A provably secure variant of NTRU cryptosystem

In 1996 Hoffstein, Pipher ad Silverman presented NTRUEncrypt, which is to date the fastest known lattice-based encryption scheme. Its moderate key-sizes, excellent asymptotic performance and conjectured resistance to quantum attacks make it a perfect candidate to succeed where factorization and discrete log fail. Unfortunately, no security proof has been produced for NTRUEncrypt nor for its signature counterpart NTRUSign. In 2013 Stehlé and Steinfield proposed to apply some mild modification to the encryption and signature scheme to make them provably secure, under the assumed quantum hardness of standard worst-case lattice problems, restricted to a family of lattices related to some cyclotomic fields. In particular they showed that if the secret key polynomials of the encryption scheme are chosen from discrete Gaussians, then the public key, i.e their ratio, is statistically indistinguishable from uniform. The security will then follow from the hardness of the R-LWE problem.The aim of this thesis is to present Stehlé's and Steinfield's work in a slightly more accessi-ble form, providing some more background and details in some points.