Implementation of Pollard Rho attack on elliptic curve cryptography over binary fields

2015 ◽  
Author(s):  
Wienardo ◽  
Fajar Yuliawan ◽  
Intan Muchtadi-Alamsyah ◽  
Budi Rahardjo
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Binary Fields

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

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Chong Guo ◽  
Bei Gong
Keyword(s):  
Internet Of Things ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Elliptic Curve Cryptography ◽  
Computational Cost ◽  
Scalar Multiplication ◽  
Lightweight Cryptography ◽  
Multiplication Algorithm ◽  
Binary Fields ◽  
Division Polynomial

AbstractIn 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.

scholarly journals Karatsuba-Block-Comb technique for elliptic curve cryptography over binary fields

2015 ◽  
Vol 8 (17) ◽  
pp. 3121-3130 ◽  
Author(s):  
Hwajeong Seo ◽  
Zhe Liu ◽  
Jongseok Choi ◽  
Howon Kim
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Binary Fields

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

Electronics ◽  
2020 ◽  
Vol 9 (12) ◽  
pp. 2126
Author(s):  
Muhammad Rashid ◽  
Malik Imran ◽  
Asher Sajid
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
High Speed ◽  
Hardware Architecture ◽  
Computational Time ◽  
Point Multiplication ◽  
Heterogeneous Devices ◽  
Binary Fields ◽  
Time Required ◽  
Place And Route

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.

Study of Safe Elliptic Curve Cryptography over Gaussian Integer

2020 ◽  
Vol E103.A (12) ◽  
pp. 1624-1628
Author(s):  
Kazuki NAGANUMA ◽  
Takashi SUZUKI ◽  
Hiroyuki TSUJI ◽  
Tomoaki KIMURA
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Gaussian Integer

Enhanced Security Authentication of WiMAX using EC3A

2017 ◽  
Vol 7 (8) ◽  
pp. 219
Author(s):  
Mohd Javed ◽  
Khaleel Ahmad ◽  
Ahmad Talha Siddiqui
Keyword(s):  
Cellular Automata ◽  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Information Rate ◽  
Security Authentication ◽  
Encryption And Decryption ◽  
High Information

WiMAX is the innovation and upgradation of 802.16 benchmarks given by IEEE. It has numerous remarkable qualities, for example, high information rate, the nature of the service, versatility, security and portability putting it heads and shoulder over the current advancements like broadband link, DSL and remote systems. Though like its competitors the concern for security remains mandatory. Since the remote medium is accessible to call, the assailants can undoubtedly get into the system, making the powerless against the client. Many modern confirmations and encryption methods have been installed into WiMAX; however, regardless it opens with up different dangers. In this paper, we proposed Elliptic curve Cryptography based on Cellular Automata (EC3A) for encryption and decryption the message for improving the WiMAX security

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