Fast Three-Input Multipliers over Small Composite Fields for Multivariate Public Key Cryptography

Yi, Haibo; Li, Weijian

doi:10.14257/ijsia.2015.9.9.15

IJSIA

2015

DOI: 10.14257/ijsia.2015.9.9.15

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Fast Three-Input Multipliers over Small Composite Fields for Multivariate Public Key Cryptography

Haibo Yi¹,

Weijian Li²

Abstract: Since quantum computer attacks will be threats to the current public key cryptographic systems

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Cited by 3 publications

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References 17 publications

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“…Finite field operations have gained increasing importance due to the fact that they are fundamental operations frequently encountered in areas of mathematic [1,5,23,26,27,29,[36][37][38] and engineering [4,7,16,28]. Generally, operations are computed via using a specific basis [2,3,6,9,10,13,[19][20][21][22]25,32,34,35], i.e. polynomial basis, normal basis, triangular basis, dual basis and other bases.…”

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confidence: 99%

Efficient systolic multiplications in composite fields for cryptographic systems

Yi¹

2019

Discrete &Amp; Continuous Dynamical Systems - S

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Multiplications in finite fields are playing a key role in areas of cryptography and mathematic. We present approaches to exploit systolic architecture for multiplications in composite fields, which are expected to reduce the time-area product substantially. We design a pipelined architecture for multiplications in composite fields GF ((2 n) 2), where n is a positive integer. Besides, we design systolic architectures for multiplications and additions in finite fields GF (2 n). By integrating main improvements and other minor optimizations for multiplications in GF ((2 n) 2), the non-pipelined versions of our design takes 8n + 4 AND gates and 8n XOR gates to compute multiplications with the executing time of nT AN D + 4nT XOR , where T AN D and T XOR are delays of AND and XOR gates respectively; with the aid of pipelining, the pipelined version of our design has a throughput rate of one result per 2nT XOR. Other words, the time complexity and area complexity of our design are O(n). Thus, the complexity of time-area product of our design is O(n 2). Experimental results and comparisons show that our design provides significant reductions in executing time and area of multiplications. 2010 Mathematics Subject Classification. 12Y05.

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Efficient systolic multiplications in composite fields for cryptographic systems

Yi¹

2019

Discrete &Amp; Continuous Dynamical Systems - S

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Towards Wearability in Cryptographic Systems: A Novel Architecture Based on Rainbow Scheme for Wearable Devices

2017

Wireless Pers Commun

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Parallel Finite Field Algorithms for Communications and Sensor Networks

2023

ACM Trans. Sen. Netw.

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Sensor network integrates sensor technology, embedded computing technology, modern network and wireless communication technology, distributed information processing technology, etc. It can monitor, perceive and collect the information of various environments or monitoring objects in real time through various integrated micro sensors, and process the information through the embedded system. The perceived information is transmitted to the user terminal by multi-hop relay through the random ad-hoc wireless communication network. The coding of communications and sensor networks affects the efficiency of communication. The main coding technology is based on finite field. Among operations in finite fields, divisions are time-consuming operations since they are generally computed via inversions and multiplications. We present techniques to exploit extend binary trees for fast divisions in finite fields. We implement the finite field algorithm on Field Programmable Logic Arrays (FPGAs) in a parallel way. The implementation result from FPGAs shows that the parallel finite field algorithm can speed up the process of coding of communications and sensor networks.

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Fast Three-Input Multipliers over Small Composite Fields for Multivariate Public Key Cryptography

Abstract: Since quantum computer attacks will be threats to the current public key cryptographic systems

Cited by 3 publications

References 17 publications

Efficient systolic multiplications in composite fields for cryptographic systems

Efficient systolic multiplications in composite fields for cryptographic systems

Towards Wearability in Cryptographic Systems: A Novel Architecture Based on Rainbow Scheme for Wearable Devices

Parallel Finite Field Algorithms for Communications and Sensor Networks

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