Efficient Implementation of Karatsuba Algorithm Based Three-Operand Multiplication Over Binary Extension Field

Three-operation multiplication (TOM) over binary extension field is frequently encountered in cryptosystems such as elliptic curve cryptography. Though digit-serial polynomial basis multipliers are usually preferred for the realization of TOM due to their efficient tradeoff in implementation complex...

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Vydáno v:IEEE access Ročník 6; s. 38234 - 38242
Hlavní autoři: Lee, Chiou-Yng, Fan, Chia-Chen, Xie, Jiafeng, Yuan, Shyan-Ming
Médium: Journal Article
Jazyk:angličtina
Vydáno: Piscataway IEEE 01.01.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithms
Complexity
Complexity theory
Computer architecture
Computer systems
Cryptography
Curves
Delays
Digit-level serial-in parallel-out (DL-SIPO) multiplier
Elliptic curve cryptography
Karatsuba-algorithm (KA) decomposition
Logic gates
low-complexity
Multiplication
Polynomials
Pulse width modulation
three-operand multiplication (TOM)
ISSN:2169-3536, 2169-3536
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Shrnutí:Three-operation multiplication (TOM) over binary extension field is frequently encountered in cryptosystems such as elliptic curve cryptography. Though digit-serial polynomial basis multipliers are usually preferred for the realization of TOM due to their efficient tradeoff in implementation complexity, the Karatsuba algorithm (KA)-based strategy is rarely employed to reduce the complexity further. Based on this reason, in this paper, we derive a novel low-complexity implementation of TOM based on a new KA-based digit-serial multiplier. The proposed TOM is obtained through two novel coherent interdependent efforts: 1) mapping an efficient KA-based algorithm into a novel digit-serial multiplier and 2) obtaining a new TOM structure through the novel derivation of the TOM algorithm. From the estimated results, it is shown that the proposed structure has significant lower area-time-complexities when compared with the existing competing TOMs. The proposed TOM is highly regular with low-complexity, and hence can be employed in many cryptographic applications.
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ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2018.2851662