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A Mathematical Approach to Research Problems of Science and Technology pp 47–55Cite as

Code-Based Public-Key Encryption

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Part of the book series: Mathematics for Industry ((MFI,volume 5))

Abstract

We present a short survey of public-key encryption (PKE) schemes based on hardness of general decoding. Such the schemes are believed to be resistant even against attacks using quantum computers, which makes them candidates for the so-called post-quantum cryptography. First, we briefly introduce the state-of-the-art in the area of code-based PKE. Then, we describe the McEliece PKE, two major attacks against this scheme and the proposed parameters. Finally, we survey recent results on the variants of this PKE which are proven to be indistinguishable under chosen plaintext and chosen ciphertext attacks.

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Notes

  1. 1.

    Note that this collection of references is by no means comprehensive—it only contains some of the representative works on the topics in question.

  2. 2.

    Such the codes are not typically used for public-key encryption, but rather for constructing code-based digital signatures [9].

  3. 3.

    See e.g. [20] for a formal definition of LPN problem—it is similar to G-SD problem except that in the error vector \(e\), each bit has Bernoulli distribution with fixed \(p\), \(0<p<0.5\).

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Authors and Affiliations

  1. Institute of Mathematics for Industry, Kyushu University, 744, Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Kirill Morozov

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  1. Kirill Morozov
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Correspondence to Kirill Morozov .

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Editors and Affiliations

  1. Kyushu University, Fukuoka, Japan

    Ryuei Nishii

  2. Department of Mathematics, Hokkaido University, Sapporo, Japan

    Shin-ichiro Ei

  3. Kyushu University Institute of Mathematics for Industry, Fukuoka, Japan

    Miyuki Koiso

  4. Kyushu University Institute of Mathematics for Industry, Fukuoka, Japan

    Hiroyuki Ochiai

  5. Kyushu University Institute of Mathematics for Industry, Fukuoka, Japan

    Kanzo Okada

  6. Faculty of Arts and Science, Kyushu University, Fukuoka, Japan

    Shingo Saito

  7. Kyushu University Institute of Mathematics for Industry, Fukuoka, Japan

    Tomoyuki Shirai

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Morozov, K. (2014). Code-Based Public-Key Encryption. In: Nishii, R., et al. A Mathematical Approach to Research Problems of Science and Technology. Mathematics for Industry, vol 5. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55060-0_4

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  • DOI: https://doi.org/10.1007/978-4-431-55060-0_4

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