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Recovering Short Generators of Principal Fractional Ideals in Cyclotomic Fields of Conductor pαqβ
Lattice-based cryptography principal ideal lattices SG-PIP
2017/6/6
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...
Short generators without quantum computers: the case of multiquadratics
Public-key encryption lattice-based cryptography ideal lattices
2017/5/12
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...
Recovering Short Generators of Principal Ideals in Cyclotomic Rings
Ideal Lattices Cryptanalysis
2015/12/31
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 ...
Security Analysis of Cryptosystems Using Short Generators over Ideal Lattices
Short generators Cyclotomic fields Log-unit lattices
2015/12/22
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...