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On IND-CCA1 Security of Randomized McEliece Encryption in the Standard Model

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Code-Based Cryptography (CBC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11666))

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Abstract

We show that a modification of Nojima et al.’s Randomized McEliece Encryption (RME), where receiver verifies the correctness of the decrypted plaintext, achieves IND-CCA1 security in the standard model. We rely on the two (standard) assumptions used also for RME: hardness of general decoding and Goppa code indistinguishability (sometimes they are jointly referred to as “the McEliece assumptions”), plus an extra assumption on non-falsifiability of the McEliece ciphertexts. The later one implies that an adversary is unable to sample a McEliece ciphertext for which the message and error vector are unknown. This assumption is non-standard, however it represents a win-win argument, in the sense that breaking it would imply efficient sampling of McEliece ciphertexts, which in turn may potentially lead us to a Full Domain Hash code-based signature based on the McEliece PKE—without rejection sampling as in the Courtois-Finiasz-Sendrier signature from Asiacrypt 2001—a long-standing open problem in code-based cryptography.

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Notes

  1. 1.

    In the context of commitments, this follows from a perfect binding of the commitment scheme based on the McEliece PKE [22].

  2. 2.

    Such the codes are not typically used for public-key encryption, but rather for constructing code-based digital signatures [5].

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Acknowledgements

We would like to thank the anonymous reviewers for their helpful comments.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University of North Texas, Denton, TX, 76207, USA

    Franz Aguirre Farro & Kirill Morozov

Authors
  1. Franz Aguirre Farro
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  2. Kirill Morozov
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Correspondence to Franz Aguirre Farro .

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Editors and Affiliations

  1. Marche Polytechnic University, Ancona, Italy

    Marco Baldi

  2. Florida Atlantic University, Boca Raton, FL, USA

    Edoardo Persichetti

  3. Marche Polytechnic University, Ancona, Italy

    Paolo Santini

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Aguirre Farro, F., Morozov, K. (2019). On IND-CCA1 Security of Randomized McEliece Encryption in the Standard Model. In: Baldi, M., Persichetti, E., Santini, P. (eds) Code-Based Cryptography. CBC 2019. Lecture Notes in Computer Science(), vol 11666. Springer, Cham. https://doi.org/10.1007/978-3-030-25922-8_8

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  • DOI: https://doi.org/10.1007/978-3-030-25922-8_8

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