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Zaytun: Lattice Based PKE and KEM with Shorter Ciphertext Size

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Selected Areas in Cryptography (SAC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13203))

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Abstract

In this paper, we propose a lattice-based encryption scheme with a short ciphertext size. Our scheme is somewhat hybrid of the NTRU type encryptions and RLWE based encryptions. In particular, the ciphertext of the scheme is a ring element as NTRU type encryptions, yet it can be compressible as RLWE based encryption schemes. Furthermore, we present a key-encapsulation mechanism that is more efficient than a direct construction from our encryption scheme.

The IND-CPA security of the schemes is based on the RLWE assumption and the NTRU assumption. Our parameterizations show that the schemes enjoy almost the same public key size as the NIST PQC finalist lattice-based candidates, yet the ciphertext size is only about \(37\%\) of them.

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Notes

  1. 1.

    Since the encryption style is the same, we treat the module LWE in [5, 14] as the same dimensional RLWE for simplicity.

  2. 2.

    Informally, we say an encryption scheme is one-way secure if it is infeasible to decrypt ciphertexts of random plaintexts.

  3. 3.

    Public key compression in the NTRU type encryption schemes will increases the decryption failure probability, yet it is theoretically feasible.

  4. 4.

    We use the normal form definition of RLWE here, and \(\chi \) should close to discrete gaussian over \(R_q\).

  5. 5.

    For the sake of simplicity, we just use the notation s here, yet letting s= pf +1 for some integer p and small coefficient ring element \(f\in R_q\) results in more efficient decryption.

  6. 6.

    For an integer \(x\in \mathbb {Z}_q\), the notion \(\lceil x\rfloor _t:= \big \lceil \frac{t}{q} x \big \rfloor \), and it applies to the ring elements coefficient-wise.

  7. 7.

    This is the case since the element r is with small coefficients and we have \(\big \lceil \frac{q}{2}\big \rceil \cdot 2r = r \mod q\) for the odd modulus q, and \(\big \lceil \frac{q}{2}\big \rceil \cdot 2r = 0 \mod q\) when q is even number.

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Acknowledgement

We would like to thank the anonymous reviewers of SAC 2021 for their insightful advices. Parhat Abla would like to thank Abduxukur Turgun for his support and fruitfull discussion.

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Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing, China

    Parhat Abla & Mingsheng Wang

  2. School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China

    Parhat Abla

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  1. Parhat Abla
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Correspondence to Parhat Abla .

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Editors and Affiliations

  1. University of Victoria, Victoria, BC, Canada

    Riham AlTawy

  2. Eindhoven University of Technology, Eindhoven, The Netherlands

    Andreas Hülsing

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Abla, P., Wang, M. (2022). Zaytun: Lattice Based PKE and KEM with Shorter Ciphertext Size. In: AlTawy, R., Hülsing, A. (eds) Selected Areas in Cryptography. SAC 2021. Lecture Notes in Computer Science, vol 13203. Springer, Cham. https://doi.org/10.1007/978-3-030-99277-4_19

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  • DOI: https://doi.org/10.1007/978-3-030-99277-4_19

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