• Journal of the Korea Institute of Information Security & Cryptology
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• v.23 no.3
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• pp.561-566
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• 2013

We propose an efficient exponentiation method which is resistant against some side channel attacks in $T_2(p)$, Torus-Based-Cryptosystem. It is more efficient than the general exponentiation method in $T_2(p)$ and is resistant against SPA by using that the difference of squaring and multiplication costs is negligible. Moreover, we can randomize a message in exponentiation step using the characteristic of quotient group which naturally protects against the first DPA.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.6
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• pp.1492-1511
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• 2013

A novel, chaotic map that is based on concatenated torus automorphisms is proposed in this paper. As we know, cat map, which is based on torus automorphism, is highly chaotic and is often used to encrypt information. But cat map is periodic, which decreases the security of the cryptosystem. In this paper, we propose a novel chaotic map that concatenates several torus automorphisms. The concatenated mechanism provides stronger chaos and larger key space for the cryptosystem. It is proven that the period of the concatenated torus automorphisms is the total sum of each one's period. By this means, the period of the novel automorphism is increased extremely. Based on the novel, concatenated torus automorphisms, two application schemes in image encryption are proposed, i.e., 2D and 3D concatenated chaotic maps. In these schemes, both the scrambling matrices and the iteration numbers act as secret keys. Security analysis shows that the proposed, concatenated, chaotic maps have strong chaos and they are very sensitive to the secret keys. By means of concatenating several torus automorphisms, the key space of the proposed cryptosystem can be expanded to $2^{135}$. The diffusion function in the proposed scheme changes the gray values of the transferred pixels, which makes the periodicity of the concatenated torus automorphisms disappeared. Therefore, the proposed cryptosystem has high security and they can resist the brute-force attacks and the differential attacks efficiently. The diffusing speed of the proposed scheme is higher, and the computational complexity is lower, compared with the existing methods.