Top Tweets for #GFolding
🚀 Introducing #GFolding: a Generator-based Folding method which can reduce #storage requirment for sumcheck-based #PIOP protocols. We propose GFolding to address storage bloat issue when applying rotations in sumcheck-based PIOP protocols.
In the multilinear #IOP built upon PLONKish arithmetization, constraints for custom gates may query cells across different rows. This cross-row access induces relative rotations in the multilinear polynomials encoding PLONKish arithmetization columns. While these rotations significantly enhance the PIOP's expressiveness and computational efficiency, they introduce critical storage considerations in sumcheck-based PIOP protocols. Specifically, each sumcheck round requires maintaining a polynomial alongside its rotated polynomials. To optimize storage, we propose Generator-based Folding Method, which consolidats the Lagrange coefficients of a polynomial and its rotations by eliminating duplicate coefficients.
👇 This optimization achieves two advantages:
1. Memory reduction - Storing n + (b - a) coefficients instead of n × m (where m rotations span the interval [a, b], with a, b ∈ [-n/2, n/2)).
2. Computational acceleration - Reducing folding operations of bounding one variable to a random challenge to O(n/2 + m) multiplications versus the naive approach's Θ(n/2 × m) complexity.
👀 This optimization reduces memory overhead by a factor of m compared to conventional implementations that store polynomial rotations separately. 💰⬇️ @tamirhemo @SuccinctJT @srinathtv
![AntChainOpenLab's tweet photo. 🚀 Introducing #GFolding: a Generator-based Folding method which can reduce #storage requirment for sumcheck-based #PIOP protocols. We propose GFolding to address storage bloat issue when applying rotations in sumcheck-based PIOP protocols.
In the multilinear #IOP built upon PLONKish arithmetization, constraints for custom gates may query cells across different rows. This cross-row access induces relative rotations in the multilinear polynomials encoding PLONKish arithmetization columns. While these rotations significantly enhance the PIOP's expressiveness and computational efficiency, they introduce critical storage considerations in sumcheck-based PIOP protocols. Specifically, each sumcheck round requires maintaining a polynomial alongside its rotated polynomials. To optimize storage, we propose Generator-based Folding Method, which consolidats the Lagrange coefficients of a polynomial and its rotations by eliminating duplicate coefficients.
👇 This optimization achieves two advantages:
1. Memory reduction - Storing n + (b - a) coefficients instead of n × m (where m rotations span the interval [a, b], with a, b ∈ [-n/2, n/2)).
2. Computational acceleration - Reducing folding operations of bounding one variable to a random challenge to O(n/2 + m) multiplications versus the naive approach's Θ(n/2 × m) complexity.
👀 This optimization reduces memory overhead by a factor of m compared to conventional implementations that store polynomial rotations separately. 💰⬇️ @tamirhemo @SuccinctJT @srinathtv](https://pbs.twimg.com/media/GwXArWJXcAAqk5x.jpg)
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