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• W2406585997 abstract "We introduce a new variant of the number field sieve algorithm for discrete logarithms in $$mathbb {F}_{p^n}$$ called exTNFS. The most important modification is done in the polynomial selection step, which determines the cost of the whole algorithm: if one knows how to select good polynomials to tackle discrete logarithms in $$mathbb {F}_{p^kappa }$$ , exTNFS allows to use this method when tackling $$mathbb {F}_{p^{eta kappa }}$$ whenever $$gcd (eta ,kappa )=1$$ . This simple fact has consequences on the asymptotic complexity of NFS in the medium prime case, where the complexity is reduced from $$L_Q(1/3,root 3 of {96/9})$$ to $$L_Q(1/3,root 3 of {48/9})$$ , $$Q=p^n$$ , respectively from $$L_Q(1/3,2.15)$$ to $$L_Q(1/3,1.71)$$ if multiple number fields are used. On the practical side, exTNFS can be used when $$n=6$$ and $$n=12$$ and this requires to updating the keysizes used for the associated pairing-based cryptosystems." @default.
• W2406585997 created "2016-06-24" @default.
• W2406585997 creator A5067172615 @default.
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• W2406585997 date "2016-01-01" @default.
• W2406585997 modified "2023-09-30" @default.
• W2406585997 title "Extended Tower Number Field Sieve: A New Complexity for the Medium Prime Case" @default.
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• W2406585997 doi "https://doi.org/10.1007/978-3-662-53018-4_20" @default.
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