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A Panorama of Post-quantum Cryptography

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Open Problems in Mathematics and Computational Science

Abstract

In 1994, Peter Shor published a quantum algorithm capable of factoring large integers and computing discrete logarithms in Abelian groups in polynomial time. Since these computational problems provide the security basis of conventional asymmetric cryptosystems (e.g., RSA, ECC), information encrypted under such schemes today may well become insecure in a future scenario where quantum computers are a technological reality. Fortunately, certain classical cryptosystems based on entirely different intractability assumptions appear to resist Shor’s attack, as well as others similarly based on quantum computing. The security of these schemes, which are dubbed post-quantum cryptosystems, stems from hard problems on lattices, error-correcting codes, multivariate quadratic systems, and hash functions. Here we introduce the essential notions related to each of these schemes and explore the state of the art on practical aspects of their adoption and deployment, like key sizes and cryptogram/signature bandwidth overhead.

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Acknowledgements

Paulo S. L. M. Barreto, Ricardo Dahab and Julio López acknowledge support by the Brazilian National Council for Scientific and Technological Development (CNPq) research productivity grants 306935/2012-0, 311530/2011-7, and 309258/2011-1, respectively.

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  1. Escola Politécnica, University of Sãao Paulo, Av. Prof. Luciano Gualberto, trav 3, no. 158, São Paulo (SP), Brazil

    Paulo S. L. M. Barreto, Felipe Piazza Biasi, Geovandro C. C. F. Pereira & Jefferson E. Ricardini

  2. Instituto de Computação, University of Campinas, Av. Albert Einstein, 1251, Campinas (SP), Brazil

    Ricardo Dahab, Julio César López-Hernández, Eduardo M. de Morais & Ana D. Salina de Oliveira

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    Çetin Kaya Koç

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Barreto, P.S.L.M. et al. (2014). A Panorama of Post-quantum Cryptography. In: Koç, Ç. (eds) Open Problems in Mathematics and Computational Science. Springer, Cham. https://doi.org/10.1007/978-3-319-10683-0_16

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