Bhaskar KrishnamachariUnderstanding Zero-Knowledge Proofs: Part 6-Quadratic Arithmetic ProgramsIn the previous article (part 5) in this series on zk-SNARKs, we looked at how computations that need verification can be first encoded in…Jul 14Jul 14

Bhaskar KrishnamachariUnderstanding Zero-Knowledge Proofs: Part 5-Arithmetic Circuits and R1CSIn previous posts, we have looked at some basics of zero-knowledge proofs for privacy-sensitive verifiable computation. In part 4 we looked…Jul 14Jul 14

Bhaskar KrishnamachariUnderstanding Zero-Knowledge Proofs: Part 4— Polynomial CommitmentsIn part 2 of this series, we went over some basic mathematical background needed for cryptography, namely finite fields, cyclic groups, and…Jul 14Jul 14

Bhaskar KrishnamachariUnderstanding Zero-Knowledge Proofs: Part 3—Elliptic Curve CryptographyWe continue our journey to explore how zero-knowledge proofs work. After a broad overview of zero-knowledge proofs and how they enable…Jul 14Jul 14

Bhaskar KrishnamachariUnderstanding Zero-Knowledge Proofs: Part 2 — Math Basics for CryptographyWe started this series with a previous article giving a broad-overview of zero-knowledge proofs and their role in enabling verifiable…Jul 14Jul 14

Bhaskar KrishnamachariUnderstanding Zero-Knowledge Proofs: Part 1— Verifiable Computation with zk-SNARKsIn my view, one of the most consequential developments in cryptography as well as distributed computing in the past decade has been the…Jul 14Jul 14

Bhaskar KrishnamachariNotes on Kolmogorov-Arnold Networks (KAN)A little over a month ago, Liu et al. posted a paper titled “KAN: Kolmogorov-Arnold Networks” [1]. It’s a truly novel piece of work…Jun 7Jun 7

Bhaskar KrishnamachariMindful AI: Aligning Technology with Spiritual ValuesAs AI technology continues to advance, so does the need to ensure that these systems are aligned with human values and objectives. One…Apr 9, 2023Apr 9, 2023

Bhaskar KrishnamachariBuying and Selling on the BlockchainImagine a buyer and seller that do not know each other, interacting over the Internet. The seller offers to sell a digital document online…Mar 21, 2023Mar 21, 2023

Bhaskar KrishnamachariModeling a Speculative Asset BubbleA simple mathematical model of how speculative asset bubbles form and burst. Applicable to cryptocurrencies, stocks, or any other asset.May 16, 2022May 16, 2022