Portal de Periódicos da CAPES

Short Generators Without Quantum Computers: The Case of Multiquadratics

2017; Springer Science+Business Media; Linguagem: Inglês

10.1007/978-3-319-56620-7_2

1611-3349

Jens Bauch, Daniel J. Bernstein, Henry de Valence, Tanja Lange, Christine van Vredendaal,

Coding theory and cryptography

Finding a short element g of a number field, given the ideal generated by g, is a classic problem in computational algebraic number theory. Solving this problem recovers the private key in cryptosystems introduced by Gentry, Smart–Vercauteren, Gentry–Halevi, Garg–Gentry–Halevi, et al. Work over the last few years has shown that for some number fields this problem has a surprisingly low post-quantum security level. This paper shows, and experimentally verifies, that for some number fields this problem has a surprisingly low pre-quantum security level.