A Concrete LIP-Based KEM With Simple Lattices
Recent developments have been made in the construction of cryptosystems with security based on the hardness of the lattice isomorphism problem (LIP). Due to lattice conjectures, one may expect in the future that breaking such schemes is computationally harder than most current lattice-based cryptosy...
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IEEE
2024-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10417023/ |
| _version_ | 1797323884945473536 |
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| author | Gustavo de Castro Biage Gustavo Zambonin Thais B. Idalino Daniel Panario Ricardo Custodio |
| author_facet | Gustavo de Castro Biage Gustavo Zambonin Thais B. Idalino Daniel Panario Ricardo Custodio |
| author_sort | Gustavo de Castro Biage |
| collection | DOAJ |
| description | Recent developments have been made in the construction of cryptosystems with security based on the hardness of the lattice isomorphism problem (LIP). Due to lattice conjectures, one may expect in the future that breaking such schemes is computationally harder than most current lattice-based cryptosystems. To the best of our knowledge, there have not been any attempts to concretely instantiate a key encapsulation mechanism (KEM) based on LIP. In this work, we propose the first instance of such a KEM, following the framework of Ducas and van Woerden (EUROCRYPT 2022), using simple lattices. We present a randomness extractor derived from a hash function based on the short integer solution problem; define a concrete set of parameters for instantiating the scheme; provide a rigorous security estimation of an attacker trying to decode an encapsulated key through reductions to hard lattice problems; and use well-known methods to convert the IND-CPA secure KEM into an IND-CCA2 secure KEM, comparing the latter with other modern lattice-based KEMs. The resulting security is estimated under the assumption that an adversary cannot efficiently solve related instances of LIP, which is a consequence of the lack of cryptanalysis towards identifying isomorphism between lattices. |
| first_indexed | 2024-03-08T05:34:35Z |
| format | Article |
| id | doaj.art-08bf5927dc754d3d8420593f073f01db |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-03-08T05:34:35Z |
| publishDate | 2024-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-08bf5927dc754d3d8420593f073f01db2024-02-06T00:01:08ZengIEEEIEEE Access2169-35362024-01-0112164081642010.1109/ACCESS.2024.335867010417023A Concrete LIP-Based KEM With Simple LatticesGustavo de Castro Biage0https://orcid.org/0009-0008-0102-1993Gustavo Zambonin1https://orcid.org/0000-0002-6962-9347Thais B. Idalino2https://orcid.org/0000-0002-8836-1104Daniel Panario3https://orcid.org/0000-0003-3551-4063Ricardo Custodio4https://orcid.org/0000-0001-9611-5694Departamento de Informática e Estatística, Universidade Federal de Santa Catarina, Florianópolis, BrazilDepartamento de Informática e Estatística, Universidade Federal de Santa Catarina, Florianópolis, BrazilDepartamento de Informática e Estatística, Universidade Federal de Santa Catarina, Florianópolis, BrazilSchool of Mathematics and Statistics, Carleton University, Ottawa, CanadaDepartamento de Informática e Estatística, Universidade Federal de Santa Catarina, Florianópolis, BrazilRecent developments have been made in the construction of cryptosystems with security based on the hardness of the lattice isomorphism problem (LIP). Due to lattice conjectures, one may expect in the future that breaking such schemes is computationally harder than most current lattice-based cryptosystems. To the best of our knowledge, there have not been any attempts to concretely instantiate a key encapsulation mechanism (KEM) based on LIP. In this work, we propose the first instance of such a KEM, following the framework of Ducas and van Woerden (EUROCRYPT 2022), using simple lattices. We present a randomness extractor derived from a hash function based on the short integer solution problem; define a concrete set of parameters for instantiating the scheme; provide a rigorous security estimation of an attacker trying to decode an encapsulated key through reductions to hard lattice problems; and use well-known methods to convert the IND-CPA secure KEM into an IND-CCA2 secure KEM, comparing the latter with other modern lattice-based KEMs. The resulting security is estimated under the assumption that an adversary cannot efficiently solve related instances of LIP, which is a consequence of the lack of cryptanalysis towards identifying isomorphism between lattices.https://ieeexplore.ieee.org/document/10417023/Key encapsulation mechanismlattice isomorphism problempost-quantum cryptography |
| spellingShingle | Gustavo de Castro Biage Gustavo Zambonin Thais B. Idalino Daniel Panario Ricardo Custodio A Concrete LIP-Based KEM With Simple Lattices IEEE Access Key encapsulation mechanism lattice isomorphism problem post-quantum cryptography |
| title | A Concrete LIP-Based KEM With Simple Lattices |
| title_full | A Concrete LIP-Based KEM With Simple Lattices |
| title_fullStr | A Concrete LIP-Based KEM With Simple Lattices |
| title_full_unstemmed | A Concrete LIP-Based KEM With Simple Lattices |
| title_short | A Concrete LIP-Based KEM With Simple Lattices |
| title_sort | concrete lip based kem with simple lattices |
| topic | Key encapsulation mechanism lattice isomorphism problem post-quantum cryptography |
| url | https://ieeexplore.ieee.org/document/10417023/ |
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