This technical note generalizes the concept of spend outputs using basic set theory. The definition captures a variety of earlier work on identifying such outputs. We quantify the effects of this analysis on the Monero blockchain and give a brief overview of mitigations.
This technical note describes an algorithm used to prove knowledge of the same discrete logarithm across different groups. The scheme expresses the common value as a scalar representation of bits, and uses a set of ring signatures to prove each bit is a valid value that is the same (up to an equivalence) across both scalar groups.
This research bulletin describes a plausible attack on a ring-signature based anonymity system. We use as motivation the cryptocurrency protocol CryptoNote 2.0 ostensibly published by Nicolas van Saberhagen in 2012. It has been previously demonstrated that the untraceability obscuring a one-time key pair can be dependent upon the untraceability of all of the keys used in composing that ring signature. This allows for the possibility of chain reactions in traceability between ring signatures, causing a critical loss in untraceability across the whole network if parameters are poorly chosen and if an attacker owns a sufficient percentage of the network. The signatures are still one-time, however, and any such attack will still not necessarily violate the anonymity of users. However, such an attack could plausibly weaken the resistance CryptoNote demonstrates against blockchain analysis. This research bulletin has not undergone peer review, and reflects only the results of internal investigation.
This bulletin describes a modification to Monero's linkable ring signature scheme that permits dual-key outputs as ring members. Key images are tied to both output one-time public keys in a dual, preventing both keys in that transaction from being spent separately. This method has applications to non-interactive refund transactions. We discuss the security implications of the scheme.
This article introduces a method of hiding transaction amounts in the strongly decentralized anonymous cryptocurrency Monero. Similar to Bitcoin, Monero is a cryptocurrency which is distributed through a proof of work “mining” process. The original Monero protocol was based on CryptoNote, which uses ring signatures and one-time keys to hide the destination and origin of transactions. Recently the technique of using a commitment scheme to hide the amount of a transaction has been discussed and implemented by Bitcoin Core Developer Gregory Maxwell. In this article, a new type of ring signature, A Multi-layered Linkable Spontaneous Anonymous Group signature is described which allows for hidden amounts, origins and destinations of transactions with reasonable efficiency and verifiable, trustless coin generation. Some extensions of the protocol are provided, such as Aggregate Schnorr Range Proofs, and Ring Multisignature. The author would like to note that early drafts of this were publicized in the Monero Community and on the bitcoin research irc channel. Blockchain hashed drafts are available in [14] showing that this work was started in Summer 2015, and completed in early October 2015. An eprint is also available at http://eprint.iacr.org/2015/1098.
