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research-lab->mrlhtp_summary Monero uses a unique hash function that transforms scalars into elliptic curve points. It is useful for creating key images, in particular. This document, authored by Shen Noether, translates its code implementation (the ge_fromfe_frombytes_vartime() function) into mathematical expressions. Monero uses a unique hash function that transforms scalars into elliptic curve points. It is useful for creating key images, in particular. This document, authored by Shen Noether, translates its code implementation (the ge_fromfe_frombytes_vartime() function) into mathematical expressions.
research-lab->mrlhtp Understanding ge_fromfe_frombytes_vartime Understanding ge_fromfe_frombytes_vartime
research-lab->mrl9_abstract We present threshold ring multi-signatures (thring signatures) for collaborative computation of ring signatures, present a game of existential forgery for thring signatures, and discuss uses of thring signatures in digital currencies that include spender-ambiguous cross-chain atomic swaps for confidential amounts without a trusted setup. We present an implementation of thring signatures that we call linkable spontaneous threshold anonymous group signatures, and prove the implementation existentially unforgeable. We present threshold ring multi-signatures (thring signatures) for collaborative computation of ring signatures, present a game of existential forgery for thring signatures, and discuss uses of thring signatures in digital currencies that include spender-ambiguous cross-chain atomic swaps for confidential amounts without a trusted setup. We present an implementation of thring signatures that we call linkable spontaneous threshold anonymous group signatures, and prove the implementation existentially unforgeable.
research-lab->mrl9 Thring Signatures and their Applications to Spender-Ambiguous Digital Currencies Thring Signatures and their Applications to Spender-Ambiguous Digital Currencies
research-lab->mrl8_abstract 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 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.
research-lab->mrl8 Dual Linkable Ring Signatures Dual Linkable Ring Signatures
research-lab->mrl7_abstract 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 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.
research-lab->mrl7 Sets of Spent Outputs Sets of Spent Outputs
research-lab->mrl5_abstract 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. 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.
research-lab->mrl5 Ring Signature Confidential Transactions Ring Signature Confidential Transactions
research-lab->mrl4_abstract We identify several blockchain analysis attacks available to degrade the untraceability of the CryptoNote 2.0 protocol. We analyze possible solutions, discuss the relative merits and drawbacks to those solutions, and recommend improvements to the Monero protocol that will hopefully provide long-term resistance of the cryptocurrency against blockchain analysis. Our recommended improvements to Monero include a protocol-level network-wide minimum mix-in policy of n = 2 foreign outputs per ring signature, a protocol-level increase of this value to n = 4 after two years, and a wallet-level default value of n = 4 in the interim. We also recommend a torrent-style method of sending Monero output. We also discuss a non-uniform, age-dependent mix-in selection method to mitigate the other forms of blockchain analysis identified herein, but we make no formal recommendations on implementation for a variety of reasons. The ramifications following these improvements are also discussed in some detail. This research bulletin has not undergone peer review, and reflects only the results of internal investigation. We identify several blockchain analysis attacks available to degrade the untraceability of the CryptoNote 2.0 protocol. We analyze possible solutions, discuss the relative merits and drawbacks to those solutions, and recommend improvements to the Monero protocol that will hopefully provide long-term resistance of the cryptocurrency against blockchain analysis. Our recommended improvements to Monero include a protocol-level network-wide minimum mix-in policy of n = 2 foreign outputs per ring signature, a protocol-level increase of this value to n = 4 after two years, and a wallet-level default value of n = 4 in the interim. We also recommend a torrent-style method of sending Monero output. We also discuss a non-uniform, age-dependent mix-in selection method to mitigate the other forms of blockchain analysis identified herein, but we make no formal recommendations on implementation for a variety of reasons. The ramifications following these improvements are also discussed in some detail. This research bulletin has not undergone peer review, and reflects only the results of internal investigation.
research-lab->mrl4 Improving Obfuscation in the CryptoNote Protocol Improving Obfuscation in the CryptoNote Protocol
research-lab->mrl3_abstract Recently, there have been some vague fears about the CryptoNote source code and protocol floating around the internet based on the fact that it is a more complicated protocol than, for instance, Bitcoin. The purpose of this note is to try and clear up some misconceptions, and hopefully remove some of the mystery surrounding Monero Ring Signatures. I will start by comparing the mathematics involved in CryptoNote ring signatures (as described in [CN]) to the mathematics in [FS], on which CryptoNote is based. After this, I will compare the mathematics of the ring signature to what is actually in the CryptoNote codebase. Recently, there have been some vague fears about the CryptoNote source code and protocol floating around the internet based on the fact that it is a more complicated protocol than, for instance, Bitcoin. The purpose of this note is to try and clear up some misconceptions, and hopefully remove some of the mystery surrounding Monero Ring Signatures. I will start by comparing the mathematics involved in CryptoNote ring signatures (as described in [CN]) to the mathematics in [FS], on which CryptoNote is based. After this, I will compare the mathematics of the ring signature to what is actually in the CryptoNote codebase.
research-lab->mrl3 Monero is Not That Mysterious Monero is Not That Mysterious
research-lab->mrl2_abstract On 4 September 2014, an unusual and novel attack was executed against the Monero cryptocurrency network. This attack partitioned the network into two distinct subsets which refused to accept the legitimacy of the other subset. This had myriad effects, not all of which are yet known. The attacker had a short window of time during which a sort of counterfeiting could occur, for example. This research bulletin describes deficiencies in the CryptoNote reference code allowing for this attack, describes the solution initially put forth by Rafal Freeman from Tigusoft.pl and subsequently by the CryptoNote team, describes the current fix in the Monero code base, and elaborates upon exactly what the offending block did to the network. This research bulletin has not undergone peer review, and reflects only the results of internal investigation. On 4 September 2014, an unusual and novel attack was executed against the Monero cryptocurrency network. This attack partitioned the network into two distinct subsets which refused to accept the legitimacy of the other subset. This had myriad effects, not all of which are yet known. The attacker had a short window of time during which a sort of counterfeiting could occur, for example. This research bulletin describes deficiencies in the CryptoNote reference code allowing for this attack, describes the solution initially put forth by Rafal Freeman from Tigusoft.pl and subsequently by the CryptoNote team, describes the current fix in the Monero code base, and elaborates upon exactly what the offending block did to the network. This research bulletin has not undergone peer review, and reflects only the results of internal investigation.
research-lab->mrl2 Counterfeiting via Merkle Tree Exploits within Virtual Currencies Employing the CryptoNote Protocol Counterfeiting via Merkle Tree Exploits within Virtual Currencies Employing the CryptoNote Protocol
research-lab->mrl1_abstract 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 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.
research-lab->mrl10_abstract 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 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.
research-lab->mrl10 Discrete Logarithm Equality Across Groups Discrete Logarithm Equality Across Groups
research-lab->mrl1 A Note on Chain Reactions in Traceability in CryptoNote 2.0 A Note on Chain Reactions in Traceability in CryptoNote 2.0