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Efficient reductions in cyclotomic rings - Application to R-LWE based FHE schemes
Polynomial Reduction Number Theoretic Transform Residue Number Systems
2017/8/9
With Fully Homomorphic Encryption (FHE), it is possible to process encrypted data without having an access to the private-key. This has a wide range of applications, most notably the offloading of sen...
Provably Secure NTRUEncrypt over More General Cyclotomic Rings
Lattice-based cryptography NTRU Learning With Errors
2017/4/11
NTRUEncrypt is a fast and standardized lattice-based public key encryption scheme, but it lacks a solid security guarantee. In 2011, Stehlé and Steinfeld first proposed a provably secure variant of NT...
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 ...
Polynomial Time Reduction from Approximate Shortest Vector Problem to Principal Ideal Problem for Lattices in Some Cyclotomic Rings
Cyclotomic Rings Principal Ideal Problem
2015/12/29
Many cryptographic schemes have been established based on the hardness of lattice problems. For the asymptotic efficiency, ideal lattices in the ring of cyclotomic integers are suggested to be used in...