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This work describes a pipelined architecture targeting FPGA binary field multiplication. It comprises a generic real time crypto coprocessor able to operate over any field, without a specific vendor specific technology. A performance comparison of this synthesized coprocessor is presented for two major FPGA vendors. The results show that the parallelism levels, often applied as a key point for decision-making,...
Elliptic curve cryptography is a public key cryptography technique based on the algebraic structure of elliptic curves over finite fields. It provides the same level of security that other alternatives provide, but it performs its process in less time, less memory, less computations and less power consumption. Thus it is suitable for environments with constraints like computing power, memory and battery...
Various cryptographic techniques use finite field multiplication. An efficient implementation of finite field multiplication is essential. Especially, elliptic curve cryptography (ECC), which provides high security with shorter key lengths, requires many multiplications during encryption and decryption phases. It is imperative to choose a faster and less resource consuming multiplier. Many algorithms...
Elliptic curve cryptography is a rather new, efficient technology for security. However, its implementation is complex and software versions can be prohibitively slow. The main original contribution of this paper is the proposition of a highly parameterizable soft intellectual property core that implements all the operations needed to perform elliptic curve cryptography in hardware. This core supports...
Bernstein and Lange recently proposed to use Edwards coordinates for ECC (Elliptic Curve Cryptography). They claimed them to be more efficient, not only in terms of operation count but also in terms of side-channel security. The latter is thanks to unified point addition and doubling. This work takes on this claim about improved side-channel security of Edwards curves using unified formulas. Our analysis...
Elliptic curve cryptography is a public key cryptosystem based on the elliptic curve discrete logarithm problem. The reason for the attractiveness of ECC is that there is no sub-exponential algorithm known to solve the elliptic curve discrete logarithm problem. This leads to lower memory requirements, lower computation requirements and higher security than other public key cryptosystems. This project...
Two elliptic curve scalar multiplications (ECMLT) are used in some important elliptic curve encryption algorithms, a pseudo-pipelined VLSI architecture of two ECMLTs over GF(2m) is proposed for these algorithms. The proposed architecture includes three word-serial finite field (FF) multipliers, and each FF multiplier has word size w. Implemented using FPGA, two ECMLTs are computed in approximately...
The spectral hash algorithm is one of the round 1 candidates for the SHA-3 family, and is based on spectral arithmetic over a finite field, involving multidimensional discrete Fourier transformations over a finite field, data dependent permutations, rubic-type rotations, and affine and nonlinear functions. The underlying mathematical structures and operations pose interesting and challenging tasks...
In this paper, a generic elliptic curve (EC) arithmetic unit with high flexibility and small chip covered area is proposed. This EC arithmetic unit is based on the one dimensional systolic architectural realization of a proposed modified multiplication - inversion algorithm that through appropriate initialization uses the algorithmic structure of inversion to also perform multiplication. The proposed...
The information security is emphasized with a development of Internet systems. In the measures as securing digital information, there are cryptosystems that protect secrecy of digital documents and digital signature scheme that ensure validity of digital documents. In the case of reality, i.e. hardware devices are used in cryptosystems, there is a possibility that secret information leaks via side-channel...
The paper describes computer system consisting of a central server and a distributed computing system composed of multiprocessor servers using the MPI, computer clusters, computers of the PC and dedicated FPGA units. The field programmable gate array (FPGA) units will be connected to the system through PC. The communication of computational units with the server is realized through Internet and LAN...
This is the first implementation in FPGA of the recently published class of public key algorithms - MQQ, that are based on quasigroup string transformations. Our implementation achieves decryption throughput of 399 Mbps on an Xilinx Virtex-5 FPGA that is running on 249.4 MHz. The encryption throughput of our implementation achieves 44.27 Gbps on an Xilinx Virtex-5 chip that is running on 276.7 MHz...
This paper describes an efficient arithmetic processor for elliptic curve cryptography. The proposed processor consists of special architectural components, the most important of which is a modular multiplication unit implemented using the systolic montgomery multiplication algorithm. Another novelty of our proposed architecture is that it implements the field GF(3m), which provides significant performance...
In this paper a processor that supports elliptic curve cryptographic applications over GF (2m) is proposed. The proposed structure is capable of calculating point multiplication and addition using a single coordinate to contain the point information. This compression allows for a better usage of the bandwidth resources. For the point multiplication procedure, all coordinate pre-calculations are completely...
This work presents the implementation of a tightly-coupled hardware architectural enhancement to the Altera FPGA-based Nios II embedded processor. The goal is to accelerate finite field arithmetic operations in the binary fields of F2163 and F2193, for application in a high-performance embedded system implementing elliptic-curve cryptography (ECC). The concept is to augment the embedded processor...
This paper studies the polynomial residue representation of Galois field (2m) elements and polynomial residue arithmetic (PRA), according to which a novel approach of performing GF(2m) multiplication using polynomial residue number system (PRNS) is introduced. A channel-serial and a channel-parallel architecture of the PRNS multiplier over GF(2m) are presented. Conclusion is drawn by comparing the...
Cryptanalysis of symmetric and asymmetric ciphers is a challenging task due to the enormous amount of involved computations. To tackle this computational complexity, usually the employment of special-purpose hardware is considered as best approach. We have built a massively parallel cluster system (COPACOBANA) based on low-cost FPGAs as a cost-efficient platform primarily targeting cryptanalytical...
This paper presents a versatile public-key cryptographic processor suitable for wireless sensor networks which uses minimal hardware resources while maintaining high flexibility. The processor architecture is scalable and all hardware configurations support arbitrary bit-lengths and domain parameters. The tradeoffs between hardware area and timing for the public-key operations are demonstrated on...
Public-key cryptosystems allow secure connections and data exchange through unsafe communication channel without the need of a previous secure key exchange. The most popular cryptosystem used nowadays is RSA. However recently a serious rival appeared - elliptic curve cryptosystems (ECC).Cryptanalytic attack on ECC system involves solving the elliptic curve discrete logarithm problem (ECDLP). The best...
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