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Cloud Computing via Homomorphic Encryption and Multilinear Maps

Periodic Reporting for period 3 - CLOUDMAP (Cloud Computing via Homomorphic Encryption and Multilinear Maps)

Reporting period: 2021-10-01 to 2023-03-31

The past thirty years have seen cryptography move from arcane to commonplace: Internet, mobile phones, banking system, etc. Homomorphic cryptography now offers the tantalizing goal of being able to process sensitive information in encrypted form, without needing to compromise on the privacy and security of the citizens and organizations that provide the input data. More recently, cryptographic multilinear maps have revolutionized cryptography with the emergence of indistinguishability obfuscation (iO), which in theory can been used to realize numerous advanced cryptographic functionalities that previously seemed beyond reach. However the security of multilinear maps is still poorly understood, and many iO schemes have been broken; moreover all constructions of iO are currently unpractical.

The goal of the CLOUDMAP project is to make the new advanced cryptographic tasks usable in practice, so that citizens do not have to compromise on the privacy and security of their input data. This goal can only be achieved by considering the mathematical foundations of these primitives, working “from first principles”, rather than focusing on premature optimizations. To achieve this goal, our first objective will be to better understand the security of the underlying primitives of multilinear maps and iO schemes. Our second objective will be to develop new approaches to significantly improve their efficiency. Our third objective will be to build applications of multilinear maps and iO that can be implemented in practice, and also the efficient implementation of lattice-based schemes.
We have published the following papers, which have appeared at the top conferences in our field (CRYPTO, EUROCRYPT, ASIACRYPT and TCHES)

1) Jean-Sébastien Coron, Hilder V. L. Pereira. On Kilian's Randomization of Multilinear Map Encodings. ASIACRYPT (2) 2019: 325-355
In this work, we have described a new multipartite key-exchange, based on multilinear maps.

2) Jean-Sébastien Coron, Luca Notarnicola. Cryptanalysis of CLT13 Multilinear Maps with Independent Slots. ASIACRYPT (2) 2019: 356-385
In this work, we have described an attack against CLT13 multilinear maps with independent slots.

3) Jean-Sébastien Coron, Lorenzo Spignoli: Secure Wire Shuffling in the Probing Model. CRYPTO (3) 2021: 215-244
In this work, we have developed an efficient shuffling method for side-change masking, with a possible application to obfuscation.

4) Jean-Sébastien Coron, François Gérard, Simon Montoya, Rina Zeitoun. High-order Table-based Conversion Algorithms and Masking Lattice-based Encryption. IACR Trans. Cryptogr. Hardw. Embed. Syst. 2022(2): 1-40 (2022)
In this work, we have developed an efficient conversion method for implementing lattice-based encryption.

5) Davide Bellizia, Clément Hoffmann, Dina Kamel, Pierrick Méaux, François-Xavier Standaert. When Bad News Become Good News Towards Usable Instances of Learning with Physical Errors. IACR Trans. Cryptogr. Hardw. Embed. Syst. 2022(4): 1-24 (2022)
In this work, we develop new side-channel countermeasures based on the LPN problem.

6) Jean-Sébastien Coron, François Gérard, Matthias Trannoy, Rina Zeitoun. High-order masking of NTRU. IACR Trans. Cryptogr. Hardw. Embed. Syst. 2023(2): 180-211 (2023)
In this work, we have developed an efficient side-channel masking of the lattice-based NTRU scheme.

7)Jean-Sébastien Coron, François Gérard, Simon Montoya, Rina Zeitoun. High-order Polynomial Comparison and Masking Lattice-based Encryption. IACR Trans. Cryptogr. Hardw. Embed. Syst. 2023(1): 153-192 (2023)
In this work, we describe an efficient side-channel secure implementation of the lattice-based Kyber scheme.

8) Loïc Masure, Pierrick Méaux, Thorben Moos, François-Xavier Standaert. Effective and Efficient Masking with Low Noise Using Small-Mersenne-Prime Ciphers. EUROCRYPT (4) 2023: 596-627
In this work, we describe a new masking technique for side-channel security.
We have described a new technique to build a multivariate key-exchange protocol based on multilinear maps.
We have also introduced new cryptanalytic techniques for better understanding the security of multilinear maps.
The expected results are improvements in the performances and security of fully homomorphic encryption and multilinear map algorithms.
We have also developed efficient side-channel countermeasures for lattice-based encryption and signature schemes.
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