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tl;dr: Notes on WHIR[^ACFY24e].

tl;dr: PIOPs, as originally introduced in the DARK paper[^BFS20]. (Although I think they were kind of already defined in PLONK[^GWC19] and Marlin[^CHMplus19e]?)

tl;dr: Ligero + <?> = Ligerito!

tl;dr: A relaxation of IOPs that is central to hash-based proof systems like FRI, STIR[^ACFY24eSTIR] and WHIR.

tl;dr: An interactive oracle proof (IOP) is an interactive proof system where the verifier has oracle access to the prover’s messages rather than reading them in full. This combines the expressiveness of interactive proofs with the efficiency of PCPs. Introduced in [BCS16][^BCS16].

tl;dr: Too many FRI[^BBHR18FRI] conjectures that need to be understood, so here we are…

tl;dr: Pedersen commitments[^Pede91Comm] are one of the most important cryptographic primitives for a beginner to understand, in my opinion.

tl;dr: Notes on our current use of Groth16 for Aptos Keyless and how we might improve upon it. Should have applications to anonymous payments, confidential assets, zkVM proof wrapping etc.