Encryption and signatures are foundational to all security and, luckily, all evidence 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 knowledge 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 protocol 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 using 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 was 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 proved to be a major challenge mostly due to the difficulty of constructing efficient zero-knowledge proofs – and this is the problem that the project
proposed to solve.
The PLAZA project successfully bridged the gap between theoretical mathematics and real-world cybersecurity, ensuring our digital data can remain private even against future quantum computers. Our work transformed lattice-based proofs into the smallest quantum-safe proofs available. To demonstrate that these breakthroughs could actually work outside papers, we developed a practical software proof of concept, proving our methods are highly efficient for everyday computing. Today, our zero-knowledge proofs serve as the foundational building blocks for a wide variety of advanced privacy research.
