• Journal of KIISE:Computer Systems and Theory
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• v.32 no.4
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• pp.160-167
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• 2005

Among finite filed arithmetic operations, division/inverse is known as a basic operation for public-key cryptosystems over $GF(2^{m})$ and it is computed by performing the repetitive $AB^{2}$ multiplication. This paper presents a digit-serial-in-serial-out systolic architecture for performing the $AB^2$ operation in GF$(2^{m})$. To obtain L×L digit-serial-in-serial-out architecture, new $AB^{2}$ algorithm is proposed and partitioning, index transformation and merging the cell of the architecture, which is derived from the algorithm, are proposed. Based on the area-time product, when the digit-size of digit-serial architecture, L, is selected to be less than about m, the proposed digit-serial architecture is efficient than bit-parallel architecture, and L is selected to be less than about $(1/5)log_{2}(m+1)$, the proposed is efficient than bit-serial. In addition, the area-time product complexity of pipelined digit-serial $AB^{2}$ systolic architecture is approximately $10.9\%$ lower than that of nonpipelined one, when it is assumed that m=160 and L=8. Additionally, since the proposed architecture can be utilized for the basic architecture of crypto-processor and it is well suited to VLSI implementation because of its simplicity, regularity and pipelinability.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.4C
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• pp.337-342
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• 2010

In this paper, a new architecture for digit-parallel/bit-serial GF($2^m$) multiplier with low complexity is proposed. The proposed multiplier operates in polynomial basis of GF($2^m$) and produces multiplication results at a rate of one per D clock cycles, where D is the selected digit size. The digit-parallel/bit-serial multiplier is faster than bit-serial ones but with lower area complexity than bit-parallel ones. The most significant feature of the digit-parallel/bit-serial architecture is that a trade-off between hardware complexity and delay time can be achieved. But the traditional digit-parallel/bit-serial multiplier needs extra hardware for high speed. In this paper a new low complexity efficient digit-parallel/bit-serial multiplier is presented.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.11 no.2
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• pp.37-44
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• 2001

In this paper, an efficient architecture for the ECC multiplier in GF(2") is proposed. We give a design example for the irreducible trinomials $x_{193}\;+\;x_{15}\;+\;1$. In hardware implementations, it is often desirable to use the irreducible trinomial equations. A digit-serial multiplier with a digit size of 32 is proposed, which has more advantages than the 193bit serial LFSR architecture. The proposed multiplier is verified with a VHDL description using an elliptic curve addition. The elliptic curve used in this implementation is defined by Weierstrass equations. The measured results show that the proposed multiplier it 0.3 times smaller than the bit-serial LFSR multiplier.lier.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.1
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• pp.157-165
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• 2013

In this paper, efficient digit-serial VLSI architecture for 1D (9,7) lifting-based discrete wavelet transform (DWT) filter has been proposed. The proposed architecture computes the DWT in digit basis, so that the required hardware is reduced. Also, the multiplication is replaced with the shift and add operation to minimize the hardware requirement. Bit allocation for input, output, and the internal data has been determined by analyzing the PSNR. We have carefully designed the data feedback latency not to degrade the performance in the recursive folded scheduling. The proposed digit-serial architecture requires small amount of hardware but achieve 100% of hardware utilization, so we try to optimize the tradeoffs between the hardware cost and the performance. The proposed architecture has been designed and verified by VerilogHDL and synthesized by Synopsys Design Compiler with a DongbuHitek $0.18{\mu}m$ STD cell library. The maximum operating frequency is 330MHz with 3,770 gates in equivalent two input NAND gates.

• The KIPS Transactions:PartA
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• v.15A no.3
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• pp.161-166
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• 2008

In this paper, an efficient digit-serial systolic array is proposed for multiplication in finite field GF($2^m$) using the polynomial basis representation. The proposed systolic array is based on the most significant digit first (MSD-first) multiplication algorithm and produces multiplication results at a rate of one every "m/D" clock cycles, where D is the selected digit size. Since the inner structure of the proposed multiplier is tree-type, critical path increases logarithmically proportional to D. Therefore, the computation delay of the proposed architecture is significantly less than previously proposed digit-serial systolic multipliers whose critical path increases proportional to D. Furthermore, since the new architecture has the features of a high regularity, modularity, and unidirectional data flow, it is well suited to VLSI implementation.

• Proceedings of the IEEK Conference
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• 2001.06b
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• pp.337-340
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• 2001

In this Paper, 3 digit-Serial multilier With 3 digit size of 32 is proposed, which has more advantages than the 193bit serial LFSR architecture. We give a design example for the irreducible trinomials $x^{193}$＋ $x^{15＋1}$. In hardware implementations, it is often desirable to use the irreducible trinomial equations. The proposed multiplier is verified with a VHDL description using an elliptic curve addition. The measured results show that the proposed multiplier is 0.3 times smaller than the bit-serial LFSR multiplier..

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.45 no.10
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• pp.23-30
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• 2008

Recently, a considerable number of studies have been conducted on pairing based cryptosystems. The efficiency of pairing based cryptosystems depends on finite fields, similar to existing public key cryptosystems. In general, pairing based ctyptosystems are defined over finite fields of chracteristic three, GF($3^m$), based on trinomials. A multiplication in GF($3^m$) is the most dominant operation. This paper proposes a new most significant digit(MSD)-first digit- serial multiplier. The proposed MSD-first digit-serial multiplier has the same area complexity compared to previous multipliers, since the modular reduction step is performed in parallel. And the critical path delay is reduced from 1MUL+(log ${\lceil}n{\rceil}$+1)ADD to 1MUL+(log ${\lceil}n+1{\rceil}$)ADD. Therefore, when the digit size is not $2^k$, the time delay is reduced by one addition.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.11C
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• pp.892-897
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• 2008

In this paper, a new architecture for digit-parallel/bit-serial GF$(2^m)$ multiplier with low latency is proposed. The proposed multiplier operates in polynomial basis of GF$(2^m)$ and produces multiplication results at a rate of one per D clock cycles, where D is the selected digit size. The digit-parallel/bit-serial multiplier is faster than bit-serial ones but with lower area complexity than bit-parallel ones. The most significant feature of the proposed architecture is that a trade-off between hardware complexity and delay time can be achieved.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.4C
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• pp.342-349
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• 2008

This paper presents a new digit-serial systolic multiplier over $CF(2^m)$ for cryptographic applications. When input data come in continuously, the proposed array produces multiplication results at a rate of one every ${\lceil}m/D{\rceil}$ clock cycles, where D is the selected digit size. Since the inner structure of the proposed array is tree-type, critical path increases logarithmically proportional to D. Therefore, the computation delay of the proposed architecture is significantly less than previously proposed digit-serial systolic multipliers whose critical path increases proportional to D. Furthermore, since the new architecture has the features of regularity, modularity, and unidirectional data flow, it is well suited to VLSI implementations.

• The KIPS Transactions:PartA
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• v.9A no.3
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• pp.281-286
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• 2002

In this paper we, implement LSB-first digit-serial systolic multiplier for computing modular multiplication $A({\times})B$mod G ({\times})in finite fields GF $(2^m)$. If input data come in continuously, the implemented multiplier can produce multiplication results at a rate of one every [m/L] clock cycles, where L is the selected digit size. The analysis results show that the proposed architecture leads to a reduction of computational delay time and it has more simple structure than existing digit-serial systolic multiplier. Furthermore, since the propose architecture has the features of regularity, modularity, and unidirectional data flow, it shows good extension characteristics with respect to m and L.