The Elliptic Curve Cryptosystem shortly called as (ECC) is one of the asymmetric key cryptosystems, which provides a high security for wireless applications compared to other asymmetric key cryptosystem. The implementation of this algorithm over prime field Z p has a set of point operations, which are point addition, point subtraction, point multiplication, point division, point inversion, and point doubling. In these operations, the time complexity of the point multiplication is higher than any other time complexity of ECC point operations. So, it is necessary to find out an alternative implementation for point multiplication to take minimum amount of clock cycles, to reduce power consumption, and to support the software scheduling for parallel processing on arithmetic operations during execution. Considering this, the proposed implementation is very useful to perform encryption or decryption on texts, and also for analysing the strength of encryption or decryption computation.

Analyzing the Point Multiplication Operation of Elliptic Curve Cryptosystem over Prime Field for Parallel Processing

Elliptic Curve Cryptography (ECC) is one of the safest standard algorithms, based on public-key, for providing the security in communication and networks. One of the most time consuming processes in ECC algorithm for encryption/decryption is the scalar multiplication, i.e., KP, where P is the text which is on the elliptic curve. This paper examines that computation can be speeded up by using Ancient Indian Vedic Mathematics. Coding is done using Verilog-HDL and downloaded on target device as Virtex 5. Our proposed work is six times faster than the previous work when applied in point doubling using Spartan3 as target device.

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Efficient Implementation of Scalar Multiplication for Elliptic Curve Cryptography using Ancient Indian Vedic Mathematics over GF(p)

A wireless network has a set of limitations such as low power consume, limited bandwidth, less memory space, less security access and architecture design issues. Considering these limitations, the best way of providing high security system for wireless network is to use Elliptic curve cryptography(ECC) which is one of the public key cryptography. The implementation of ECC has a set of point manipulation operations such as addition, subtraction, division, multiplication, inversion and doubling. In these operations, the point doubling is high time complexity which needs more clock cycles to compute its result. So it is necessary to reduce the time complexity of point doubling during processing. The proposed technique schedules coding for fast processing and reduces number of clock cycles during its atomic operations. It also reduces number of hazards and stalls during its processing. This is useful when it is implemented by using parallel processing.

Decreasing point multiplication over ECC (Z p ) using tree computations

This paper presents the design and implementation of an integrated architecture for key exchange and authentication in wireless sensor networks (WSNs) employing elliptic curve cryptography (ECC) for key management. Instead of implementing a standard algorithm such as SHA or AES for authentication, this paper considers an elliptic curve based message authentication code (MAC) for optimized design of overall structure through hardware reuse. The proposed architecture time shares the point multiplication unit between functionalities of key exchange and MAC there by reducing the structural complexity. The proposed architecture is implemented over GF(2163) on a Kintex 7 FPGA board using Xilinx ISE. The EC point multiplication is done using Lopez-Dahab algorithm and the finite field elements are represented using Gaussian normal basis to reduce the computational complexity and resist side channel attack.

Optimized hardware design and implementation of EC based key management scheme for WSN

Today a wireless network has minimum power consume and less security access. Based on these the suitable way of providing a security system for wireless application is to select the Elliptic Curve Cryptography. But this public key cryptography has required more number of clock cycles to compute its point operations. One of the point operations called point multiplication requires a lot of clock cycles to compute result. This proposed technique reduces the number of clock cycles of point multiplication for parallel processing by reducing number of dependent and independent operations. General Terms Wireless network,security system and dependent and independent operations.

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Optimizing point Doubling Operations in ECC Zp

Elliptic curve cryptography (ECC) is recognized as a fast cryptography system and has many applications in security systems. In this paper, a novel sharing scheme is proposed to significantly reduce the number of field multiplications and the usage of lookup tables, providing high speed operations for both hard-ware and software realizations.

Hardware organization to achieve high-speed elliptic curve cryptography for mobile devices

One embodiment is a method including selecting a first integer which is substantially random over the set {0, 1, 2,..., 2s- 1} where s is a positive security integer, selecting a second integer which is substantially random over the set {0, 1, 2,..., 2s-1}, combining the first integer, the second integer and a key, and determining a scalar multiple of the combination of the first integer, the second integer, and the key. Other embodiments include unique apparatuses, systems and methods relating to hardware fault attack countermeasures. Another embodiment includes a computer readable medium storing a program executable to randomize a CRT calculation, calculate a value which is a function of the CRT calculation, the value being a pseudo-random number if a fault has been induced in the program, the value being a predetermined value if a fault has not been induced in the program, and generate a signature which is a function of the value. Other embodiments include unique apparatuses, systems, computer accessible media, and methods relating to hardware fault attack countermeasures.

Liu Sining

Papers

Hardware organization to achieve high-speed elliptic curve cryptography for mobile devices

Security attack countermeasures