• Proceedings of the Korean Information Science Society Conference
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• 2003.10a
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• pp.415-417
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• 2003

본 논문에서는 유한 필드 GF(2$^{m}$ ) 상에서 A$B^2$연산을 수행하는 디지트 시리얼(digit-serial) 시스톨릭 구조를 제안하였다. 제안한 구조는 디지트 크기를 적당히 선택했을 때, 비트-패러럴(bit-parallel) 구조에 비해 적은 하드웨어를 사용하고 비트-시리얼(bit-serial) 구조에 비해 빠르다 또한, 제안한 디지트 시리얼 구조에 파이프라인 기법을 적용하면 그렇지 않은 구조에 비해 m=160, L=2 일 때 공간-시간 복잡도가 10.9% 적다.

• Proceedings of the Korean Information Science Society Conference
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• 2000.10a
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• pp.605-607
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• 2000

본 논문에서는 유한 필드 GF(2m)상에서 모듈러 곱셈 A(x)B(x) mod p(x)를 수행하는 2-디지트 시리얼 (2-digit-serial) 시스톨릭 어레이 구조인 곱셈기를 제안하였다. LSB-first 곱셈 알고리즘을 분석한 후 2-디지트 시리얼 형태의 자료의존 그래프(data dependency graph, 이하 DG)를 생성하여 시스톨릭 어레이를 설계하였다. 제안한 구조는 정규적이고 서로 반대 방향으로 진행하는 에지들이 없다. 그래서 VLSI 구현에 적합하다. 제안한 2-디지트 시리얼 곱셈기는 비트-패러럴(bit-parallel) 곱셈기 보다는 적은 하드웨어를 사용하며 비트-시리얼(bit-serial) 곱셈기 보다는 빠르다. 본 논문에서 제안한 2-디지트 시리얼 시스톨릭 곱셈기는 기존의 같은 종류의 곱셈기 보다 처리기의 최대 지연 시간이 적다. 그러므로 전체 시스톨릭 곱셈기의 처리시간을 향상시킬 수 있다.

• 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 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.

• 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 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.6C
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• pp.625-631
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• 2002

This paper presents a MSB-first digit-serial systolic array for computing modular multiplication of A(x)B(x) mod G(x) in finite fields $GF(2^m)$. From the MSB-first multiplication algorithm in $GF(2^m)$, we obtain a new data dependence graph and design an efficient digit-serial systolic multiplier. For circuit synthesis, we obtain VHDL code for multiplier, 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 much more simple structure than existing digit-serial systolic multiplier. Furthermore, since the propose architecture has the features of unidirectional data flow and regularity, it shows good extension characteristics with respect to m and L.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.42 no.8 s.338
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• pp.15-26
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• 2005

In this paper, we propose an efficient $GF(2^m)$ multi-segment multiplier architecture and study its application to elliptic curve cryptography processors. The multi-segment based ECC datapath has a very small combinational multiplier to compute partial products, most of its internal data buses are word-sized, and it has only a single m bit multiplexer and a single m bit register. Hence, the resource requirements of the proposed ECC datapath can be minimized as the segment number increases and word-size is decreased. Hence, as compared to the ECC processor based on digit-serial multiplication, the proposed ECC datapath is more efficient in resource usage. The resource requirement of ECC Processor implementation depends not only on the number of basic hardware components but also on the complexity of interconnection among them. To show the realistic area efficiency of proposed ECC processors, we implemented both the ECC processors based on the proposed multi-segment multiplication and digit serial multiplication and compared their FPGA resource usages. The experimental results show that the Proposed multi-segment multiplication method allows to implement ECC coprocessors, requiring about half of FPGA resources as compared to digit serial multiplication.