A versatile Montgomery multiplier architecture with characteristic three support

We present a novel unified core design which is extended to realize Montgomery multiplication in the fields GF(2n), GF(3m), and GF(p). Our unified design supports RSA and elliptic curve schemes, as well as the identity-based encryption which requires a pairing computation on an elliptic curve. The architecture is pipelined and is highly scalable. The unified core utilizes the redundant signed digit representation to reduce the critical path delay. While the carry-save representation used in classical unified architectures is only good for addition and multiplication operations, the redundant signed digit representation also facilitates efficient computation of comparison and subtraction operations besides addition and multiplication. Thus, there is no need for a transformation between the redundant and the non-redundant representations of field elements, which would be required in the classical unified architectures to realize the subtraction and comparison operations. We also quantify the benefits of the unified architectures in terms of area and critical path delay. We provide detailed implementation results. The metric shows that the new unified architecture provides an improvement over a hypothetical non-unified architecture of at least 24.88%, while the improvement over a classical unified architecture is at least 32.07%

Performance Evaluation of Optimal Ate Pairing on Low-Cost Single Microprocessor Platform

The framework of low-cost interconnected devices forms a new kind of cryptographic environment with diverse requirements. Due to the minimal resource capacity of the devices, light-weight cryptographic algorithms are favored. Many applications of IoT work autonomously and process sensible data, which emphasizes security needs, and might also cause a need for specific security measures. A bilinear pairing is a mapping based on groups formed by elliptic curves over extension fields. The pairings are the key-enabler for versatile cryptosystems, such as certificateless signatures and searchable encryption. However, they have a major computational overhead, which coincides with the requirements of the low-cost devices. Nonetheless, the bilinear pairings are the only known approach for many cryptographic protocols so their feasibility should certainly be studied, as they might turn out to be necessary for some future IoT solutions. Promising results already exist for high-frequency CPU:s and platforms with hardware extensions. In this work, we study the feasibility of computing the optimal ate pairing over the BN254 curve, on a 64 MHz Cortex-M33 based platform by utilizing an optimized open-source library. The project is carried out for the company Nordic Semiconductor. As a result, the pairing was effectively computed in under 26* 10^6 cycles, or in 410 ms. The resulting pairing enables a limited usage of pairing-based cryptography, with a capacity of at most few cryptographic operations, such as ID-based key verifications per second. Referring to other relevant works, a competent pairing application would require either a high-frequency - and thus high consuming - microprocessor, or a customized FPGA. Moreover, it is noted that the research in efficient pairing-based cryptography is constantly taking steps forward in every front-line: efficient algorithms, protocols, and hardware-solutions

Elliptic Curve Cryptography on Modern Processor Architectures

Abstract Elliptic Curve Cryptography (ECC) has been adopted by the US National Security Agency (NSA) in Suite "B" as part of its "Cryptographic Modernisation Program ". Additionally, it has been favoured by an entire host of mobile devices due to its superior performance characteristics. ECC is also the building block on which the exciting field of pairing/identity based cryptography is based. This widespread use means that there is potentially a lot to be gained by researching efficient implementations on modern processors such as IBM's Cell Broadband Engine and Philip's next generation smart card cores. ECC operations can be thought of as a pyramid of building blocks, from instructions on a core, modular operations on a finite field, point addition & doubling, elliptic curve scalar multiplication to application level protocols. In this thesis we examine an implementation of these components for ECC focusing on a range of optimising techniques for the Cell's SPU and the MIPS smart card. We show significant performance improvements that can be achieved through of adoption of EC

KALwEN: A New Practical and Interoperable Key Management Scheme for Body Sensor Networks

Key management is the pillar of a security architecture. Body sensor networks(BSNs) pose several challenges -- some inherited from wireless sensor networks(WSNs), some unique to themselves -- that require a new key management scheme to be tailor-made. The challenge is taken on, and the result is KALwEN, a new lightweight scheme that combines the best-suited cryptographic techniques in a seamless framework. KALwEN is user-friendly in the sense that it requires no expert knowledge of a user, and instead only requires a user to follow a simple set of instructions when bootstrapping or extending a network. One of KALwEN's key features is that it allows sensor devices from different manufacturers, which expectedly do not have any pre-shared secret, to establish secure communications with each other. KALwEN is decentralized, such that it does not rely on the availability of a local processing unit (LPU). KALwEN supports global broadcast, local broadcast and neighbor-to-neighbor unicast, while preserving past key secrecry and future key secrecy. The fact that the cryptographic protocols of KALwEN have been formally verified also makes a convincing case

Theory and Practice of Cryptography and Network Security Protocols and Technologies

In an age of explosive worldwide growth of electronic data storage and communications, effective protection of information has become a critical requirement. When used in coordination with other tools for ensuring information security, cryptography in all of its applications, including data confidentiality, data integrity, and user authentication, is a most powerful tool for protecting information. This book presents a collection of research work in the field of cryptography. It discusses some of the critical challenges that are being faced by the current computing world and also describes some mechanisms to defend against these challenges. It is a valuable source of knowledge for researchers, engineers, graduate and doctoral students working in the field of cryptography. It will also be useful for faculty members of graduate schools and universities

A Survey Report On Elliptic Curve Cryptography

The paper presents an extensive and careful study of elliptic curve cryptography (ECC) and its applications. This paper also discuss the arithmetic involved in elliptic curve  and how these curve operations is crucial in determining the performance of cryptographic systems. It also presents  different forms of elliptic curve in various coordinate system , specifying which is most widely used and why. It also explains how isogenenies between elliptic curve  provides the secure ECC. Exentended form of elliptic curve i.e hyperelliptic curve has been presented here with its pros and cons. Performance of ECC and HEC is also discussed based on scalar multiplication and DLP. Keywords: Elliptic curve cryptography (ECC), isogenies, hyperelliptic curve (HEC) , Discrete Logarithm Problem (DLP), Integer  Factorization , Binary Field, Prime FieldDOI:http://dx.doi.org/10.11591/ijece.v1i2.8

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