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Several recent cryptographic constructions - including a public key encryption scheme, a fully homomorphic encryption scheme, and a candidate multilinear map construction - rely on the hardness of the...
Finding a short element gg of a number field, given the ideal generated by gg, is a classic problem in computational algebraic number theory. Solving this problem recovers the private key in cryptosys...
A handful of recent cryptographic proposals rely on the conjectured hardness of the following problem in the ring of integers of a cyclotomic number field: given a basis of a principal ideal that is ...
In this paper, we analyze the security of cryptosystems using short generators over ideal lattices such as candidate multilinear maps by Garg, Gentry and Halevi and fully homomorphic encryption by S...

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