Some cryptographic references and blockchain applications

 

• Boneh–Shoup A Graduate Course in Applied Cryptography

Preface: [...] This book is about exactly that: constructing practical cryptosystems for which we can argue security under plausible assumptions. The book covers many constructions for different tasks in cryptography. For each task we define a precise security goal that we aim to achieve and then present constructions that achieve the required goal. To analyze the constructions, we develop a unified framework for doing cryptographic proofs. A reader who masters this framework will be capable of applying it to new constructions that may not be covered in the book.[...]

 

• Dan Boneh, Manu Drijvers, Gregory Neven Compact Multi-Signatures for Smaller Blockchains

Abstract: We construct new multi-signature schemes that provide new

functionality. Our schemes are designed to reduce the size of the Bitcoin

blockchain, but are useful in many other settings where multi-signatures

are needed. All our constructions support both signature compression

and public-key aggregation. Hence, to verify that a number of parties

signed a common message m, the verifier only needs a short multi-

signature, a short aggregation of their public keys, and the message m.

We give new constructions that are derived from Schnorr signatures and

from BLS signatures. Our constructions are in the plain public key model,

meaning that users do not need to prove knowledge or possession of their

secret key.

 

• Rogue Key Attack in BLS Signature and Harmony Security

Intro: Consensus algorithm is one of the most important components in blockchain. Harmony Blockchain achieves consensus through the Fast Byzantine Fault Tolerance (FBFT) algorithm. In FBFT, instead of asking all validators to broadcast their votes, the leader runs a multi-signature signing process to collect the validators’ votes in a O(1)-sized multi-signature and then broadcast it to all validators. Consensus is reached when all the validators validate the aggregated signature against the aggregated public keys for this round of consensus.