• Journal of the Korea Institute of Information and Communication Engineering
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• v.12 no.7
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• pp.1209-1217
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• 2008

In this paper, we present a new bit-parallel multiplier for performing the bit-parallel multiplication of two polynomials in the finite fields $GF(2^m)$. Prior to construct the multiplier circuits, we consist of the vector code generator(VCG) to generate the result of bit-parallel multiplication with one coefficient of a multiplicative polynomial after performing the parallel multiplication of a multiplicand polynomial with a irreducible polynomial. The basic cells of VCG have two AND gates and two XOR gates. Using these VCG, we can obtain the multiplication results performing the bit-parallel multiplication of two polynomials. Extending this process, we show the design of the generalized circuits for degree m and a simple example of constructing the multiplier circuit over finite fields $GF(2^4)$. Also, the presented multiplier is simulated by PSpice. The multiplier presented in this paper use the VCGs with the basic cells repeatedly, and is easy to extend the multiplication of two polynomials in the finite fields with very large degree m, and is suitable to VLSI.

• Journal of the Korea Society of Computer and Information
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• v.28 no.2
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• pp.69-75
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• 2023

Finite field arithmetic operations play an important role in a variety of applications, including modern cryptography and error correction codes. In this paper, we propose an efficient multiplication algorithm over finite fields using the Montgomery multiplication algorithm. Existing multipliers can be implemented using AND and XOR gates, but in order to reduce time and space complexity, we propose an algorithm using NAND and NOR gates. Also, based on the proposed algorithm, an efficient semi-systolic finite field multiplier with low space and low latency is proposed. The proposed multiplier has a lower area-time complexity than the existing multipliers. Compared to existing structures, the proposed multiplier over finite fields reduces space-time complexity by about 71%, 66%, and 33% compared to the multipliers of Chiou et al., Huang et al., and Kim-Jeon. As a result, our multiplier is proper for VLSI and can be successfully implemented as an essential module for various applications.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.46 no.11
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• pp.8-15
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• 2009

Side-channel attacks including the differential power analysis attack are often more powerful than classical cryptanalysis and have to be seriously considered by cryptographic algorithm's implementers. Various countermeasures have been proposed against such attacks. In this paper, we deal with the masking method, which is known to be a very effective countermeasure against the differential power analysis attack and propose new gate-level conversion methods between Boolean and arithmetic masks. The new methods require only 6n-5 XOR and 2n-2 AND gates with 3n-2 gate delay for converting n-bit masks. The basic idea of the proposed methods is that the carry and the sum bits in the ripple adder are manipulated in a way that the adversary cannot detect the relation between these bits and the original raw data. Since the proposed methods use only bitwise operations, they are especially useful for DPA-securely implementing cryptographic algorithms in hardware which use both Boolean and arithmetic operations. For example, we applied them to securely implement the block encryption algorithm SEED in hardware and present its detailed implementation result.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.45 no.12
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• pp.29-40
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• 2008

The efficient hardware design of finite field multiplication is an very important research topic for and efficient $f(x)=x^n+x^k+1$ implementation of cryptosystem based on arithmetic in finite field GF($2^n$). We used special generating trinomial to construct a bit-parallel multiplier over finite field with low space complexity. To reduce processing time, The hardware architecture of proposed multiplier is similar with existing Mastrovito multiplier. The complexity of proposed multiplier is depend on the degree of intermediate term $x^k$ and the space complexity of the new multiplier is $2k^2-2k+1$ lower than existing multiplier's. The time complexity of the proposed multiplier is equal to that of existing multiplier or increased to $1T_X(10%{\sim}12.5%$) but space complexity is reduced to maximum 25%.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.34 no.7C
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• pp.663-670
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• 2009

In this paper, we propose the image encryption method which gradually uses NFSR(Non-linear Feedback Shift Register) and 20 CAT(Two-Dimensional Cellular Automata Transform). The encryption method is processed in the following order. First, NFSR is used to create a PN(pseudo noise) sequence, which matches the size of the original image. Then, the created sequence goes through a XOR operation with the original image and process the encipherment. Next, the gateway value is set to produce a 20 CAT basis function. The produced basis function is multiplied by encryption image that has been converted to process the 20 CAT encipherment. Lastly, the results of the experiment which are key space analysis, entropy analysis, and sensitivity analysis verify that the proposed method is efficient and very secure.

• Journal of Korea Society of Industrial Information Systems
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• v.10 no.3
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• pp.57-63
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• 2005

Kim and Fenn et al. proposed two modular AB multipliers based on LFSR(Linear Feedback Shift Register) architecture. These multipliers use AOP, which has all coefficients with '1', as an irreducible polynomial. Thereby, they have good hardware complexity compared to the previous architectures. This paper proposes a modular $AB^2$ multiplier based on LFSR architecture and a modular exponentiation architecture to improve the hardware complexity of the Kim's. Our multiplier also use the AOP as an irreducible polynomial as the Kim architecture. Simulation result shows that our multiplier reduces the hardware complexity about $50\%$ in the perspective of XOR and AND gates compared to the Kim's. The architecture could be used as a basic block to implement public-key cryptosystems.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.35C no.6
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• pp.1-8
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• 1998

In this paper, we designed a low power 8bit ELM adder with static CMOS and hybrid logic styles on a chip. The designed 8bit ELM adder with both logic styles was fabricated in a 0.8$\mu\textrm{m}$ single-poly double-metal, LG CMOS process and tested. Hybrid logic style consists of CCPL(Combinative Complementary Pass-transistor Logic), Wang's XOR gate and static CMOS for critical path which determines the speed of ELM adder. As a result of chip test, the ELM adder with hybrid logic style is superior to the one with static CMOS by 9.29% in power consumption, 14.9% in delay time and 22.8% in PDP(Power Delay Product) at 5.0V supply voltage, respectively.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.13 no.6
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• pp.1150-1156
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• 2009

In this paper, we propose the gradual encryption method of image using LFSR(Linear Feedback Shift Register) and 2D CAT(Two-Dimensional Cellular Automata Transform). First, an LFSR is used to create a PN(pseudo noise) sequence, which is identical to the size of the original image. Then the created sequence goes through an XOR operation with the original image resulting to the first encrypted image. Next, the gateway value is set to produce a 2D CAT basis function.The created basis function multiplied with the first encrypted image produces the 2D CAT encrypted image which is the final output. Lastly, the stability analysis verifies that the proposed method holds a high encryption quality status.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2012.10a
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• pp.263-266
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• 2012

This paper describes an efficient hardware implementation of Whirlpool hash function as ISO/IEC 10118-3 standard. Optimized timing is achieved by using pipelined small LUTs, and Whirlpool block cipher and key schedule have been implemented in parallel for improving throughput. In key schedule, key addition is area-optimized by using inverters and muxes instead of using rom and xor gates. This hardware has been implemented on Virtex5-XC5VSX50T FPGA device. Its maximum operating frequency is about 151MHz, and throughput is about 950Mbps.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2009.05a
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• pp.164-167
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• 2009

In this paper, we propose the image encryption using LFSR(Linear Feedback Shift Register) and 2D CAT(Two-Dimensional Cellular Automata Transform). First, a LFSR is used to create a PN(pseudo noise) sequence, which is identical to the size of the original image. Then, the created sequence goes through a XOR operation with the original image to convert the original image. Next, the gateway value is set to produce a 2D CAT basis function. Using the created basis function, multiplication is done with the converted original image to process 2D CAT image encipherment. Lastly, the stability analysis verifies that the proposed method holds a high encryption quality status.