cryptographic_primitives

cryptographic primitives

bls signatures

• used in the beacon chain to verify large numbers of signtures.
• invented by dan boneh, ben lynn, and hovav shacham.
• in optimistic rollups such as arbitrum and optimism, each tx must be accompanied by its own signature. these signatures are stored on l1 calldata, a read-only format that's commited as a part of a transaction rather than to (expensive) contract storage.
• storing txs and signatures as calldata is the cheapst method available for rollups to keep data on l1.
• the key property of bls signatures is that multiple signatures can be combined into one - so only one aggregate signature needs to be verified and stored on-chain (meaning less gas fees).

---

shamir's secret sharing

• secret sharing algorithm to distribute private information among a group, and the secret cannot be revealed unless a quorum of the groups acts together to pool their knowledge.
• the secret is matematically divided into parts. if an attacker steals some shares, it's impossible for the attacker to reconstrcut the secret unless they have stolen a quorum number of shares.
• uses cases: password managers, encrypted emails, and crypto wallets.

---

cool resources

cool courses

• number theory course by stanford (2023)
• galois fields, part one (2020)

cool papers

• bls multi-signatures with pub-key aggregation (2018)
• ring confidential transactions (2015)
• intro to differential power analysis (2011)
• pairing-friendly elliptic curves of prime order (2005)

cool talks

• an introduction to cryptography, new and old, by atheartengineer et al. (2024)
• programmable cryptography devcon panel, by barry and gang (2024)