Foundations and Trends® in Theoretical Computer Science
Lattice-based identification schemes secure under active attacks
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
Asymptotically efficient lattice-based digital signatures
TCC'08 Proceedings of the 5th conference on Theory of cryptography
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For every constant $\epsilon 0$, we obtain a $2^{O(n(1/2 + 1/\epsilon))}$ time randomized algorithm to approximate the length of the shortest vector in an n-dimensional lattice to within a factor of $n^{3 + \epsilon}$.