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Reducing the Key Size of McEliece Cryptosystem from Automorphism-induced Goppa Codes via Permutations

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Public-Key Cryptography – PKC 2019 (PKC 2019)

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Abstract

In this paper, we propose a new general construction to reduce the public key size of McEliece cryptosystems constructed from automorphism-induced Goppa codes. In particular, we generalize the ideas of automorphism-induced Goppa codes by considering nontrivial subsets of automorphism groups to construct Goppa codes with a nice block structure. By considering additive and multiplicative automorphism subgroups, we provide explicit constructions to demonstrate our technique. We show that our technique can be applied to automorphism-induced Goppa codes based cryptosystems to further reduce their key sizes.

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Acknowledgements

Chaoping Xing was supported by the National Research Foundation, Prime Minister’s Office, Singapore under its Strategic Capability Research Centres Funding Initiative; and the Singapore MoE Tier 1 grants RG25/16 and RG21/18.

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Correspondence to Zhe Li .

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Li, Z., Xing, C., Yeo, S.L. (2019). Reducing the Key Size of McEliece Cryptosystem from Automorphism-induced Goppa Codes via Permutations. In: Lin, D., Sako, K. (eds) Public-Key Cryptography – PKC 2019. PKC 2019. Lecture Notes in Computer Science(), vol 11443. Springer, Cham. https://doi.org/10.1007/978-3-030-17259-6_20

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  • DOI: https://doi.org/10.1007/978-3-030-17259-6_20

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