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.

mrl11:Compact linkable ring signatures and applications

mrl11_abstract:We describe an efficient linkable ring signature scheme, compact linkable spontaneous anonymous group (CLSAG) signatures, for use in confidential transactions. Compared to the existing signature scheme used in Monero, CLSAG signatures are both smaller and more efficient to generate and verify for ring sizes of interest. We generalize the construction and show how it can be used to produce signatures with coins of different type in the same transaction.

iacr2020018_abstract:Ring signatures are a common construction used to provide signer ambiguity among a non-interactive set of public keys specified at the time of signing. Unlike early approaches where signature size is linear in the size of the signer anonymity set, current optimal solutions either require centralized trusted setups or produce signatures logarithmic in size. However, few also provide linkability, a property used to determine whether the signer of a message has signed any previous message, possibly with restrictions on the anonymity set choice. Here we introduce Triptych, a family of linkable ring signatures without trusted setup that is based on generalizations of zero-knowledge proofs of knowledge of commitment openings to zero. We demonstrate applications of Triptych in signer-ambiguous transaction protocols by extending the construction to openings of parallel commitments in independent anonymity sets. Signatures are logarithmic in the anonymity set size and, while verification complexity is linear, collections of proofs can be efficiently verified in batches. We show that for anonymity set sizes practical for use in distributed protocols, Triptych offers competitive performance with a straightforward construction.

cryptonote:الورقه البيضاء لكريبتونوت (CryptoNote)

cryptonote-whitepaper:الورقه البيضاء لكريبتونوت (CryptoNote)

cryptonote-whitepaper_para:هذه هي الورقه الرسميه لكريبتونوت المكتوبه بواسطه فريق كريبتونوت. قرائتها سوف يعطيك فِهماً حول آليه عمل خوارزميه كريبتونوت في العموم.

mrl10_abstract:Diese technische Abhandlung beschreibt einen Algorithmus, der verwendet wird, um die Kenntnis desselben diskreten Logarithmus über verschiedene Gruppen hinweg zu beweisen. Diese Methode beschreibt einen gemeinsamen Wert als eine skalare Repräsentation von Bits und nutzt diese als eine Menge von Ringsignaturen um zu beweisen, dass jedes Bit ein gültiger Wert ist, der der gleiche (bis zu einem bestimmen Äquivalent) über beide Skalargruppen ist.

mrl11:Compact linkable ring signatures and applications

mrl11_abstract:We describe an efficient linkable ring signature scheme, compact linkable spontaneous anonymous group (CLSAG) signatures, for use in confidential transactions. Compared to the existing signature scheme used in Monero, CLSAG signatures are both smaller and more efficient to generate and verify for ring sizes of interest. We generalize the construction and show how it can be used to produce signatures with coins of different type in the same transaction.

iacr2020018_abstract:Ring signatures are a common construction used to provide signer ambiguity among a non-interactive set of public keys specified at the time of signing. Unlike early approaches where signature size is linear in the size of the signer anonymity set, current optimal solutions either require centralized trusted setups or produce signatures logarithmic in size. However, few also provide linkability, a property used to determine whether the signer of a message has signed any previous message, possibly with restrictions on the anonymity set choice. Here we introduce Triptych, a family of linkable ring signatures without trusted setup that is based on generalizations of zero-knowledge proofs of knowledge of commitment openings to zero. We demonstrate applications of Triptych in signer-ambiguous transaction protocols by extending the construction to openings of parallel commitments in independent anonymity sets. Signatures are logarithmic in the anonymity set size and, while verification complexity is linear, collections of proofs can be efficiently verified in batches. We show that for anonymity set sizes practical for use in distributed protocols, Triptych offers competitive performance with a straightforward construction.

cryptonote:CryptoNote-Whitepapers

cryptonote-whitepaper:CryptoNote-Whitepaper

cryptonote-whitepaper_para:Dies ist die originale Abhandlung über CryptoNote, welche vom CryptoNote-Team geschrieben wurde. Eine Lektüre hiervon wird eine grundlegende Einsicht in die Funktionsweise des CryptoNote-Algorithmus geben.

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.

mrl11:Compact linkable ring signatures and applications

mrl11_abstract:We describe an efficient linkable ring signature scheme, compact linkable spontaneous anonymous group (CLSAG) signatures, for use in confidential transactions. Compared to the existing signature scheme used in Monero, CLSAG signatures are both smaller and more efficient to generate and verify for ring sizes of interest. We generalize the construction and show how it can be used to produce signatures with coins of different type in the same transaction.

iacr2020018_abstract:Ring signatures are a common construction used to provide signer ambiguity among a non-interactive set of public keys specified at the time of signing. Unlike early approaches where signature size is linear in the size of the signer anonymity set, current optimal solutions either require centralized trusted setups or produce signatures logarithmic in size. However, few also provide linkability, a property used to determine whether the signer of a message has signed any previous message, possibly with restrictions on the anonymity set choice. Here we introduce Triptych, a family of linkable ring signatures without trusted setup that is based on generalizations of zero-knowledge proofs of knowledge of commitment openings to zero. We demonstrate applications of Triptych in signer-ambiguous transaction protocols by extending the construction to openings of parallel commitments in independent anonymity sets. Signatures are logarithmic in the anonymity set size and, while verification complexity is linear, collections of proofs can be efficiently verified in batches. We show that for anonymity set sizes practical for use in distributed protocols, Triptych offers competitive performance with a straightforward construction.

cryptonote:Cryptonote Whitepapers

cryptonote-whitepaper:Cryptonote Whitepaper

cryptonote-whitepaper_para:This is the original cryptonote paper written by the cryptonote team. Reading it will give an understanding about how the cryptonote algorithm works in general.

mrl10_abstract:Esta nota técnica describe un algoritmo usado para demostrar conocimiento del mismo logaritmo discreto a través de diferentes grupos. El esquema expresa el valor común cómo una representación escalado de bits y usa una serie de firmas de círculo que demuestra que cada bit es un valor legítimo, que es el mismo (hasta una equivalencia), a través de los grupos escalados.

mrl11:Compact linkable ring signatures and applications

mrl11_abstract:We describe an efficient linkable ring signature scheme, compact linkable spontaneous anonymous group (CLSAG) signatures, for use in confidential transactions. Compared to the existing signature scheme used in Monero, CLSAG signatures are both smaller and more efficient to generate and verify for ring sizes of interest. We generalize the construction and show how it can be used to produce signatures with coins of different type in the same transaction.

iacr2020018_abstract:Ring signatures are a common construction used to provide signer ambiguity among a non-interactive set of public keys specified at the time of signing. Unlike early approaches where signature size is linear in the size of the signer anonymity set, current optimal solutions either require centralized trusted setups or produce signatures logarithmic in size. However, few also provide linkability, a property used to determine whether the signer of a message has signed any previous message, possibly with restrictions on the anonymity set choice. Here we introduce Triptych, a family of linkable ring signatures without trusted setup that is based on generalizations of zero-knowledge proofs of knowledge of commitment openings to zero. We demonstrate applications of Triptych in signer-ambiguous transaction protocols by extending the construction to openings of parallel commitments in independent anonymity sets. Signatures are logarithmic in the anonymity set size and, while verification complexity is linear, collections of proofs can be efficiently verified in batches. We show that for anonymity set sizes practical for use in distributed protocols, Triptych offers competitive performance with a straightforward construction.

cryptonote:Libros Blancos de Cryptonote

cryptonote-whitepaper:Libro Blanco de Cryptonote

cryptonote-whitepaper_para:Este es el libro blanco original de CryptoNote escrito por el equipo de CryptoNote. Leerlo dará un entendimiento acerca de cómo funciona el algoritmo CryptoNote en general.

mrl10_abstract:Cette note technique décrit un algorithme utilisé pour prouver la connaissance du même logarithme discret dans différents groupes. Le schéma exprime la valeur commune sous la forme d'une représentation scalaire des bits et utilise un ensemble de signatures de cercle pour prouver que chaque bit est une valeur valide et identique (jusqu'à une équivalence) entres les deux groupes scalaires.

mrl11:Compact linkable ring signatures and applications

mrl11_abstract:We describe an efficient linkable ring signature scheme, compact linkable spontaneous anonymous group (CLSAG) signatures, for use in confidential transactions. Compared to the existing signature scheme used in Monero, CLSAG signatures are both smaller and more efficient to generate and verify for ring sizes of interest. We generalize the construction and show how it can be used to produce signatures with coins of different type in the same transaction.

iacr2020018_abstract:Ring signatures are a common construction used to provide signer ambiguity among a non-interactive set of public keys specified at the time of signing. Unlike early approaches where signature size is linear in the size of the signer anonymity set, current optimal solutions either require centralized trusted setups or produce signatures logarithmic in size. However, few also provide linkability, a property used to determine whether the signer of a message has signed any previous message, possibly with restrictions on the anonymity set choice. Here we introduce Triptych, a family of linkable ring signatures without trusted setup that is based on generalizations of zero-knowledge proofs of knowledge of commitment openings to zero. We demonstrate applications of Triptych in signer-ambiguous transaction protocols by extending the construction to openings of parallel commitments in independent anonymity sets. Signatures are logarithmic in the anonymity set size and, while verification complexity is linear, collections of proofs can be efficiently verified in batches. We show that for anonymity set sizes practical for use in distributed protocols, Triptych offers competitive performance with a straightforward construction.

cryptonote:Livres Blancs CryptoNote

cryptonote-whitepaper:Livre Blanc Cryptonote

cryptonote-whitepaper_para:Voici le document originel de CryptoNote écrit par l'équipe CryptoNote. En le lisant, vous comprendrez comment l'algorithme CryptoNote fonctionne d'une manière générale.

mrl9_abstract:Presentiamo multifirme a soglia (firme thring) per il calcolo collaborativo delle firme ad anello, presentiamo un gioco di falsificazione esistenziale per le firme e discutiamo gli usi delle firme in monete digitali che includono scambi atomici a catena incrociata ambigui in spesa per importi confidenziali senza una configurazione affidabile. Presentiamo un'implementazione di firme thring che chiamiamo firme di gruppo anonime con soglia spontanea collegabile e dimostriamo che l'implementazione non è falsificabile.

mrl10:Uguaglianza del logaritmo discreto fra i gruppi

mrl10_abstract:Questa nota tecnica descrive un algoritmo usato per provare la conoscenza del medesimo logaritmo discreto fra gruppi diversi. Lo schema esprime il valore comune come una rappresetazione scalare di bit, ed usa un set di firme ad anello per provare che ogni bit è un valore valido che è lo stesso (fino ad un'equivalenza) fra entrambi i gruppi scalari.

iacr2020018_abstract:Ring signatures are a common construction used to provide signer ambiguity among a non-interactive set of public keys specified at the time of signing. Unlike early approaches where signature size is linear in the size of the signer anonymity set, current optimal solutions either require centralized trusted setups or produce signatures logarithmic in size. However, few also provide linkability, a property used to determine whether the signer of a message has signed any previous message, possibly with restrictions on the anonymity set choice. Here we introduce Triptych, a family of linkable ring signatures without trusted setup that is based on generalizations of zero-knowledge proofs of knowledge of commitment openings to zero. We demonstrate applications of Triptych in signer-ambiguous transaction protocols by extending the construction to openings of parallel commitments in independent anonymity sets. Signatures are logarithmic in the anonymity set size and, while verification complexity is linear, collections of proofs can be efficiently verified in batches. We show that for anonymity set sizes practical for use in distributed protocols, Triptych offers competitive performance with a straightforward construction.

cryptonote:Whitepaper Cryptonote

cryptonote-whitepaper:Whitepaper Cryptonote

cryptonote-whitepaper_para:Questo è l'articolo originale su Cryptonote scritto dal team Cryptonote. La sua lettura fornirà una buona idea su come funziona l'algoritmo Cryptonote in generale.

mrl10_abstract:Deze technische notitie beschrijft een algoritme waarmee kennis van hetzelfde discrete logaritme tussen verschillende groepen kan worden bewezen. Hierin wordt de gedeelde waarde uitgedrukt als een scalaire weergave van bits, en wordt een verzameling ring-handtekeningen gebruikt om te bewijzen dat alle bits een geldige waarde hebben die hetzelfde is (tot een bepaalde equivalentie) in beide scalaire groepen.

mrl11:Compact linkable ring signatures and applications

mrl11_abstract:We describe an efficient linkable ring signature scheme, compact linkable spontaneous anonymous group (CLSAG) signatures, for use in confidential transactions. Compared to the existing signature scheme used in Monero, CLSAG signatures are both smaller and more efficient to generate and verify for ring sizes of interest. We generalize the construction and show how it can be used to produce signatures with coins of different type in the same transaction.

iacr2020018_abstract:Ring signatures are a common construction used to provide signer ambiguity among a non-interactive set of public keys specified at the time of signing. Unlike early approaches where signature size is linear in the size of the signer anonymity set, current optimal solutions either require centralized trusted setups or produce signatures logarithmic in size. However, few also provide linkability, a property used to determine whether the signer of a message has signed any previous message, possibly with restrictions on the anonymity set choice. Here we introduce Triptych, a family of linkable ring signatures without trusted setup that is based on generalizations of zero-knowledge proofs of knowledge of commitment openings to zero. We demonstrate applications of Triptych in signer-ambiguous transaction protocols by extending the construction to openings of parallel commitments in independent anonymity sets. Signatures are logarithmic in the anonymity set size and, while verification complexity is linear, collections of proofs can be efficiently verified in batches. We show that for anonymity set sizes practical for use in distributed protocols, Triptych offers competitive performance with a straightforward construction.

cryptonote:Cryptonote-whitepapers

cryptonote-whitepaper:Cryptonote Whitepaper

cryptonote-whitepaper_para:Dit is het oorspronkelijke Cryptonote-paper, geschreven door het Cryptonote-team. Het geeft een indruk van hoe het Cryptonote-algoritme in het algemeen werkt.

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.

mrl11:Compact linkable ring signatures and applications

mrl11_abstract:We describe an efficient linkable ring signature scheme, compact linkable spontaneous anonymous group (CLSAG) signatures, for use in confidential transactions. Compared to the existing signature scheme used in Monero, CLSAG signatures are both smaller and more efficient to generate and verify for ring sizes of interest. We generalize the construction and show how it can be used to produce signatures with coins of different type in the same transaction.

iacr2020018_abstract:Ring signatures are a common construction used to provide signer ambiguity among a non-interactive set of public keys specified at the time of signing. Unlike early approaches where signature size is linear in the size of the signer anonymity set, current optimal solutions either require centralized trusted setups or produce signatures logarithmic in size. However, few also provide linkability, a property used to determine whether the signer of a message has signed any previous message, possibly with restrictions on the anonymity set choice. Here we introduce Triptych, a family of linkable ring signatures without trusted setup that is based on generalizations of zero-knowledge proofs of knowledge of commitment openings to zero. We demonstrate applications of Triptych in signer-ambiguous transaction protocols by extending the construction to openings of parallel commitments in independent anonymity sets. Signatures are logarithmic in the anonymity set size and, while verification complexity is linear, collections of proofs can be efficiently verified in batches. We show that for anonymity set sizes practical for use in distributed protocols, Triptych offers competitive performance with a straightforward construction.

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.

mrl11:Compact linkable ring signatures and applications

mrl11_abstract:We describe an efficient linkable ring signature scheme, compact linkable spontaneous anonymous group (CLSAG) signatures, for use in confidential transactions. Compared to the existing signature scheme used in Monero, CLSAG signatures are both smaller and more efficient to generate and verify for ring sizes of interest. We generalize the construction and show how it can be used to produce signatures with coins of different type in the same transaction.

iacr2020018_abstract:Ring signatures are a common construction used to provide signer ambiguity among a non-interactive set of public keys specified at the time of signing. Unlike early approaches where signature size is linear in the size of the signer anonymity set, current optimal solutions either require centralized trusted setups or produce signatures logarithmic in size. However, few also provide linkability, a property used to determine whether the signer of a message has signed any previous message, possibly with restrictions on the anonymity set choice. Here we introduce Triptych, a family of linkable ring signatures without trusted setup that is based on generalizations of zero-knowledge proofs of knowledge of commitment openings to zero. We demonstrate applications of Triptych in signer-ambiguous transaction protocols by extending the construction to openings of parallel commitments in independent anonymity sets. Signatures are logarithmic in the anonymity set size and, while verification complexity is linear, collections of proofs can be efficiently verified in batches. We show that for anonymity set sizes practical for use in distributed protocols, Triptych offers competitive performance with a straightforward construction.

cryptonote:Livros Brancos do CryptoNote

cryptonote-whitepaper:Livro Branco do CryptoNote

cryptonote-whitepaper_para:Este é o artigo original escrito pela equipe do CryptoNote. Sua leitura dá um entendimento básico sobre como funciona o algoritmo do CryptoNote.

mrl10_abstract:В данной технической записке содержится описание алгоритма, обеспечивающего доказательство знания дискретного логарифма в различных группах. Схема выражает общее значение в виде скалярного представления битов и использует набор кольцевых подписей для доказательства того, что значение каждого бита действительно и одинаково (вплоть до полной эквивалентности) в обеих скалярных группах.

mrl11:Компактные связываемые кольцевые подписи и приложения

mrl11_abstract:Мы описываем эффективную схему связываемой кольцевой подписи - компактную, спонтанно связываемую анонимную групповую подпись (CLSAG) для использования в конфиденциальных транзакциях. По сравнению с существующей схемой подписи, используемой в Monero, подписи CLSAG меньше и более эффективны для генерации и проверки размеров колец. Мы объединяем конструкцию и показываем, как ее можно использовать для получения подписей с монетами разного типа в одной транзакции.

iacr2020018_abstract:Ring signatures are a common construction used to provide signer ambiguity among a non-interactive set of public keys specified at the time of signing. Unlike early approaches where signature size is linear in the size of the signer anonymity set, current optimal solutions either require centralized trusted setups or produce signatures logarithmic in size. However, few also provide linkability, a property used to determine whether the signer of a message has signed any previous message, possibly with restrictions on the anonymity set choice. Here we introduce Triptych, a family of linkable ring signatures without trusted setup that is based on generalizations of zero-knowledge proofs of knowledge of commitment openings to zero. We demonstrate applications of Triptych in signer-ambiguous transaction protocols by extending the construction to openings of parallel commitments in independent anonymity sets. Signatures are logarithmic in the anonymity set size and, while verification complexity is linear, collections of proofs can be efficiently verified in batches. We show that for anonymity set sizes practical for use in distributed protocols, Triptych offers competitive performance with a straightforward construction.

cryptonote-whitepaper_para:Это оригинальный документ по Cryptonote, написанный командой Cryptonote. Благодаря ему читатель может понять, как в целом работает алгоритм Cryptonote.

mrl10_abstract:Bu teknik not farklı gruplar arasında aynı ayrık logaritmanın bilgisini kanıtlamakta kullanılan bir algoritmayı betimler. Şema bitlerin skalar bir temsilini ortak değer olarak ifade eder ve bir halka imzalar kümesini her bitin iki skalar grup arasında (bir denkliğe kadar) aynı olan geçerli bir değer olduğunu kanıtlamak için kullanır.

mrl11:Compact linkable ring signatures and applications

mrl11_abstract:We describe an efficient linkable ring signature scheme, compact linkable spontaneous anonymous group (CLSAG) signatures, for use in confidential transactions. Compared to the existing signature scheme used in Monero, CLSAG signatures are both smaller and more efficient to generate and verify for ring sizes of interest. We generalize the construction and show how it can be used to produce signatures with coins of different type in the same transaction.

iacr2020018_abstract:Ring signatures are a common construction used to provide signer ambiguity among a non-interactive set of public keys specified at the time of signing. Unlike early approaches where signature size is linear in the size of the signer anonymity set, current optimal solutions either require centralized trusted setups or produce signatures logarithmic in size. However, few also provide linkability, a property used to determine whether the signer of a message has signed any previous message, possibly with restrictions on the anonymity set choice. Here we introduce Triptych, a family of linkable ring signatures without trusted setup that is based on generalizations of zero-knowledge proofs of knowledge of commitment openings to zero. We demonstrate applications of Triptych in signer-ambiguous transaction protocols by extending the construction to openings of parallel commitments in independent anonymity sets. Signatures are logarithmic in the anonymity set size and, while verification complexity is linear, collections of proofs can be efficiently verified in batches. We show that for anonymity set sizes practical for use in distributed protocols, Triptych offers competitive performance with a straightforward construction.

cryptonote:Cryptonote Beyaz Bültenleri

cryptonote-whitepaper:Cryptonote Beyaz Bülteni

cryptonote-whitepaper_para:Bu, Cryptonote ekibi tarafından yazılan orijinal cryptonote makalesidir. Okumak size cryptonote algoritmasının genelde nasıl çalıştığı anlayışını verecektir.

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.

mrl10:Discrete Logarithm Equality Across Groups

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.

iacr2020018_abstract:Ring signatures are a common construction used to provide signer ambiguity among a non-interactive set of public keys specified at the time of signing. Unlike early approaches where signature size is linear in the size of the signer anonymity set, current optimal solutions either require centralized trusted setups or produce signatures logarithmic in size. However, few also provide linkability, a property used to determine whether the signer of a message has signed any previous message, possibly with restrictions on the anonymity set choice. Here we introduce Triptych, a family of linkable ring signatures without trusted setup that is based on generalizations of zero-knowledge proofs of knowledge of commitment openings to zero. We demonstrate applications of Triptych in signer-ambiguous transaction protocols by extending the construction to openings of parallel commitments in independent anonymity sets. Signatures are logarithmic in the anonymity set size and, while verification complexity is linear, collections of proofs can be efficiently verified in batches. We show that for anonymity set sizes practical for use in distributed protocols, Triptych offers competitive performance with a straightforward construction.

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.

mrl10:Discrete Logarithm Equality Across Groups

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.

iacr2020018_abstract:Ring signatures are a common construction used to provide signer ambiguity among a non-interactive set of public keys specified at the time of signing. Unlike early approaches where signature size is linear in the size of the signer anonymity set, current optimal solutions either require centralized trusted setups or produce signatures logarithmic in size. However, few also provide linkability, a property used to determine whether the signer of a message has signed any previous message, possibly with restrictions on the anonymity set choice. Here we introduce Triptych, a family of linkable ring signatures without trusted setup that is based on generalizations of zero-knowledge proofs of knowledge of commitment openings to zero. We demonstrate applications of Triptych in signer-ambiguous transaction protocols by extending the construction to openings of parallel commitments in independent anonymity sets. Signatures are logarithmic in the anonymity set size and, while verification complexity is linear, collections of proofs can be efficiently verified in batches. We show that for anonymity set sizes practical for use in distributed protocols, Triptych offers competitive performance with a straightforward construction.