Lattice-based cryptography is the use of conjectured hard problems on point lattices in Rn
as the foundation for secure cryptographic systems. Attractive features of lattice cryptography …

The advent of quantum computing threatens to break many classical cryptographic
schemes, leading to innovations in public key cryptography that focus on post-quantum …

This document is the supporting documentation of Falcon. It is organized as follows. Chapter
2 explains the overall design of Falcon and its rationale. Chapter 3 is a complete …

Our main result is a construction of a lattice-based digital signature scheme that represents
an improvement, both in theory and in practice, over today's most efficient lattice schemes …

We provide an alternative method for constructing lattice-based digital signatures which
does not use the “hash-and-sign” methodology of Gentry, Peikert, and Vaikuntanathan …

We describe plausible lattice-based constructions with properties that approximate the
sought-after multilinear maps in hard-discrete-logarithm groups, and show an example …

Cryptography is essential for the security of online communication, cars and implanted
medical devices. However, many commonly used cryptosystems will be completely broken …

We show how to construct a variety of" trapdoor" cryptographic tools assuming the worst-
case hardness of standard lattice problems (such as approximating the length of the shortest …

We introduce a new lattice-based cryptographic structure called a bonsai tree, and use it to
resolve some important open problems in the area. Applications of bonsai trees include an …

The subfield attack exploits the presence of a subfield to solve overstretched versions of the
NTRU assumption: norming the public key h down to a subfield may lead to an easier lattice …