Geodesic
Efficient Implementation for QUAD Stream Cipher with GPUs
Computer Science and Information Systems, Tome 10 (2013) no. 2.

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QUAD stream cipher uses multivariate polynomial systems. It has provable security based on the computational hardness assumption. More specifically, the security of QUAD depends on hardness of solving non-linear multivariate systems over a finite field, and it is known as an NP-complete problem. However, QUAD is slower than other stream ciphers, and an efficient implementation, which has a reduced computational cost, is required. In this paper, we propose an efficient implementation of computing multivariate polynomial systems for multivariate cryptography on GPU and evaluate efficiency of the proposal. GPU is considered to be a commodity parallel arithmetic unit. Moreover, we give an evaluation of our proposal. Our proposal parallelizes an algorithm of multivariate cryptography, and makes it efficient by optimizing the algorithm with GPU.
Keywords: stream cipher, efficient implementation, Multivariate Cryptography, GPGPU 
@article{CSIS_2013_10_2_a18,
     author = {Satoshi Tanaka and Takashi Nishide and Kouichi Sakurai},
     title = {Efficient {Implementation} for {QUAD} {Stream} {Cipher} with {GPUs}},
     journal = {Computer Science and Information Systems},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2013},
     url = {http://geodesic.mathdoc.fr/item/CSIS_2013_10_2_a18/}
}
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Satoshi Tanaka; Takashi Nishide; Kouichi Sakurai. Efficient Implementation for QUAD Stream Cipher with GPUs. Computer Science and Information Systems, Tome 10 (2013) no. 2. http://geodesic.mathdoc.fr/item/CSIS_2013_10_2_a18/