The Monero Building Blocks series is the result of a personal interest in the mathematical underpinnings of Monero. My interest is primarily derived from Monero’s ability to conceal information about senders, receivers and transacted amounts, all the while maintaining proper operation of the network. It is my hope that this typescript help the reader understand …
Download pdf here: Elliptic Curve Groups 1. Introduction and motivation The sempiternel question of how to gain and maintain power has haunted the minds of humanity’s brightest and darkest since the dawn of civilization. Be it physical (e.g., military) or economical (e.g., wealth), power’s very existence relied in part on access to information. Asymmetric information that …
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Download pdf here: Groups and Finite Fields 1. Introduction Group, field and elliptic curve theories make a regular appearance in the study of crypto-assets including but not limited to cryptocurrencies. For example, the security strength of a number of crypto-specific primitives relies on the math of elliptic curve groups over finite fields. These groups constitute a …
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Download pdf here: The Stealth Address System 1. Introduction The previous nine parts introduced Monero’s privacy and confidentiality attributes in so far as senders’ identities and transaction amounts were concerned. This part focuses on privacy with respect to the recipients of funds. To that end, we introduce the stealth address system [8] to ensure that any …
Download pdf here: RingCT and Anatomy of Monero Transactions 1. Introduction In part 7 we introduced the MLSAG ring signature scheme. Among other things, it safeguarded the anonymity of the signer. In part 8 we discussed the notions of Pedersen Commitments and Confidential Transactions. They were used to mask transaction amounts without compromising the proper bookkeeping …
Download pdf here: CT and Pedersen Commitment 1. Introduction Pedersen Commitments are at the heart of how Monero conceals transaction amounts. The notion of a confidential transaction as enabled by Pedersen Commitments were outlined and defined by Gregory Maxwell in [1]. In what follows we first introduce the notion of a group homomorphism (of which the …
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Download pdf here: MLSAG Signature Scheme 1. Introduction Monero stands out from other cryptocurrencies in its ability to hide the signer, conceal the transaction amount, and protect the identity of the recepient. Parts 1, 2, 3, 4, 5, and 6 helped us build the foundation to better understand and appreciate the security properties of ring signatures …
Download pdf here: LSAG Signature Scheme 1. Introduction For a given ring size , Cryptonote’s original scheme (as introduced in part 5), generates signatures of the form consisting of arguments. It turns out that a more efficient scheme initially introduce in [3] and later adapted by Adam Back in [1] can achieve the same security properties …
Download pdf here: Cryptonote’s Ring Signature Scheme 1. Introduction In this part, we introduce Monero’s original signature scheme as described in van Saberhagen’s seminal Cryptonote paper [2]. The scheme is an adaptation of the Traceable Ring Signature introduced by Fujisaki and Suzuki [1]. The most recent version of Monero implements a different signature known as RingCT. …
Download pdf here: Herranz & Saèz Generic Ring Signature 1. Introduction In the next 4 parts of this series, we look at various ring signature schemes and prove their security in the RO model. This part is dedicated to the analysis of a generic class of ring signature schemes introduced in [1] and inspired by [2]. …