Summary of ZKP MOOC Lecture 9: SNARKs based on Linear PCP
The video delves into the realm of SNARKs based on Linear PCP, exploring various construction techniques like bilinear pairings, Linear PCP, and quadratic arithmetic programs. It compares implementations such as Halo 2, Bulletproofs, Dory Dark, and Hierarchs. Linear PCP is introduced as a pivotal technique in building SNARKs, with a historical context provided. The model of Linear PCP is explained, showcasing how it compiles a quadratic arithmetic program into a SNARK, utilizing bilinear pairings to achieve a constant size proof.
Moving on, the video details key aspects of SNARKs based on Linear PCP, covering key generation, proof generation, and verification processes. It emphasizes the significance of zero knowledge in ensuring protocol security. The generation of proving keys, evaluation of selector polynomials, and circuit-dependent pre-processing are elucidated. Compression of message proofs using extendedness and quotient polynomials is outlined. Verification involves bilinear pairing operations to validate computations, addressing security concerns with malicious provers through the knowledge of exponent assumption and the generic group model.
Additionally, the Rank One Constraint System (R1CS) is introduced for efficient SNARK construction. The optimization of proof size in the Cross 16 variant is discussed, combining three group elements into one to reduce proof size. Zero knowledge properties are emphasized, with insights into adding randomizers for enhanced security.
Notable Quotes
— 47:11 — « So then, in the quadratic arithmetic program, we are trying to convince the verifier that this master polynomial computed using the extended witness C and the public selector polynomials LAX, RX, and NOAX can be written as the product between management polynomial. »
— 49:38 — « Therefore, a similar reason lets take a look at P of X evaluated at Omega Square. Again, by the properties of these selector polynomials were essentially selecting the left input, right input, and output of gate 2. »
Category
Educational