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In Part 1 of this series, I demonstrated how we convert the interactive Schnorr protocol into a non-interactive variant, using something called a Fiat-Shamir transformation. This sets the foundation for the Schnorr signature scheme.

AOS signatures, the first type of ring signature we will be discussing, builds heavily off of Schnorr.

The idea of AOS rings work as follows: Bob gathers public keys belonging to Alice, Carol and Dave from some directory. …

Interactive Zero-Knowledge Proof Schemes

Before we get into ring signatures, we need to differentiate between interactive and noninteractive proofs of knowledge. Interactive proofs engage in a pre-processing round where the two parties (prover and verifier) exchange relevant information in order to construct a signature. The hand waving overview looks like this:

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Interactive “Sigma” Protocol

The prover has a keypair (x,P), where x is the private key and P is the public key. P is publicly broadcast, while x remains hidden to the prover alone.

When dealing with signatures, specifically of the Schnorr family, our commitment is constructed by picking a random nonce value r, then encrypting it to create R. Specifically, the encryption process works by performing R=r*G (mod n), where G is some specified elliptic curve generator point. The discreet logarithm assumption now makes it safe for us to give R out to the rest of the world, because trying to reverse engineer r given only R is computationally infeasible. …


In 2014, a group of notable Bitcoin developers published Enabling Blockchain Innovations with Pegged Sidechains. This whitepaper outlined a very high level framework on how sidechains might look, but lacked significant technical specifications with regard to implementation. …


The Lightning Network is a protocol layer that seeks to provide instantaneous, trustless Bitcoin payments. In this article, I walk through the construction process for Lightning Channels and illustrate how multi-hop transfers are initiated. This article is the third piece in a multi-part series where I attempt to deep dive into notable cryptoasset projects.


The Lightning Network is Layer 2 infrastructure built on top of the Bitcoin protocol, and hopes to increase transactional throughput. Bitcoin has a hardcoded upper bound limit on the number of transactions it can process. In traditional payment rails, ledgers are updated every few seconds and can achieve high degrees of scalability. …


Ripple is a financial services company that looks to facilitate global payments through blockchain-based technologies. …

TL;DR: Monero is a privacy centered coin that uses novel cryptography to solve the fungibility challenges plaguing blockchain-based assets. In this piece, I explore the technical architecture underpinning the Monero protocol, core competencies/weaknesses of the project, governance mechanisms, and trade-offs against competing currencies. This research report is the primer of a multi-part series where I attempt to deep dive into notable cryptoasset projects from a non-biased perspective.


Monero (XMR) is a distributed ledger project touted as one of the world’s leading privacy-centric coins. The Monero project has carved out a deep niche in its respective community by placing heavy emphasis around being private, electronic cash. While the system itself utilizes the same UTXO structure as Bitcoin, it’s design shifts in the way these UTXO’s are packaged and broadcast to the network, utilizing one-time ring signature architecture, effectively creating an unlinkable transaction where an on looking third party cannot identify the output. The Monero protocol also utilizes a concept called stealth addressing, in which senders initiate transactions by producing a one-time public key visible only to the recipient. The recipient alone possesses the ability to recover the corresponding private part of the key to redeem the funds. By protecting both the sender’s and recipient’s transactional information, Monero possess many inherent strengths compared to the Bitcoin protocol and other leading digital currency systems due to its strong fungibility properties.

Joe Kendzicky

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