Jens Groth explains that zero-knowledge proofs “allow you to prove a statement is true without revealing anything else but the fact the statement is true.”
He also pulls out a deck of cards “to illustrate what he means by this.”
He adds:
“Let’s say I pick a card, look at it, and tell you it’s a red card. What I tell you could be true or false, and sure, I could show you the card to prove it’s really red, but showing you the card would reveal more than just the fact that the card is, in fact, red.”
Groth then spreads out a pile of all the black cards with the red card face down.
He points out that “now you know the card is red, but not that it’s the queen of hearts, for example.”
This is how Groth — a cryptographer known for improving the area of zero-knowledge proofs with the invention of practical pairing-based non-interactive zero-knowledge (NIZK) proofs — explains “the essence of the research paper he co-authored with Amit Sahai.”
This paper, titled Efficient Non-interactive Proof Systems for Bilinear Groups, has been used in many research works that followed “to develop practical cryptographic schemes and applications, since its publication at Eurocrypt 2008.”
Today, the International Association for Cryptologic Research (IACR) is acknowledging the work of the authors with a Test-of-Time award “for the lasting impact their proofs have had on public key cryptography.”
“I’m very happy and proud that the Test-of-Time award recognizes this piece of research as an important step in that evolution. I long had an intuition that zero-knowledge proofs hold a lot of potential for applications, but back then the actual use cases were still specialized to specific cryptographic protocols. Now, the whole field of zero-knowledge proofs is blooming, and seeing both research and engineering making a lot of progress in tandem shows how important the general field has become.”
As noted in a blog post, it all started “with a love for mathematics but also a desire to work in a field where research can be translated into practical applications.”
Groth began “to attend various cryptography courses during his time at Aarhus University, fully unaware of his luck in being taught by world-class cryptographers like Prof. Peter Landrock and Prof. Ivan Damgaard.”
He ended up “doing a MSc under Prof. Damgaard’s supervision, and later an industrial PhD in collaboration with a company called Cryptomathic, which was developing an e-voting solution at the time.”
After completing his PhD, Groth “took a postdoc position at UCLA where he met his co-author Amit Sahai.”
The line of research “leading to the Groth-Sahai winning paper got started by wanting to connect the construction of non-interactive zero-knowledge proofs to pairing-based cryptography, which had shown itself versatile in other cryptographic constructions.”
An initial work with Rafail Ostrovsky and Amit Sahai first “showed that you could use pairings to build efficient NIZK proofs that show a Boolean circuit has a satisfying input that makes the circuit output true.”
However, the kind of statements you want “to prove in cryptographic protocols are usually not expressed directly as Boolean circuits.”
In a later paper, “which won the IACR test-of-time award in 2021, Groth demonstrated that it’s possible to give pairing-based NIZK proofs that work directly for the kind of statements that arise naturally in pairing-based cryptography.”
The downside is “that these NIZK proofs are very expensive. Persisting, Groth asked the next logical question: whether there are NIZK proofs that are both efficient and broadly applicable in pairing-based cryptographic protocol design.”
Over several months Groth and Sahai “managed to continually reduce the complexity of the NIZK proofs to be small in size, and also formulate a general description of statements they can prove that express most of the operations in pairing-based cryptography.”
For more details on this update, check here.
