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DME: A Full Encryption, Signature and KEM Multivariate Public Key Cryptosystem

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Post-Quantum Cryptography (PQCrypto 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14154))

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Abstract

Multivariate public key cryptography is one of the most studied techniques used in post-quantum cryptography [21, 24, 28]. In [22] we introduced a new multivariate scheme DME that is based in the composition of linear and non linear maps as many other multivariate schemes, the main difference with other schemes is that the nonlinear components have very high degree and it can be used for KEM and signature. In this paper we present a new version of DME [23] that is simpler than the original in the sense that it uses only two fields \(\mathbb {F}_q\) and \(\mathbb {F}_{q^2}\) instead of three. The new design allows us to increase the number of exponentials to 3, 4 or more and it gives more resistance to decomposition attacks [18, 35] while keeping a moderate number of monomials in the public key. With this setup the composition of exponentials and linear maps gives a deterministic trapdoor one way permutation which can be used for KEM and signature when combined with the standard padding OAEP and PSS [2, 3] whose security is well understood.

In the paper we describe the setup of the scheme, the most important part of it is the Configuration Matrices (\(\mathcal{C}\mathcal{M}\)) and the algorithm for the reduction of monomials. We give a preliminary security analysis of the resistance against Gröbner basis, Weil descent and structural attacks but more research on the security of DME is needed. We describe also the \(\mathcal{C}\mathcal{M}\) that we have implemented with three and four rounds, 8 variables and \(q=2^{64}\). We provide the SUPERCOP timings of DME-OAEP and DME-PSS00 for them and a comparison with NIST finalists. For NIST security level 5 the size of our ciphertext and signature is only 64 bytes.

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Authors and Affiliations

  1. Department of Algebra, Geometry and Topology, Faculty of Mathematics, Universidad Complutense de Madrid, Madrid, Spain

    Ignacio Luengo, Martín Avendaño & Pilar Coscojuela

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  1. Ignacio Luengo
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  2. Martín Avendaño
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  3. Pilar Coscojuela
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Correspondence to Ignacio Luengo .

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Editors and Affiliations

  1. Lund University, Lund, Sweden

    Thomas Johansson

  2. National Institute of Standards and Technology, Gaithersburg, MD, USA

    Daniel Smith-Tone

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Luengo, I., Avendaño, M., Coscojuela, P. (2023). DME: A Full Encryption, Signature and KEM Multivariate Public Key Cryptosystem. In: Johansson, T., Smith-Tone, D. (eds) Post-Quantum Cryptography. PQCrypto 2023. Lecture Notes in Computer Science, vol 14154. Springer, Cham. https://doi.org/10.1007/978-3-031-40003-2_14

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  • DOI: https://doi.org/10.1007/978-3-031-40003-2_14

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