[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-46278-en":3,"doc-seo-46278-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},46278,13056703019662,"Evangeline","https://ap-avatar.wpscdn.com/avatar/be000253a8e92610077?_k=1778726343310543188",6,"Technology","Zero to Monero Second Edition Technical Guide to a Private Digital Currency","Cryptography-based foundations of the private digital currency Monero are taught for readers with basic algebra and simple computer science knowledge. The guide explains why secure communication and cryptocurrencies rely on cryptographic primitives, and how blockchains enable public verification through distributed ledgers. It then details how transactions can hide participants and amounts while remaining verifiable, highlighting Monero’s use of Ed25519 elliptic-curve cryptography, linkable signatures, concealed amounts, and range proofs such as Bulletproofs.","Zero to Monero: Second Edition  \na technical guide to a private digital currency; for beginners, amateurs, and experts  \nPublished April 4, 2020 (v2.0.0)  \nkoe 1 , Kurt M. Alonso2 , Sarang Noether3  \nLicense: Zero to Monero: Second Edition is released into the public domain.  \n[1](1 ukoe@protonmail.com)[ ukoe@protonmail.com](1 ukoe@protonmail.com)  \n[2](2 kurt@oktav.se)[ kurt@oktav.se](2 kurt@oktav.se)  \n[3](3 sarang.noether@protonmail.com)[ sarang.noether@protonmail.com](3 sarang.noether@protonmail.com)  \nAbstract  \nCryptography. It may seem like only mathematicians and computer scientists have access to this obscure, esoteric, powerful, elegant topic. In fact, many kinds of cryptography are simple enough that anyone can learn their fundamental concepts.  \nIt is common knowledge that cryptography is used to secure communications, whether they be coded letters or private digital interactions. Another application isin so-called cryptocurrencies. These digital moneys use cryptography to assign and transfer ownership of funds. To ensure that no piece of money can be duplicated or created at will, cryptocurrencies usually rely on `blockchains', which are public, distributed ledgers containing records of currency transactions that can be veri􀀌ed by third parties [97] .  \nIt might seem at 􀀌rst glance that transactions need to be sent and stored in plain text format to make them publicly veri􀀌able. In fact, it is possible to conceal a transaction's participants, as well as the amounts involved, using cryptographic tools that nevertheless allow transactions to be veri􀀌ed and agreed upon by observers [136] . This is exempli􀀌ed in the cryptocurrency Monero.  \nWe endeavor here to teach anyone who knows basic algebra and simple computer science concepts like the `bit representation' of a number not only how Monero works at a deep and comprehensive level, but also how useful and beautiful cryptography can be.  \nFor our experienced readers: Monero is a standard one-dimensional distributed acyclic graph (DAG) cryptocurrency blockchain [97] where transactions are based on elliptic curve cryptography using curve Ed25519 [38], transaction inputs are signed with Schnorr-style multilayered linkable spontaneous anonymous group signatures (MLSAG) [108], and output amounts (communicated to recipients via ECDH [52]) are concealed with Pedersen commitments [88] and proven in a legitimate range with Bulletproofs [43] . Much of the 􀀌rst part of this report is spent explaining these ideas.  \nContents  \n1 Introduction 1  \n1.1 Objectives ......................................... 2  \n1.2 Readership ........................................ 3  \n1.3 Origins of the Monero cryptocurrency ......................... 3  \n1.4 Outline .......................................... 4  \n1.4.1 Part 1: `Essentials' ................................ 4  \n1.4.2 Part 2: `Extensions' ............................... 4  \n1.4.3 Additional content ................................ 5  \n1.5 Disclaimer ......................................... 5  \n1.6 History of Zero to Monero ................................ 5  \n1.7 Acknowledgements .................................... 6  \nI Essentials 7  \n2 Basic Concepts 8  \n2.1 A few words about notation ............................... 8  \n2.2 Modular arithmetic .................................... 9  \n2.2.1 Modular addition and multiplication ...................... 10  \n2.2.2 Modular exponentiation ............................. 11  \n2.2.3 Modular multiplicative inverse ......................... 11  \n2.2.4 Modular equations ................................ 12  \n2.3 Elliptic curve cryptography ............................... 13  \n2.3.1 What are elliptic curves? ............................ 13  \n2.3.2 Public key cryptography with elliptic curves .................. 16  \n2.3.3 Di􀀎e-Hellman key exchange with elliptic curves ................ 16  \n2.3.4 Schnorr signatures and the Fiat-Shamir transform .............. 16  \n2.3.5 Signing messages ...............","cbCaioQcfperGCjC","https://ap.wps.com/l/cbCaioQcfperGCjC","pdf",1025788,4,1,154,"English","en",105,"# Introduction\n## Objectives\n## Readership\n## Origins of the Monero cryptocurrency\n## Outline\n## Disclaimer\n## History of Zero to Monero\n## Acknowledgements\n# Essentials\n## Basic Concepts\n## Elliptic curve cryptography\n## Advanced Schnorr-like Signatures\n## Monero Addresses\n## Monero Amount Hiding\n## Monero Ring Confidential Transactions (RingCT)","[{\"question\":\"What cryptography concepts does the guide focus on for learning Monero?\",\"answer\":\"It focuses on cryptographic fundamentals used by Monero, including elliptic curve cryptography (such as Ed25519), signatures built from Schnorr-style approaches, and techniques for hiding transaction participants and amounts while preserving verifiability.\"},{\"question\":\"How does Monero allow transactions to be publicly verifiable without revealing participants or amounts?\",\"answer\":\"The guide explains that cryptographic tools can conceal participants and amounts yet still enable observers to verify and agree on the transaction. Monero exemplifies this approach using privacy-preserving transaction constructions.\"},{\"question\":\"Which cryptographic mechanisms does the guide mention as core components of Monero?\",\"answer\":\"It highlights elliptic curve cryptography using curve Ed25519, transaction input signing with linkable spontaneous anonymous group signatures (MLSAG), amount concealment communicated via ECDH with Pedersen commitments, and range proofs using Bulletproofs.\"}]",1783516426,388,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"zero-to-monero-second-edition-technical-guide-to-a-private-digital-currency","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/technology/",3,{"item":52,"name":13,"@type":43,"position":20},"https://docshare.wps.com/document/zero-to-monero-second-edition-technical-guide-to-a-private-digital-currency/46278/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-15","2026-07-08",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What cryptography concepts does the guide focus on for learning Monero?","Question",{"text":75,"@type":76},"It focuses on cryptographic fundamentals used by Monero, including elliptic curve cryptography (such as Ed25519), signatures built from Schnorr-style approaches, and techniques for hiding transaction participants and amounts while preserving verifiability.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does Monero allow transactions to be publicly verifiable without revealing participants or amounts?",{"text":80,"@type":76},"The guide explains that cryptographic tools can conceal participants and amounts yet still enable observers to verify and agree on the transaction. Monero exemplifies this approach using privacy-preserving transaction constructions.",{"name":82,"@type":73,"acceptedAnswer":83},"Which cryptographic mechanisms does the guide mention as core components of Monero?",{"text":84,"@type":76},"It highlights elliptic curve cryptography using curve Ed25519, transaction input signing with linkable spontaneous anonymous group signatures (MLSAG), amount concealment communicated via ECDH with Pedersen commitments, and range proofs using Bulletproofs.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,113,118,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":111,"slug":112},50,"technology",{"id":114,"doc_module":4,"doc_module_name":46,"category_name":115,"show_sort_weight":116,"slug":117},7,"Healthcare",40,"healthcare",{"id":119,"doc_module":4,"doc_module_name":46,"category_name":120,"show_sort_weight":121,"slug":122},8,"Research & Report",30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]