The article delves into zero-knowledge implementation in STARKs, using structured randomness to mask witness and DEEP composition polynomials, ensuring verifiers learn nothing beyond computation correctness while maintaining transparency and post-quantum security.

• https://hexens.io/blog/zk-in-starks

The article explores the mathematical foundations of the Binius protocol, focusing on binary tower constructions, finite field element representation, and optimized multiplication via Karatsuba, supporting efficient zero-knowledge proof systems.

• https://blog.lambdaclass.com/the-fields-powering-binius/

The article introduces Circle FFT, the core algorithm of Circle STARKs, leveraging circle curves, group structures, twin-cosets, and standard position cosets for efficient polynomial interpolation and evaluation, suitable for small fields like Mersenne prime 2³¹-1.

• https://www.rareskills.io/post/circle-starks

The article explains Ethereum's Merkle Patricia Trie (MPT), combining Trie's efficient key navigation with Merkle tree's cryptographic verification for state management and consensus, enabling efficient storage, verification, and rollback.

• https://blog.lambdaclass.com/an-introduction-to-merkle-patricia-trie/

• https://www.youtube.com/watch?v=_y43boNNoVo

• https://www.youtube.com/watch?v=zrZHPil0BTA

• https://www.youtube.com/watch?app=desktop&v=8JuWdXrCmWg

• https://blog.trailofbits.com/2025/06/10/what-we-learned-reviewing-one-of-the-first-dkls23-libraries-from-silence-laboratories/

• https://blog.cryptographyengineering.com/2025/06/09/a-bit-more-on-twitter-xs-new-encrypted-messaging/

• https://crypto.iacr.org/2025/acceptedpapers.php

• https://www.youtube.com/watch?v=zrZHPil0BTA

• https://eprint.iacr.org/2025/1056

• https://eprint.iacr.org/2025/1071

• https://eprint.iacr.org/2025/1085

• https://eprint.iacr.org/2025/1103

• https://eprint.iacr.org/2025/1110