits of security to protect against attackers equipped with quantum computing capabilities; and 2) provide at least 20 Gbps (Gigabits per second) speed in pure software environments, which is the downlink peak data rate in 5G. The reason for considering software environments is that the encryption in 5G will likely be moved to the cloud and implemented in software. Therefore, it is crucial to investigate existing algorithms in 4G, checking if they can satisfy the 5G requirements in terms of security and speed, and possibly propose new dedicated algorithms targeting these goals. This is the motivation of this thesis, which focuses on the confidentiality and integrity algorithms for 5G. The results can be summarised as follows.1. We investigate the security of SNOW 3G under 256-bit keys and propose two linear attacks against it with complexities 2172 and 2177, respectively. These cryptanalysis results indicate that SNOW 3G cannot provide the full 256-bit security level. 2. We design some spectral tools for linear cryptanalysis and apply these tools to investigate the security of ZUC-256, the 256-bit version of ZUC. We propose a distinguishing attack against ZUC-256 with complexity 2236, which is 220 faster than exhaustive key search. 3. We design a new stream cipher called SNOW-V in response to the new requirements for 5G confidentiality and integrity protection, in terms of security and speed. SNOW-V can provide a 256-bit security level and achieve a speed as high as 58 Gbps in software based on our extensive evaluation. The cipher is currently under evaluation in ETSI SAGE (Security Algorithms Group of Experts) as a promising candidate for 5G confidentiality and integrity algorithms. 4. We perform deeper cryptanalysis of SNOW-V to ensure that two common cryptanalysis techniques, guess-and-determine attacks and linear cryptanalysis, do not apply to SNOW-V faster than exhaustive key search. 5. We introduce two minor modifications in SNOW-V and propose an extreme performance variant, called SNOW-Vi, in response to the feedback about SNOW-V that some use cases are not fully covered. SNOW-Vi covers more use cases, especially some platforms with less capabilities. The speeds in software are increased by 50% in average over SNOW-V and can be up to 92 Gbps.Besides these works on 5G confidentiality and integrity algorithms, the thesis is also devoted to local pseudorandom generators (PRGs). 6. We investigate the security of local PRGs and propose two attacks against some constructions instantiated on the P5 predicate. The attacks improve existing results with a large gap and narrow down the secure parameter regime. We also extend the attacks to other local PRGs instantiated on general XOR-AND and XOR-MAJ predicates and provide some insight in the choice of safe parameters

Hardware Implementations of the WG-16 Stream Cipher with Composite Field Arithmetic

The WG stream cipher family consists of stream ciphers based on the Welch-Gong (WG) transformations that are used as a nonlinear filter applied to the output of a linear feedback shift register (LFSR). The aim of this thesis is an exploration of the design space of the WG-16 stream cipher. Five different representations of the field elements were analyzed, namely the polynomial basis representation, the normal basis representation and three isomorphic tower field constructions of F216: F(((22)2)2)2, F(24)4 and F(28)2. Each design option begins with an in-depth description of different field constructions and their impact on the top-level WG transformation circuit. Normal basis representation of elements for each level of the tower was chosen for field constructions F(((22)2)2)2 and F(24)4, and a mixed basis, with polynomial basis for the lower and normal basis for the higher level of the tower for F(28)2. Representation of field elements affects the field arithmetic, which in turn affects the entire design. Targeting high throughput, pipelined architectures were developed, and pipelining was based on the particular field construction: each extension over the prime field offers a new pipelining possibility. Pipelining at a lower level of the tower field reduces the clock period. Most flexible pipelining options are possible for F(((22)2)2)2, a highly regular construction, which permits an algebraic optimization of the WG transformation resulting in two multiplications being removed. High speed, achieved by adequate pipelining granularity, and smaller area due to removed multipliers deem the F(((22)2)2)2 to be the most suitable field construction for the implementation of WG-16. The best WG-16 modules achieve a throughput of 222 Mbit/s with 476 slices used on the Xilinx Spartan-6 FPGA device xc6slx9 (using Xilinx Synthesis Tool (XST) for synthesis and ISE for implementation [47]) and a throughput of 529 Mbit/s with area cost of 12215 GEs for ASIC implementation, using the 65 nm CMOS technology (using Synopsys Design Compiler for synthesis [45] and Cadence SoC Encounter to complete the Place-and-Route phase)

Role of Cryptographic Welch-Gong (WG-5) Stream Cipher in RFID Security

The purpose of this thesis is to design a secure and optimized cryptographic stream cipher for passive type Radio Frequency Identification (RFID) tags. RFID technology is a wireless automatic tracking and identification device. It has become an integral part of our daily life and it is used in many applications such as electronic passports, contactless payment systems, supply chain management and so on. But the information carried on RFID tags are vulnerable to unauthorized access (or various threats) which raises the security and privacy concern over RFID devices. One of the possible solutions to protect the confidentiality, integrity and to provide authentication is, to use a cryptographic stream cipher which encrypts the original information with a pseudo-random bit sequence. Besides that RFID tags require a resource constrained environment such as efficient area, power and high performance cryptographic systems with large security margins. Therefore, the architecture of stream cipher provides the best trade-off between the cryptographic security and the hardware efficiency. In this thesis, we first described the RFID technology and explain the design requirements for passive type RFID tags. The hardware design for passive tags is more challenging due to its stringent requirements like power consumption and the silicon area. We presented different design measures and some of the optimization techniques required to achieve low-resource cryptographic hardware implementation for passive tags. Secondly, we propose and implement a lightweight WG-5 stream cipher, which has good proven cryptographic mathematical properties. Based on these properties we measured the security analysis of WG-5 and showed that the WG-5 is immune to different types of attacks such as algebraic attack, correlation attack, cube attack, differential attack, Discrete Fourier Transform attack (DFT), Time-Memory-Data trade-off attack. The implementation of WG-5 was carried out using 65 nm and 130 nm CMOS technologies. We achieved promising results of WG-5 implementation in terms of area, power, speed and optimality. Our results outperforms most of the other stream ciphers which are selected in eSTREAM project. Finally, we proposed RFID mutual authentication protocol based on WG-5. The security and privacy analysis of the proposed protocol showed that it is resistant to various RFID attacks such as replay attacks, Denial-of-service (DoS) attack, ensures forward privacy and impersonation attack

Cryptography for Ultra-Low Power Devices

Ubiquitous computing describes the notion that computing devices will be everywhere: clothing, walls and floors of buildings, cars, forests, deserts, etc. Ubiquitous computing is becoming a reality: RFIDs are currently being introduced into the supply chain. Wireless distributed sensor networks (WSN) are already being used to monitor wildlife and to track military targets. Many more applications are being envisioned. For most of these applications some level of security is of utmost importance. Common to WSN and RFIDs are their severely limited power resources, which classify them as ultra-low power devices. Early sensor nodes used simple 8-bit microprocessors to implement basic communication, sensing and computing services. Security was an afterthought. The main power consumer is the RF-transceiver, or radio for short. In the past years specialized hardware for low-data rate and low-power radios has been developed. The new bottleneck are security services which employ computationally intensive cryptographic operations. Customized hardware implementations hold the promise of enabling security for severely power constrained devices. Most research groups are concerned with developing secure wireless communication protocols, others with designing efficient software implementations of cryptographic algorithms. There has not been a comprehensive study on hardware implementations of cryptographic algorithms tailored for ultra-low power applications. The goal of this dissertation is to develop a suite of cryptographic functions for authentication, encryption and integrity that is specifically fashioned to the needs of ultra-low power devices. This dissertation gives an introduction to the specific problems that security engineers face when they try to solve the seemingly contradictory challenge of providing lightweight cryptographic services that can perform on ultra-low power devices and shows an overview of our current work and its future direction