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

The AXIOM software layers

AXIOM project aims at developing a heterogeneous computing board (SMP-FPGA).The Software Layers developed at the AXIOM project are explained.OmpSs provides an easy way to execute heterogeneous codes in multiple cores. People and objects will soon share the same digital network for information exchange in a world named as the age of the cyber-physical systems. The general expectation is that people and systems will interact in real-time. This poses pressure onto systems design to support increasing demands on computational power, while keeping a low power envelop. Additionally, modular scaling and easy programmability are also important to ensure these systems to become widespread. The whole set of expectations impose scientific and technological challenges that need to be properly addressed.The AXIOM project (Agile, eXtensible, fast I/O Module) will research new hardware/software architectures for cyber-physical systems to meet such expectations. The technical approach aims at solving fundamental problems to enable easy programmability of heterogeneous multi-core multi-board systems. AXIOM proposes the use of the task-based OmpSs programming model, leveraging low-level communication interfaces provided by the hardware. Modular scalability will be possible thanks to a fast interconnect embedded into each module. To this aim, an innovative ARM and FPGA-based board will be designed, with enhanced capabilities for interfacing with the physical world. Its effectiveness will be demonstrated with key scenarios such as Smart Video-Surveillance and Smart Living/Home (domotics).Peer ReviewedPostprint (author's final draft

Cryptography Engine Design for IEEE 1609.2 WAVE Secure Vehicle Communication using FPGA

Department Of Electrical EngineeringIn this paper, we implement the IEEE 1609.2 secure vehicle communication (VC) standard using FPGA by fast and efficient ways. Nowadays, smart vehicle get nearer to our everyday life. Therefore, design of safety smart vehicle is critical issue in this field. For this reason, secure VC is must implemented into the smart vehicle to support safety service. However, secure process in VC has significant overhead to communication between objectives. Because of this overhead, if circumjacent vehicles are increased, communication overhead of VC is exponentially increased along the number of adjacent vehicles. To remove this kind of overhead, we design fast and efficient IEEE 1609.2 cryptography engine using FPGA. This engine consists of AES-CCM encryption, SHA-256 hash function, Hash_DRBG random bit generator, and ECDSA digital signature algorithm and each algorithm is analyzed carefully and optimized with specific technics. For the AES-CCM, we optimized AES encryption engine. First, we use 32-bit S-box structure to remove 8-bit operation of AES. Second, we employ the key save register file architecture to reduce frequently key expansion operation when input of key value is always same for AES encryption engine. Third, to protect external attacks, we use internal register files to save processed data. Finally, we design parallel architecture for both CBC-MAC and counter in AES-CCM algorithm. SHA-256 hash function is frequently used in ECDSA algorithm that is significant reason of optimization. So, we use parallel architecture for the preprocessing block and the hash computation block. And, we design latest schedule block to reduce usage of register and combinational logics. In ECDSA, Hash-DRBG is used to generate key value and signature for vehicle message. To make Hash-DRBG, we use our SHA-256 design much fast generation of random value. ECDSA is most critical and complex module in our cryptography engine. For this module, we use affine representation of elliptic curve in ECDSA. So, we can replace the prime arithmetic operation by right shift operation and bit operation. And, we implement scalar multiplier to optimize arithmetic operation of ECDSA. This kind of replacement is hardware kindly, so we can reduce complexity of ECDSA hardware design. To implement all of algorithm in IEEE 1609.2 standard, we use Xilinx Virtex-5 FPGA chip with ISE 14.6 synthesis tool and Verilog-HDL.ope

High-Speed Area-Efficient Hardware Architecture for the Efficient Detection of Faults in a Bit-Parallel Multiplier Utilizing the Polynomial Basis of GF(2m)

The utilization of finite field multipliers is pervasive in contemporary digital systems, with hardware implementation for bit parallel operation often necessitating millions of logic gates. However, various digital design issues, whether natural or stemming from soft errors, can result in gate malfunction, ultimately leading to erroneous multiplier outputs. Thus, to prevent susceptibility to error, it is imperative to employ an effective finite field multiplier implementation that boasts a robust fault detection capability. This study proposes a novel fault detection scheme for a recent bit-parallel polynomial basis multiplier over GF(2m), intended to achieve optimal fault detection performance for finite field multipliers while simultaneously maintaining a low-complexity implementation, a favored attribute in resource-constrained applications like smart cards. The primary concept behind the proposed approach is centered on the implementation of a BCH decoder that utilizes re-encoding technique and FIBM algorithm in its first and second sub-modules, respectively. This approach serves to address hardware complexity concerns while also making use of Berlekamp-Rumsey-Solomon (BRS) algorithm and Chien search method in the third sub-module of the decoder to effectively locate errors with minimal delay. The results of our synthesis indicate that our proposed error detection and correction architecture for a 45-bit multiplier with 5-bit errors achieves a 37% and 49% reduction in critical path delay compared to existing designs. Furthermore, the hardware complexity associated with a 45-bit multiplicand that contains 5 errors is confined to a mere 80%, which is significantly lower than the most exceptional BCH-based fault recognition methodologies, including TMR, Hamming's single error correction, and LDPC-based procedures within the realm of finite field multiplication.Comment: 9 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:2209.1338

LEGaTO: first steps towards energy-efficient toolset for heterogeneous computing

LEGaTO is a three-year EU H2020 project which started in December 2017. The LEGaTO project will leverage task-based programming models to provide a software ecosystem for Made-in-Europe heterogeneous hardware composed of CPUs, GPUs, FPGAs and dataflow engines. The aim is to attain one order of magnitude energy savings from the edge to the converged cloud/HPC.Peer ReviewedPostprint (author's final draft

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

ASIC design and implementation of a parallel exponentiation algorithm using optimized scalable Montgomery multipliers

Modular exponentiation and modular multiplication are the most used operations in current cryptographic systems. Some well-known cryptographic algorithms, such as RSA, Diffie-Hellman key exchange, and DSA, require modular exponentiation operations. This is performed with a series of modular multiplications to the extent of its exponent in a certain fashion depending on the exponentiation algorithm used. Cryptographic functions are very likely to be applied in current applications that perform information exchange to secure, verify, or authenticate data. Most notable is the use of such applications in Internet based information exchange. Smart cards, hand-helds, cell phones and many other small devices also need to perform information exchange and are likely to apply cryptographic functions. A hardware solution to perform a cryptographic function is generally faster and more secure than a software solution. Thus, a fast and area efficient modular exponentiation hardware solution would provide a better infrastructure for current cryptographic techniques. In certain cryptographic algorithms, very large precisions are used. Further, the precision may vary. Most of the hardware designs for modular multiplication and modular exponentiation are fixed-precision solutions. A scalable Montgomery Multiplier (MM) to perform modular multiplication has been proposed and can operate on input values of any bit-size, but the maximum bit-size should be known and is the limiting factor. The multiplier can calculate any operand size less than the maximal precision. However, this design's parameters should be optimized depending on the operand precision for which the design is used. A software application was developed in C to find the optimized design for the scalable MM module. It performs area-time trade-off for the most commonly used precisions in order to obtain a fast and area efficient solution for the common case. A modular exponentiation system is developed using this scalable multiplier design. Since the multiplier can operate on any operand size up to a certain maximum value, the exponentiation system that utilizes the multiplier will inherit the same capability. This thesis work presents the design and implementation of an exponentiation algorithm in hardware utilizing the optimized scalable Montgomery Multiplier. The design uses a parallel exponentiation algorithm to reduce the total computation time. The modular exponentiation system experimental results are analyzed and compared with software and other hardware implementations