Encryption and signatures are foundational to all security and, luckily, all ev-
idence points to the fact that we will be able to have these primitives in a
post-quantum world. But modern cryptography has the capability to deliver
a lot more than just the basics, allowing for “fine-grained” security where the
knowledge of all information is on a strict need-to-know basis. And as the world
moves towards this more decentralized, privacy-oriented mode of storing data
and operating on it, advanced cryptography stands to play a central role.
The construction of many advanced privacy-preserving primitives often rests
on being able to create a zero-knowledge proof, which allows for showing knowl-
edge of an x satisfying f (x) = y without revealing anything else about the secret
input x. A zero-knowledge proof is the glue that holds a cryptographic proto-
col together allowing one to prove that some part of the protocol was correctly
formed / executed without giving away any other information. Having efficient
zero-knowledge proofs for various functions can thus dramatically increase what
cryptography can achieve. As a simple example, a potential borrower wishing
to prove that his income is high enough to obtain a mortgage may have his pay-
check digitally signed by his employer, and then present the encrypted version
of it to the bank and create a zero-knowledge proof of the following statement:
the ciphertext is a valid encryption of a number and this number was signed
by XYZ-corporation and it’s a number larger than ten thousand euros. By us-
ing zero-knowledge proofs, the individual didn’t reveal anything more than the
information that was demanded for his mortgage application.
The central objective of the PLAZA project will be to create practical zero-
knowledge proofs that can withstand quantum attacks by basing them on the
hardness of lattice problems. Lattice problems are a very promising set of
assumptions upon which to base cryptography and they are currently being
used to create the most efficient quantum-resistant encryption and signature
schemes. Creating more complex, but still practical, lattice-based schemes has
so far proved to be a major challenge mostly due to the difficulty of construct-
ing efficient zero-knowledge proofs – and this is the problem that the project
proposes to solve.
