Systolic Multipliers for Finite Fields GF(2m)

Yeh,; Reed,; Truong,

doi:10.1109/tc.1984.1676441

Cited by 174 publications

(78 citation statements)

References 7 publications

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“…As a result, efficient multipliers are important from a system performance point of view. Although several multipliers have been developed with a polynomial basis of GFð2 m Þ, their high space and time complexities are major limitations in cryptographic applications [1,2,3,4]. Thus, further research on efficient multiplication architectures with low space and time complexities is required.…”

Section: Introductionmentioning

confidence: 99%

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Efficient systolic modular multiplier/squarer for fast exponentiation over GF(2m)

Choi

Lee

2015

IEICE Electron. Express

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Using the concept of common components, this letter shows that field multiplication and squaring over GF(2 m ) can be efficiently combined, with little hardware overhead. The analysis results show that about 39.23% area-time (AT) complexity is improved when we employ the combined systolic multiplier/squarer instead of implementing the multiplier and the squarer separately in the least significant bit (LSB)-first exponentiation. The proposed architecture features regularity, unidirectional data flow, and local interconnection, and thus is well suited to VLSI implementation.

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Section: Introductionmentioning

confidence: 99%

“…One implementation is LSB-first multiplication based on (1), the other is most significant bit (MSB)-first multiplication based on (2). In this letter, we construct a low complexity systolic multiplier/squarer using the LSB first scheme.…”

Section: Introductionmentioning

confidence: 99%

Efficient systolic modular multiplier/squarer for fast exponentiation over GF(2m)

Choi

Lee

2015

IEICE Electron. Express

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“…Examples of the algorithms used to implement multipliers include the LSB-first multiplication algorithm [5], MSB-first multiplication algorithm [6], and Montgomery algorithm [7]. Previous research and development on modular multiplication is as follows: First, for a one-dimensional systolic array, in the case of an LSB-first algorithm, the modular multiplication is performed within 3m clock cycles using m cells [5]. While in the case of an MSB-first algorithm, the modular multiplication can be performed within 3m clock cycles using m cells [6].…”

Section: Introductionmentioning

confidence: 99%

“…With an LFSR structure, the modular multiplication can be performed within 2m clock cycles using m cells [10], the modular multiplication can be performed within m clock cycles using m cells and the modular squaring can be performed within m clock cycles using m cells [11]. The structures proposed in [5,6,10,12] are simple modular multipliers.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the properties of LSB-first multiplication, the parts of modular multiplication and squaring that can be performed in common are identified, then the remainder is processed in parallel. As a result, the multiplication and squaring can be performed much more efficiently as regards time and space compared to repeating the structure as proposed in [5,6,10] and can be performed much more efficiently as regards space compared to repeating the structure as proposed in [11,14]. Furthermore, the performance of the exponentiation is much more efficient than that of the [16] as regards time and space.…”

Section: Introductionmentioning

confidence: 99%

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Fast Exponentiaion over GF(2m) Based on Cellular Automata

Yoo

2003

Lecture Notes in Computer Science

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Abstract. In this paper, we present a new exponentiation architecture and multiplier/squarer which are the basic operations for exponentiation on GF(2 m ). The proposed multiplier/squarer is used as kernal architecture of exponentiation and processes the modular multiplication and squaring at the same time for effective exponentiation on GF(2 m ) using a cellular automata. Proposed architecture can be used efficiently for the design of the modular exponentiation on the finite field in most public key crypto systems such as Diffie-Hellman key exchange, ElGamal, etc. Also, the cellular automata architecture is simple, regular, modular, cascadable and therefore, can be utilized efficiently for the implementation of VLSI.

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Parallel Computers

2011

Algorithms and Parallel Computing

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Systolic Multipliers for Finite Fields GF(2^m)

Cited by 174 publications

References 7 publications

Efficient systolic modular multiplier/squarer for fast exponentiation over <i>GF</i>(2<i><sup>m</sup></i>)

Efficient systolic modular multiplier/squarer for fast exponentiation over <i>GF</i>(2<i><sup>m</sup></i>)

Fast Exponentiaion over GF(2m) Based on Cellular Automata

Parallel Computers

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