• The Journal of the Korea institute of electronic communication sciences
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• v.9 no.4
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• pp.409-416
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• 2014

In H/W implementation for the finite field, the use of normal basis has several advantages, especially the optimal normal basis is the most efficient to H/W implementation in $GF(2^m)$. The finite field $GF(2^m)$ with type I optimal normal basis(ONB) has the disadvantage not applicable to some cryptography since m is even. The finite field $GF(2^m)$ with type II ONB, however, such as $GF(2^{233})$ are applicable to ECDSA recommended by NIST. In this paper, we propose a bit-parallel multiplier over $GF(2^m)$ having a type II ONB, which performs multiplication over $GF(2^m)$ in the extension field $GF(2^{2m})$. The time and area complexity of the proposed multiplier is the same as or partially better than the best known type II ONB bit-parallel multiplier.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.1_2
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• pp.51-58
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• 2004

Most of pubic-key cryptosystems are built on the basis of arithmetic operations defined over the finite field GF$GF(2^m)$ .The other operations of finite fields except addition can be computed by repeated multiplications. Therefore, it is very important to implement the multiplication operation efficiently in public-key cryptosystems. We propose an efficient bit-parallel normal basis multiplier for$GF(2^m)$ fields defined by All-One Polynomials. The gate count and time complexities of our proposed multiplier are lower than or equal to those of the previously proposed multipliers of the same class. Also, since the architecture of our multiplier is regular, it is suitable for VLSI implementation.

• The Transactions of the Korea Information Processing Society
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• v.2 no.6
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• pp.969-973
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• 1995

In this paper, a new parallel Multiplier array is proposed to reduce the multiplication time by modifying CAS(carry select adder) cell structure used in the conventional parallel multiplier array. It is named MCSA(modified CSA) that assignes the addend and augend to the inputs of CSA faster than Ci(carry input). Also the designed DCSA (doubled inverted input CSA) is appended after the last product term for the carry propagation adder. The proposed scheme is designed with MCSA and DCSA, and simulated. It is verified that the circuit size is increased about 13% compared with the conventional multiplier array with CSA cell but the operation time is reduced about 52%.

• Proceedings of the IEEK Conference
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• 2000.06b
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• pp.141-144
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• 2000

In this paper, a new parallel array structure for the asynchronous array multiplier is introduced. This structure is designed for a data dependent asynchronous multiplier to reduces power which is wasted in conventional array structure. Simulation shows that this structure saves 30％ of power and 55％ of computation time comparing to conventional booth encoded array multiplier.

• Journal of the Korea Society of Computer and Information
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• v.20 no.2
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• pp.1-10
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• 2015

In this paper, we propose a new multiplication algorithm for primitive polynomial with all 1 of coefficient in case that m is odd and even on finite fields $GF(3^m)$, and design the multiplier with parallel input-output module structure using the presented multiplication algorithm. The proposed multiplier is designed $(m+1)^2$ same basic cells. Since the basic cells have no a latch circuit, the multiplicative circuit is very simple and is short the delay time $T_A+T_X$ per cell unit. The proposed multiplier is easy to extend the circuit with large m having regularity and modularity by cell array, and is suitable to the implementation of VLSI circuit.

• 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%.

• Journal of IKEEE
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• v.8 no.2 s.15
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• pp.172-180
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• 2004

In this paper, a parallel Input/Output modulo multiplier, which is applied to AOTP(All One or Two Polynomials) multiplicative algorithm over $GF(3^m)$, has been proposed using neuron-MOS Down-literal circuit on voltage mode. The three-valued input of the proposed multiplier is modulated by using neuron-MOS Down-literal circuit and the multiplication and Addition gates are implemented by the selecting of the three-valued input signals transformed by the module. The proposed circuits are simulated with the electrical parameter of a standard $0.35{\mu}m$CMOS N-well doubly-poly four-metal technology and a single +3V supply voltage. In the simulation result, the multiplier shows 4 uW power consumption and 3 MHzsampling rate and maintains output voltage level in ${\pm}0.1V$.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.15 no.3
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• pp.510-520
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• 2011

In this paper, we propose a new multiplication algorithm for primitive polynomial with all 1 of coefficient in case that m is odd and even on finite fields $GF(3^m)$, and compose the multiplier with parallel input-output module structure using the presented multiplication algorithm. The proposed multiplier is designed $(m+1)^2$ same basic cells that have a mod(3) addition gate and a mod(3) multiplication gate. Since the basic cells have no a latch circuit, the multiplicative circuit is very simple and is short the delay time $T_A+T_X$ per cell unit. The proposed multiplier is easy to extend the circuit with large m having regularity and modularity by cell array, and is suitable to the implementation of VLSI circuit.

• Journal of the Korea Society of Computer and Information
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• v.18 no.2
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• pp.9-17
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• 2013

In this paper, we propose a new multiplication algorithm for two polynomials using primitive polynomial with all 1 of coefficient on finite fields GF($2^m$), and design the multiplier with high-speed parallel input-output module structure using the presented multiplication algorithm. The proposed multiplier is designed $m^2$ same basic cells that have a 2-input XOR gate and a 2-input AND gate. Since the basic cell have no a latch circuit, the multiplicative circuit is very simple and is short the delay time $D_A+D_X$ per cell unit. The proposed multiplier is easy to extend the circuit with large m having regularity and modularity by cell array, and is suitable to the implementation of VLSI circuit.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.39 no.2
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• pp.123-131
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• 2002

In this paper, a new standard basis parallel ternary-valued multiplier circuit designed using current mode CMOS is presented. Prior to constructing the GF(3$^{ｍ}$) multiplier circuit, we provide a GF(3) adder and a GF(3) multiplier with truth tables and symbolize them, and also design them using current mode CMOS circuit. Using the basic ternary operation concept, a ternary adder and a multiplier, we develop the equations to multiply arbitrary two elements over GF(3$^{ｍ}$). Following these equations, we can design a multiplier generalized to GF(3$^{ｍ}$). For the proposed circuit in this paper, we show the example in GF(3$^{3}$). In this paper, we assemble the operation blocks into a complete GF(3$^{ｍ}$) multiplier. Therefore the proposed circuit is easy to generalize for m and advantageous for VLSI. Also, it need no memory element and the latency not less fewer than other circuit. We verify the proposed circuit by functional simulation and show its result.