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Zero-Knowledge Proofs & Cryptography

Master mathematical zero-knowledge architectures: finite fields, polynomial commitments, arithmetic circuits, SNARKs/STARKs, Succinct SP1 zkVM, and validity rollups.

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1 · Mathematical Foundations

Modular arithmetic, Galois prime fields, polynomial commitments, and elliptic curve pairings.

  1. 1. Finite Fields, Polynomial Commitments & PairingsGalois fields, the Schwartz-Zippel lemma, KZG commitments, and bilinear pairing groups.
    11m · 3 MCQs

2 · Arithmetic Circuits & R1CS

Constraint systems, QAP interpolation, and Circom circuit programming.

  1. 2. Arithmetic Circuits, R1CS and CircomFlattening procedural logic, Rank-1 Constraint Systems, witness generation, and Circom circuit programming.
    11m · 2 MCQs

3 · SNARKs vs STARKs

Groth16 trusted setups, Plonk universal proving systems, FRI protocols, and transparent verification.

  1. 3. Proving Systems: Groth16, Plonk, and STARKsTrusted setups, KZG commitments, Plonkish arithmetization, FRI protocols, and transparent proofs.
    11m · 2 MCQs

4 · zkVMs & Succinct SP1

RISC-V proving, Succinct SP1 architecture, Rust programs, and recursive proof aggregation.

  1. 4. General-Purpose zkVMs: Succinct SP1 & Validity RollupsRISC-V proving, Succinct SP1 architecture, Rust execution proving, precompiles, and recursive rollup aggregation.
    12m · 2 MCQs

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