Low-Weight Primes for Lightweight Elliptic Curve Cryptography on 8-bit AVR Processors

Small 8-bit RISC processors and micro-controllers based on the AVR instruction set architecture are widely used in the embedded domain with applications ranging from smartcards over control systems to wireless sensor nodes. Many of these applications require asymmetric encryption or authentication, which has spurred a body of research into implementation aspects of Elliptic Curve Cryptography (ECC) on the AVR platform. In this paper, we study the suitability of a special class of finite fields, the so-called Optimal Prime Fields (OPFs), for a "lightweight" implementation of ECC with a view towards high performance and security. An OPF is a finite field Fp defined by a prime of the form p = u*2^k + v, whereby both u and v are "small" (in relation to 2^k) so that they fit into one or two registers of an AVR processor. OPFs have a low Hamming weight, which allows for a very efficient implementation of the modular reduction since only the non-zero words of p need to be processed. We describe a special variant of Montgomery multiplication for OPFs that does not execute any input-dependent conditional statements (e.g. branch instructions) and is, hence, resistant against certain side-channel attacks. When executed on an Atmel ATmega processor, a multiplication in a 160-bit OPF takes just 3237 cycles, which compares favorably with other implementations of 160-bit modular multiplication on an 8-bit processor. We also describe a performance-optimized and a security-optimized implementation of elliptic curve scalar multiplication over OPFs. The former uses a GLV curve and executes in 4.19M cycles (over a 160-bit OPF), while the latter is based on a Montgomery curve and has an execution time of approximately 5.93M cycles. Both results improve the state-of-the-art in lightweight ECC on 8-bit processors

Twisted Edwards-Form Elliptic Curve Cryptography for 8-bit AVR-based Sensor Nodes

Wireless Sensor Networks (WSNs) pose a number of unique security challenges that demand innovation in several areas including the design of cryptographic primitives and protocols. Despite recent progress, the efficient implementation of Elliptic Curve Cryptography (ECC) for WSNs is still a very active research topic and techniques to further reduce the time and energy cost of ECC are eagerly sought. This paper presents an optimized ECC implementation that we developed from scratch to comply with the severe resource constraints of 8-bit sensor nodes such as the MICAz and IRIS motes. Our ECC software uses Optimal Prime Fields (OPFs) as underlying algebraic structure and supports two different families of elliptic curves, namely Weierstraß-form and twisted Edwards-form curves. Due to the combination of efficient field arithmetic and fast group operations, we achieve an execution time of 5.8*10^6 clock cycles for a full 158-bit scalar multiplication on an 8-bit ATmega128 microcontroller, which is 2.78 times faster than the widely-used TinyECC library. Our implementation also shows that the energy cost of scalar multiplication on a MICAz (or IRIS) mote amounts to just 19 mJ when using a twisted Edwards curve over a 160-bit OPF. This result compares fairly well with the energy figures of two recently-presented hardware designs of ECC based on twisted Edwards curves

MoTE-ECC: Energy-Scalable Elliptic Curve Cryptography for Wireless Sensor Networks

Wireless Sensor Networks (WSNs) are susceptible to a wide range of malicious attacks, which has stimulated a body of research on "light-weight" security protocols and cryptographic primitives that are suitable for resource-restricted sensor nodes. In this paper we introduce MoTE-ECC, a highly optimized yet scalable ECC library for Memsic's MICAz motes and other sensor nodes equipped with an 8-bit AVR processor. MoTE-ECC supports scalar multiplication on Montgomery and twisted Edwards curves over Optimal Prime Fields (OPFs) of variable size, e.g. 160, 192, 224, and 256 bits, which allows for various trade-offs between security and execution time (resp. energy consumption). OPFs are a special family of "low-weight" prime fields that, in contrast to the NIST-specified fields, facilitate a parameterized implementation of the modular arithmetic so that one and the same software function can be used for operands of different length. To demonstrate the performance of MoTE-ECC, we take (ephemeral) ECDH key exchange between two nodes as example, which requires each node to execute two scalar multiplications. The first scalar multiplication is performed on a fixed base point (to generate a key pair), whereas the second scalar multiplication gets an arbitrary point as input. Our implementation uses a fixed-base comb method on a twisted Edwards curve for the former and a simple ladder approach on a birationally-equivalent Montgomery curve for the latter. Both scalar multiplications require about 9*10^6 clock cycles in total and occupy only 380 bytes in RAM when the underlying OPF has a length of 160 bits. We also describe our efforts to harden MoTE-ECC against side-channel attacks (e.g. simple power analysis) and introduce a highly regular implementation of the comb method

Efficient and Side-Channel Resistant Implementations of Next-Generation Cryptography

The rapid development of emerging information technologies, such as quantum computing and the Internet of Things (IoT), will have or have already had a huge impact on the world. These technologies can not only improve industrial productivity but they could also bring more convenience to people’s daily lives. However, these techniques have “side effects” in the world of cryptography – they pose new difficulties and challenges from theory to practice. Specifically, when quantum computing capability (i.e., logical qubits) reaches a certain level, Shor’s algorithm will be able to break almost all public-key cryptosystems currently in use. On the other hand, a great number of devices deployed in IoT environments have very constrained computing and storage resources, so the current widely-used cryptographic algorithms may not run efficiently on those devices. A new generation of cryptography has thus emerged, including Post-Quantum Cryptography (PQC), which remains secure under both classical and quantum attacks, and LightWeight Cryptography (LWC), which is tailored for resource-constrained devices. Research on next-generation cryptography is of importance and utmost urgency, and the US National Institute of Standards and Technology in particular has initiated the standardization process for PQC and LWC in 2016 and in 2018 respectively. Since next-generation cryptography is in a premature state and has developed rapidly in recent years, its theoretical security and practical deployment are not very well explored and are in significant need of evaluation. This thesis aims to look into the engineering aspects of next-generation cryptography, i.e., the problems concerning implementation efficiency (e.g., execution time and memory consumption) and security (e.g., countermeasures against timing attacks and power side-channel attacks). In more detail, we first explore efficient software implementation approaches for lattice-based PQC on constrained devices. Then, we study how to speed up isogeny-based PQC on modern high-performance processors especially by using their powerful vector units. Moreover, we research how to design sophisticated yet low-area instruction set extensions to further accelerate software implementations of LWC and long-integer-arithmetic-based PQC. Finally, to address the threats from potential power side-channel attacks, we present a concept of using special leakage-aware instructions to eliminate overwriting leakage for masked software implementations (of next-generation cryptography)

A Family of Lightweight Twisted Edwards Curves for the Internet of Things

We introduce a set of four twisted Edwards curves that satisfy common security requirements and allow for fast implementations of scalar multiplication on 8, 16, and 32-bit processors. Our curves are defined by an equation of the form -x^2 + y^2 = 1 + dx^2y^2 over a prime field Fp, where d is a small non-square modulo p. The underlying prime fields are based on "pseudo-Mersenne" primes given by p = 2^k - c and have in common that p is congruent to 5 modulo 8, k is a multiple of 32 minus 1, and c is at most eight bits long. Due to these common features, our primes facilitate a parameterized implementation of the low-level arithmetic so that one and the same arithmetic function is able to process operands of different length. Each of the twisted Edwards curves we introduce in this paper is birationally equivalent to a Montgomery curve of the form -(A+2)y^2 = x^3 + Ax^2 + x where 4/(A+2) is small. Even though this contrasts with the usual practice of choosing A such that (A+2)/4 is small, we show that the Montgomery form of our curves allows for an equally efficient implementation of point doubling as Curve25519. The four curves we put forward roughly match the common security levels of 80, 96, 112 and 128 bits. In addition, their Weierstraß representations are isomorphic to curves of the form y^2 = x^3 - 3x + b so as to facilitate inter-operability with TinyECC and other legacy software

Cryptographic Key Distribution In Wireless Sensor Networks Using Bilinear Pairings

It is envisaged that the use of cheap and tiny wireless sensors will soon bring a third wave of evolution in computing systems. Billions of wireless senor nodes will provide a bridge between information systems and the physical world. Wireless nodes deployed around the globe will monitor the surrounding environment as well as gather information about the people therein. It is clear that this revolution will put security solutions to a great test. Wireless Sensor Networks (WSNs) are a challenging environment for applying security services. They differ in many aspects from traditional fixed networks, and standard cryptographic solutions cannot be used in this application space. Despite many research efforts, key distribution in WSNs still remains an open problem. Many of the proposed schemes suffer from high communication overhead and storage costs, low scalability and poor resilience against different types of attacks. The exclusive usage of simple and energy efficient symmetric cryptography primitives does not solve the security problem. On the other hand a full public key infrastructure which uses asymmetric techniques, digital signatures and certificate authorities seems to be far too complex for a constrained WSN environment. This thesis investigates a new approach to WSN security which addresses many of the shortcomings of existing mechanisms. It presents a detailed description on how to provide practical Public Key Cryptography solutions for wireless sensor networks. The contributions to the state-of-the-art are added on all levels of development beginning with the basic arithmetic operations and finishing with complete security protocols. This work includes a survey of different key distribution protocols that have been developed for WSNs, with an evaluation of their limitations. It also proposes Identity- Based Cryptography (IBC) as an ideal technique for key distribution in sensor networks. It presents the first in-depth study of the application and implementation of Pairing- Based Cryptography (PBC) to WSNs. This is followed by a presentation of the state of the art on the software implementation of Elliptic Curve Cryptography (ECC) on typical WSNplatforms. New optimized algorithms for performing multiprecision multiplication on a broad range of low-end CPUs are introduced as well. Three novel protocols for key distribution are proposed in this thesis. Two of these are intended for non-interactive key exchange in flat and clustered networks respectively. A third key distribution protocol uses Identity-Based Encryption (IBE) to secure communication within a heterogeneous sensor network. This thesis includes also a comprehensive security evaluation that shows that proposed schemes are resistant to various attacks that are specific to WSNs. This work shows that by using the newest achievements in cryptography like pairings and IBC it is possible to deliver affordable public-key cryptographic solutions and to apply a sufficient level of security for the most demanding WSN applications

Security is an Architectural Design Constraint

In state-of-the-art design paradigm, time, space and power efficiency are considered the primary design constraints. Quite often, this approach adversely impacts the security of the overall system, especially when security is adopted as a countermeasure after some vulnerability is identified. In this position paper, we motivate the idea that security should also be considered as an architectural design constraint in addition to time, space and power. We show that security and efficiency objectives along the three design axes of time, space and power are in fact tightly coupled while identifying that security stands in direct contrast with them across all layers of architectural design. We attempt to prove our case utilizing a proof-by-evidence approach wherein we refer to various works across literature that explicitly imply the eternal conflict between security and efficiency. Thus, security has to be treated as a design constraint from the very beginning. Additionally, we advocate a security-aware design flow starting from the choice of cryptographic primitives, protocols and system design

Efficient Cryptographic Algorithms and Protocols for Mobile Ad Hoc Networks

As the next evolutionary step in digital communication systems, mobile ad hoc networks (MANETs) and their specialization like wireless sensor networks (WSNs) have been attracting much interest in both research and industry communities. In MANETs, network nodes can come together and form a network without depending on any pre-existing infrastructure and human intervention. Unfortunately, the salient characteristics of MANETs, in particular the absence of infrastructure and the constrained resources of mobile devices, present enormous challenges when designing security mechanisms in this environment. Without necessary measures, wireless communications are easy to be intercepted and activities of users can be easily traced. This thesis presents our solutions for two important aspects of securing MANETs, namely efficient key management protocols and fast implementations of cryptographic primitives on constrained devices. Due to the tight cost and constrained resources of high-volume mobile devices used in MANETs, it is desirable to employ lightweight and specialized cryptographic primitives for many security applications. Motivated by the design of the well-known Enigma machine, we present a novel ultra-lightweight cryptographic algorithm, referred to as Hummingbird, for resource-constrained devices. Hummingbird can provide the designed security with small block size and is resistant to the most common attacks such as linear and differential cryptanalysis. Furthermore, we also present efficient software implementations of Hummingbird on 4-, 8- and 16-bit microcontrollers from Atmel and Texas Instruments as well as efficient hardware implementations on the low-cost field programmable gate arrays (FPGAs) from Xilinx, respectively. Our experimental results show that after a system initialization phase Hummingbird can achieve up to 147 and 4.7 times faster throughput for a size-optimized and a speed-optimized software implementation, respectively, when compared to the state-of-the-art ultra-lightweight block cipher PRESENT on the similar platforms. In addition, the speed optimized Hummingbird encryption core can achieve a throughput of 160.4 Mbps and the area optimized encryption core only occupies 253 slices on a Spartan-3 XC3S200 FPGA device. Bilinear pairings on the Jacobians of (hyper-)elliptic curves have received considerable attention as a building block for constructing cryptographic schemes in MANETs with new and novel properties. Motivated by the work of Scott, we investigate how to use efficiently computable automorphisms to speed up pairing computations on two families of non-supersingular genus 2 hyperelliptic curves over prime fields. Our findings lead to new variants of Miller's algorithm in which the length of the main loop can be up to 4 times shorter than that of the original Miller's algorithm in the best case. We also generalize Chatterjee et al.'s idea of encapsulating the computation of the line function with the group operations to genus 2 hyperelliptic curves, and derive new explicit formulae for the group operations in projective and new coordinates in the context of pairing computations. Efficient software implementation of computing the Tate pairing on both a supersingular and a non-supersingular genus 2 curve with the same embedding degree of k = 4 is investigated. Combining the new algorithm with known optimization techniques, we show that pairing computations on non-supersingular genus 2 curves over prime fields use up to 55.8% fewer field operations and run about 10% faster than supersingular genus 2 curves for the same security level. As an important part of a key management mechanism, efficient key revocation protocol, which revokes the cryptographic keys of malicious nodes and isolates them from the network, is crucial for the security and robustness of MANETs. We propose a novel self-organized key revocation scheme for MANETs based on the Dirichlet multinomial model and identity-based cryptography. Firmly rooted in statistics, our key revocation scheme provides a theoretically sound basis for nodes analyzing and predicting peers' behavior based on their own observations and other nodes' reports. Considering the difference of malicious behaviors, we proposed to classify the nodes' behavior into three categories, namely good behavior, suspicious behavior and malicious behavior. Each node in the network keeps track of three categories of behavior and updates its knowledge about other nodes' behavior with 3-dimension Dirichlet distribution. Based on its own analysis, each node is able to protect itself from malicious attacks by either revoking the keys of the nodes with malicious behavior or ceasing the communication with the nodes showing suspicious behavior for some time. The attack-resistant properties of the resulting scheme against false accusation attacks launched by independent and collusive adversaries are also analyzed through extensive simulations. In WSNs, broadcast authentication is a crucial security mechanism that allows a multitude of legitimate users to join in and disseminate messages into the networks in a dynamic and authenticated way. During the past few years, several public-key based multi-user broadcast authentication schemes have been proposed in the literature to achieve immediate authentication and to address the security vulnerability intrinsic to μTESLA-like schemes. Unfortunately, the relatively slow signature verification in signature-based broadcast authentication has also incurred a series of problems such as high energy consumption and long verification delay. We propose an efficient technique to accelerate the signature verification in WSNs through the cooperation among sensor nodes. By allowing some sensor nodes to release the intermediate computation results to their neighbors during the signature verification, a large number of sensor nodes can accelerate their signature verification process significantly. When applying our faster signature verification technique to the broadcast authentication in a 4×4 grid-based WSN, a quantitative performance analysis shows that our scheme needs 17.7%~34.5% less energy and runs about 50% faster than the traditional signature verification method

Privacy-preserving Payments for Transportation Systems

The operation of our society heavily relies on high mobility of people. Not only our social life but also our economy and trade are built upon a system where people need to be able to move around easily. The costs for building and maintaining a suitable transportation infrastructure to satisfy those needs are high, and to charge users is thus a central requirement. This calls for well functioning payment systems satisfying the multitude of requirements that transportation systems impose on them. Electronic payment systems have many benefits over traditional cash payments as they are easy to maintain, can be more secure, reduce revenue collection costs, and can reduce the execution time of a payment. However, as a drawback, currently employed electronic payment systems usually reveal a payer’s identity during a payment which greatly infringes customer privacy. In the transportation domain this allows to generate fine grain patterns of customers’ locations. Cryptographic payment protocols called e-cash have been proposed which allow to preserve a customer’s privacy. E-cash provides provable guarantees for both security and user privacy, as it allows secure, unlinkable payments which do not reveal the identity of the payer during a payment. From a security and privacy perspective these protocols present a good solution. However, even though e-cash protocols have been proposed three decades ago, there are relatively few actual implementations. One reason for this is their high computational complexity which makes an implementation on potential mobile payment devices rather difficult. While customers usually value their privacy they often do not accept to sacrifice convenience. A fast execution of payments is thus a hard constraint, which conflicts with the computational complexity of e-cash schemes. This dissertation analyzes how e-cash can be used to solve the issue of privacy in the domain of transportation payments while satisfying the unique requirements of transportation payment systems and achieving high security and ease of use. Highlyefficient implementations of the underlying cryptographic primitives of e-cash schemes on constrained devices as they might be used in the transportation setting are presented. Based on the efficient implementations of these primitives, e-cash schemes are analyzed with regards to speed and hardware requirements. The results show that e-cash presents a good solution for privacy-preserving payments in the domain of public transport, if the number of coins that have to be spent can be limited. It is further practically shown that this limitation can be alleviated relying on the e-cash based privacy-preserving pre-payments with refunds scheme (P4R). Moreover, it is demonstrated that the promising feature of supporting the encoding of user attributes into electronic coins can be implemented at only moderate extra cost. Finally, an ecash based e-mobility payment scheme is presented which highlights the flexibility and unique advantages of e-cash based transportation payment schemes