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Mechanics of Mobilecoin: First Edition
Mechanics of MobileCoin: First Edition exploring the foundations of a private digital currency April 6, 2021, Preview (10/11) v0.0.39 koe1,2 DRAFT INFORMATION: This is just a draft, and may not always be available wher- ever it is currently hosted. The final version will be available at https://github.com/ mobilecoinfoundation. License: `Mechanics of MobileCoin: First Edition' is released into the public domain. 1 [email protected] 2 Author `koe' worked on this document as part of a private contract with, then as an employee of, MobileCoin, Inc. Abstract Cryptography. 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. It is common knowledge that cryptography is used to secure communications, whether they be coded letters or private digital interactions. Another application is in 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 verified by third parties [115]. It might seem at first glance that transactions need to be sent and stored in plain text format to make them publicly verifiable. In truth, it is possible to conceal a transaction's participants, as well as the amounts involved, using cryptographic tools that nevertheless allow transactions to be verified and agreed upon by observers [151]. This is exemplified in the cryptocurrency MobileCoin. -
Perfectly Hiding Commitment Scheme with Two-Round from Any One-Way Permutation ∗
Perfectly Hiding Commitment Scheme with Two-Round from Any One-Way Permutation ¤ Chunming Tang1;y Dingyi Pei1 Zhuojun Liu2 Zheng-an Yao3 Mingsheng Wang4 1 School of Mathematics and Information Sciences, Guangzhou University, China(510006) 2 Key Laboratory of Mathematics Mechanization, AMSS, CAS, China(100080) 3 School of Mathematics and Statistics, Zhongshan University, China(510006) 4 State Key Laboratory of Information Security, Institute of Software, CAS China(100080) Abstract Commitment schemes are arguably among the most important and useful primitives in cryp- tography. According to the computational power of receivers, commitments can be classi¯ed into three possible types: computational hiding commitments, statistically hiding commitments and perfect computational commitments. The ¯st commitment with constant rounds had been constructed from any one-way functions in last centuries, and the second with non-constant rounds were constructed from any one-way functions in FOCS2006, STOC2006 and STOC2007 respectively, furthermore, the lower bound of round complexity of statistically hiding commit- n ments has been proven to be logn rounds under the existence of one-way function. Perfectly hiding commitments implies statistically hiding, hence, it is also infeasible to con- struct a practically perfectly hiding commitments with constant rounds under the existence of one-way function. In order to construct a perfectly hiding commitments with constant rounds, we have to relax the assumption that one-way functions exist. In this paper, we will construct a practically perfectly hiding commitment with two-round from any one-way permutation. To the best of our knowledge, these are the best results so far. Keywords: Cryptography, perfectly hiding commitments, one-way permutation, §-protocol. -
Quantum Bit Commitment and Coin Tossing Protocols
Quantum Bit Commitment and Coin Tossing Protocols Gilles Brassard * Claude Crepeau t Departement d'informatique et de R.O. Laboratoire de Recherche en Informatique Universite de Montreal University de Paris-Sud C.P. 6128, succ. "A" Batiment 490 Montreal, Quebec CANADA H3C 3J7 91405 Orsay FRANCE 1 Introduction In the late 1960's a physicist, Stephen Wiesner, had the idea that the uncertainty principle could be used for cryptography (though he published his result much later [Wie83]). One of his ideas was that it would be possible to use a stream of polarized photons to transmit two messages in a way that would make only one of them readable at the receiver's choosing. This notion, which he called "multiplexing", is remarkably similar to the "one-out-of-two oblivious transfer" to be reinvented many years later [EGL83], and it even predates Rabin's notion of oblivious transfer [Rab81] by more than a decade. In the late 1970's, Wiesner's invention was brought back to life by the work of Charles H. Bennett and Gilles Brassard, which resulted in a CRYPTO '82 paper [BBBW82]. Subsequently, Bennett and Brassard used quantum cryptographic principles to implement basic cryptographic protocols, such as secret key exchange and coin tossing by telephone [BB84]. There has been recently much excitement in the field of quantum cryptography because a working prototype of the quantum key exchange channel has been successfully built at the IBM T. J. Watson Research Laboratory, Yorktown Heights [BBBSS90]. In recent times, the importance of cryptographic primitives has been brought to light by the work of many researchers whose goal is to characterize precisely the primitives sufficient for the implementation of various cryptographic protocols. -
A New and Efficient Signature on Commitment Values
International Journal of Network Security, Vol.7, No.1, PP.101–106, July 2008 101 A New and Efficient Signature on Commitment Values Fangguo Zhang1,3, Xiaofeng Chen2,3, Yi Mu4, and Willy Susilo4 (Corresponding author: Fangguo Zhang) Department of Electronics and Communication Engineering, Sun Yat-Sen University1 Guangzhou 510275, P. R. China (Email: [email protected]) Department of Computer Science, Sun Yat-Sen University, Guangzhou 510275, P. R. China2 Guangdong Key Laboratory of Information Security Technology Guangzhou 510275, P. R. China3 School of IT and Computer Science University of Wollongong, Wollongong, NSW 2522, Australia4 (Received July 15, 2006; revised and accepted Nov. 8, 2006) Abstract user, it cannot be transferred to any one else, i.e. “non- transferability”. It is desirable that the overheads of com- We present a new short signature scheme based on a vari- munication and computation imposed by a credential sys- ant of the Boneh-Boyen’s short signatures schemes. Our tem to users and services must not heavily affect their short signature scheme is secure without requiring the performance. random oracle model. We show how to prove a commit- The studies of anonymous credential have gone through ted value embedded in our short signature. Using this several stages. After its introduction by Chaum, Brands primitive, we construct an efficient anonymous credential presented a public key based construction of anonymous system. credential in which a user can provide in zero knowledge Keywords: Anonymity, anonymous credentials, commit- that the credentials encoded by its certificate satisfy a ment, signature given linear Boolean formula [6]. This scheme allows only one show, namely, two transactions from the same user can be found performed by the same user. -
One-Way Functions Imply Secure Computation in a Quantum World
One-Way Functions Imply Secure Computation in a Quantum World James Bartusek* Andrea Coladangelo† Dakshita Khurana‡ Fermi Ma§ Abstract We prove that quantum-hard one-way functions imply simulation-secure quantum oblivious transfer (QOT), which is known to suffice for secure computation of arbitrary quantum functionalities. Further- more, our construction only makes black-box use of the quantum-hard one-way function. Our primary technical contribution is a construction of extractable and equivocal quantum bit commit- ments based on the black-box use of quantum-hard one-way functions in the standard model. Instantiating the Crépeau-Kilian (FOCS 1988) framework with these commitments yields simulation-secure QOT. arXiv:2011.13486v2 [quant-ph] 13 Aug 2021 *UC Berkeley. Email: [email protected] †UC Berkeley. Email: [email protected] ‡UIUC. Email: [email protected] §Princeton University and NTT Research. Email: [email protected] 1 Contents 1 Introduction 3 1.1 OurResults ...................................... ......... 4 1.2 RelatedWork ..................................... ......... 6 1.3 ConcurrentandIndependentWork. .............. 6 2 Technical Overview 8 2.1 Recap: Quantum Oblivious Transfer from Commitments . .................. 8 2.2 Our Construction: A High-Level Overview . ................ 10 2.3 Making Any Quantum (or Classical) Commitment Equivocal ................... 11 2.4 An Extractability Compiler for Equivocal Commitments . .................... 13 2.5 Putting it Together: From Commitments to Secure Computation. -
Practical and Provably-Secure Commitment Schemes from Collision-Free Hashing
Practical and Provably-Secure Commitment Schemes from Collision-Free Hashing Shai Halevi ? Silvio Micali MIT { Laboratory for Computer Science, 545 Technology Square, Cambridge, MA 02139 Abstract. We present a very practical string-commitment scheme which is provably secure based solely on collision-free hashing. Our scheme en- ables a computationally bounded party to commit strings to an unbounded one, and is optimal (within a small constant factor) in terms of interac- tion, communication, and computation. Our result also proves that constant round statistical zero-knowledge arguments and constant-round computational zero-knowledge proofs for NP exist based on the existence of collision-free hash functions. 1 Introduction String commitment is a fundamental primitive for cryptographic protocols. A commitment scheme is an electronic way to temporarily hide a value that cannot be changed. Such a scheme emulates by means of a protocol the following two- stage process. In Stage 1 (the Commit stage), a party called the Sender locks a message in a box, and sends the locked box to another party called the receiver. In Stage 2 (the De-commit stage), the Sender provides the Receiver with the key to the box, thus enabling him to learn the original message. Commitment-schemes are very useful building blocks in the design of larger cryptographic protocols. They are typically used as a mean of flipping fair coins between two players, and also play a crucial part in some zero-knowledge proofs and in various types of signature schemes. Commitment schemes can also be used in scenarios like bidding for a contract, where committing to a bid rather than sending it in the clear can eliminate the risk of it being \leaked" to the competitors. -
Carback, R.T.: Security Innovations In
APPROVAL SHEET Title of Thesis: Security Innovations in the Punchscan Voting System Name of Candidate: Richard T. Carback III Master of Science, 2008 Thesis and Abstract Approved: Alan T. Sherman Associate Professor Department of Computer Science and Electrical Engineering Date Approved: April 18th, 2008 Curriculum Vitae Name: Richard T. Carback III. Permanent Address: 2819 Manoff Rd, Halethorpe, MD 21227. Degree and date to be conferred: Master of Science, August 2007. Date of Birth: March 27, 1983. Place of Birth: Baltimore, Maryland. Secondary Education: Chesapeake High School, Pasadena, Maryland, 2001. Collegiate institutions attended: University of Maryland Baltimore County, Master of Science, Computer Science, 2008. Bachelor of Science, Computer Science, 2005. Major: Computer Science. Minor: None. Professional publications: • David Chaum, Richard Carback, Jeremy Clark, Aleksander Essex, Stefan Popoveniuc, Ronald L. Rivest, Peter Y.A. Ryan, Emily Shen, and Alan T. Sherman. Scantegrity II: End-to-End Verifiability for Optical Scan Election Systems using Invisible Ink Confirmation Codes. Submitted to USENIX EVT 2008. • Russell A. Fink, Alan T. Sherman, and Richard Carback. TPM Meets DRE: Reducing the Trust Base for Electronic Voting using Trusted Platform Modules. Submitted to USENIX EVT 2008. • David Chaum, Aleksander Essex, Richard Carback, Jeremy Clark, Stefan Popoveniuc, Alan T. Sherman, and Poorvi Vora. Scantegrity: End-to- end voter verifiable optical-scan voting. Accepted for publication in IEEE Security and Privacy, volume May/June, 2008. • Stefan Popoveniuc, Jeremy Clark, Richard Carback, and Aleksander Essex. Securing optical-scan voting. Presented at Dagstuhl. To be published in Towards Trustworthy Election Systems in the Lecture Notes in Computer Science series by Spinger-Verlag, date unknown. -
Ring Confidential Transactions
ISSN 2379-5980 (online) DOI 10.5195/LEDGER.2016.34 RESEARCH ARTICLE Ring Confidential Transactions Shen Noether,∗ Adam Mackenzie, the Monero Research Lab† Abstract. This article introduces a method of hiding transaction amounts in the strongly decentralized anonymous cryptocurrency Monero. Similar to Bitcoin, Monero is a cryptocur- rency which is distributed through a proof-of-work “mining” process having no central party or trusted setup. 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 dis- cussed and implemented by Bitcoin Core developer Gregory Maxwell. In this article, a new type of ring signature, A Multilayered Linkable Spontaneous Anonymous Group signature is described which allows one to include a Pedersen Commitment in a ring signature. This construction results in a digital currency with hidden amounts, origins and destinations of transactions with reasonable efficiency and verifiable, trustless coin generation. The author would like to note that early drafts of this were publicized in the Monero Community and on the #bitcoin-wizards IRC channel. Blockchain hashed drafts are available showing that this work was started in Summer 2015, and completed in early October 2015.17 An eprint is also available at http://eprint.iacr.org/2015/1098. 1. Introduction Recall that in Bitcoin each transaction is signed by the owner of the coins being sent and these signatures verify that the owner is allowed to send the coins. This is entirely analogous to the signing of a check from your bank. -
El Gamal Mix-Nets and Implementation of a Verifier
KTH Royal Institute of Technology School of Computer Science and Communication El Gamal Mix-Nets and Implementation of a Verifier SA104X Degree Project in Engineering Physics Erik Larsson ([email protected]) Carl Svensson ([email protected]) Supervisor: Douglas Wikstr¨om Abstract A mix-net is a cryptographic protocol based on public key cryptography which enables untraceable communication through a collection of nodes. One important application is electronic voting where it enables the construction of systems which satisfies many voting security requirements, including veri- fiability of correct execution. Verificatum is an implementation of a mix-net by Douglas Wikstr¨om. This report concerns the implementation of a verifier and evaluation of the implementation manual for the Verificatum mix-net. The purpose of the document is to enable third parties to convince themselves that the mix- net has behaved correctly without revealing any secret information. This implementation is a simple version of the verifier using the document and some test vectors generated by the mix-net. The document contains all information but there are still some possibilities for further clarification in order to make it comprehensible to a larger audience. Contents 1 Introduction 2 1.1 Verificatum . 2 1.2 Goals and Scope . 3 2 Background 3 2.1 El Gamal Cryptography . 3 2.1.1 Definition . 4 2.1.2 Security . 4 2.1.3 Properties . 5 2.2 Cryptographic Primitives . 6 2.2.1 Hash functions . 6 2.2.2 Pseudo Random Generators . 6 2.2.3 Random Oracles . 7 2.3 Mix Networks . 7 2.3.1 Overview . 7 2.3.2 El Gamal Mix-Nets . -
Multiparty Routing: Secure Routing for Mixnets
Multiparty Routing: Secure Routing for Mixnets Fatemeh Shirazi Elena Andreeva Markulf Kohlweiss Claudia Diaz imec - COSIC KU Leuven imec - COSIC KU Leuven Microsoft Research imec - COSIC KU Leuven Leuven, Belgium Leuven, Belgium Cambridge, UK Leuven, Belgium Abstract—Anonymous communication networks are impor- re-mailer, Freenet [5], [6] used for anonymous file-sharing, and tant building blocks for online privacy protection. One approach DC-Nets [7] that can be deployed for broadcast applications to achieve anonymity is to relay messages through multiple such as group messaging. routers, where each router shuffles messages independently. To achieve anonymity, at least one router needs to be honest. The goal of ACNs is to anonymize communications by In the presence of an adversary that is controlling a subset relaying them over multiple routers. There are three main types of the routers unbiased routing is important for guaranteeing of anonymous routing in terms of how routers are chosen to anonymity. However, the routing strategy also influenced other form the path. factors such as the scalability and the performance of the system. One solution is to use a fixed route for relaying all messages First, in deterministic routing, the paths are predetermined with many routers. If the route is not fixed the routing decision by the system configuration. Chaum’s original ACN pro- can either be made by the communication initiator or the posal [1] considered a sequence of mixes organized in a intermediate routers. However, the existing routing types each cascade. Systems that adopted the cascade network topology have limitations. For example, one faces scalability issues when in their designs include JAP [8], and voting systems, such as increasing the throughput of systems with fixed routes. -
An Implementation of Dual (Paper and Cryptographic) Voting System
Tel Aviv University Raymond and Beverly Sackler Faculty of Exact Sciences The Blatavnik School of Computer Sciences An Implementation of Dual (Paper and Cryptograhic) Voting System Submitted as a partial fulfillment of the requirements towards the Master of Science degree by Niko Farhi The research work has been conducted under the supervision of Prof. Amnon Ta-Shma March 2013 Abstract This thesis reports on the design and implementation of a cryptographic voting system, named Wombat. The system is designed to retain the ”look and feel” of standard paper- based plurality voting, while enhancing security using methods from modern electronic voting literature. To achieve this, the system executes two voting processes in parallel: one is electronic and end-to-end verifiable, while the other is paper based and emulates more traditional processes (to which the voters are accustomed). Consistency between the two processes is enforced by means of a new specially-tailored paper ballot format. In addition, this work examines the practicality of the Wombat protocol through im- plementation and field testing in two student council elections with over 2000 voters and party premiership elections with almost 900 voters. During these field test the usabilty, performance and voter satisfaction was examined. Overall, voters trusted the system and found it comfortable to use. Parts of this work were presented in EVote2012. ii Acknowledgments I wish to thank my advisor, Prof. Amnon Ta-Shma for his patience with me. I also wish to thank Mr. Ben Riva for providing aid when it was needed. iii Contents Abstract ii Acknowledgments iii 1 Introduction 1 1.1 ThesisOutline................................ -
The Scantegrity Voting System and Its Use in the Takoma Park Elections
The Scantegrity Voting System and its Use in the Takoma Park Elections David Chaum Richard T. Carback Jeremy Clark Aleksander Essex Travis Mayberry Stefan Popoveniuc Ronald L. Rivest Emily Shen Alan T. Sherman Poorvi L. Vora John Wittrock Filip Zagórski 1 Introduction The Scantegrity project began with a simple question: is it possible to design a voting system offering the strong security properties of cryptographic end-to-end (E2E) election verification with the intuitive look and feel of a paper optical-scan ballot? This chapter recounts a decade-long research effort toward answering this question, from the design of Scantegrity’s precursor Punchscan, all the way to the first governmental election run by an E2E voting system. The main focus of this chapter is on the Scantegrity II voting system (hereafter referred to as simply Scantegrity) and its use in the municipal elections of Takoma Park, MD in 2009 and 2011. To our knowledge, the Takoma Park election of 2009 was the first use of an E2E-verifiable voting system in an in-person secret-ballot governmental election anywhere in the world, as well as being the first governmental election held in the United States to run on open-source software. We also describe the Punchscan voting system and its use in the 2007 election of the the University of Ottawa Graduate Students Association/Association Étudiant(e)s Diplômé(e)s (GSAÉD), which, to our knowledge, is the first time an E2E voting system was used in a binding election.1 Additionally, this chapter describes the remote voting system Remotegrity and accessible Scantegrity variant Audiotegrity, and their use in the 2011 Takoma Park election.