High Performance Reconfigurable Elliptic Curve Cipher Processor Implementation

Elliptic Curve Encryption (ECC) has been widely used in the field of digital signatures in communication security. ECC standards and the diversification of application scenarios put forward higher requirements for the flexibility of ECC processors. Therefore, it is necessary to design a flexible and reconfigurable processor to adapt to changing standards. The cryptographic processor chip designed in this paper supports the choice of prime and binary fields, supports the maximum key length of 576 bits, uses microcode programming to achieve reconfigurable function, and significantly improves the flexibility of the dedicated cryptographic processor. At the same time, the speed of modular multiplication and modular division can be greatly improved under the condition of keeping the low level of hardware resources through a carefully designed modular unit of operation. After using FPGA for hardware implementation, it is configured into a 256-bit key length. The highest clock frequency of this design can reach 55.7MHz, occupying 12425LUTS. Compared with a similar design, the performance is also greatly improved. After MALU module optimization design, modular multiplication module division also has significant advantages in computing time consumption.

Efficient scalar multiplication of ECC using SMBR and fast septuple formula for IoT

In order to solve the problem between low power of Internet of Things devices and the high cost of cryptography, lightweight cryptography is required. The improvement of the scalar multiplication can effectively reduce the complexity of elliptic curve cryptography (ECC). In this paper, we propose a fast formula for point septupling on elliptic curves over binary fields using division polynomial and multiplexing of intermediate values to accelerate the computation by more than 14%. We also propose a scalar multiplication algorithm based on the step multi-base representation using point halving and the septuple formula we proposed, which significantly reduces the computational cost. The experimental results show that our method is more efficient over binary fields and contributes to reducing the complexity of ECC.

An Efficient Elliptic-Curve Point Multiplication Architecture for High-Speed Cryptographic Applications

This work presents an efficient high-speed hardware architecture for point multiplication (PM) computation of Elliptic-curve cryptography using binary fields over GF(2163) and GF(2571). The efficiency is achieved by reducing: (1) the time required for one PM computation and (2) the total number of required clock cycles. The required computational time for one PM computation is reduced by incorporating two modular multipliers (connected in parallel), a serially connected adder after multipliers and two serially connected squarer units (one after the first multiplier and another after the adder). To optimize the total number of required clock cycles, the point addition and point double instructions for PM computation of the Montgomery algorithm are re-structured. The implementation results after place-and-route over GF(2163) and GF(2571) on a Xilinx Virtex-7 FPGA device reveal that the proposed high-speed architecture is well-suited for the network-related applications, where millions of heterogeneous devices want to connect with the unsecured internet to reach an acceptable performance.

Opening reionization: quantitative morphology of the epoch of reionization and its connection to the cosmic density field

ABSTRACT We introduce a versatile and spatially resolved morphological characterization of binary fields, rooted in the opening transform of mathematical morphology. We subsequently apply it to the thresholded ionization field in simulations of cosmic reionization and study the morphology of ionized regions. We find that an ionized volume element typically resides in an ionized region with radius ∼8 h−1 cMpc at the midpoint of reionization (z ≈ 7.5) and follow the bubble size distribution even beyond the overlap phase. We find that percolation of the fully ionized component sets in when 25 per cent of the universe is ionized and that the resulting infinite cluster incorporates all ionized regions above ∼8 h−1 cMpc. We also quantify the clustering of ionized regions of varying radius with respect to matter and on small scales detect the formation of superbubbles in the overlap phase. On large scales, we quantify the bias values of the centres of ionized and neutral regions of different sizes and not only show that the largest ones at the high-point of reionization can reach b ≈ 30, but also that early small ionized regions are positively correlated with matter and large neutral regions and late small ionized regions are heavily antibiased with respect to matter, down to b ≲ −20.

Parallel and Regular Algorithm of Elliptic Curve Scalar Multiplication over Binary Fields

Accelerating scalar multiplication has always been a significant topic when people talk about the elliptic curve cryptosystem. Many approaches have been come up with to achieve this aim. An interesting perspective is that computers nowadays usually have multicore processors which could be used to do cryptographic computations in parallel style. Inspired by this idea, we present a new parallel and efficient algorithm to speed up scalar multiplication. First, we introduce a new regular halve-and-add method which is very efficient by utilizing λ projective coordinate. Then, we compare many different algorithms calculating double-and-add and halve-and-add. Finally, we combine the best double-and-add and halve-and-add methods to get a new faster parallel algorithm which costs around 12.0% less than the previous best. Furthermore, our algorithm is regular without any dummy operations, so it naturally provides protection against simple side-channel attacks.