Cryptocurrency with Prime Number Proof-Of-Work
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Useful Computation on the Block Chain The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Yeung, Fuk. 2019. Useful Computation on the Block Chain. Master's thesis, Harvard Extension School. Citable link https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37364565 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA 111 Useful Computation on the Block Chain Fuk Yeung A Thesis in the Field of Information Technology for the Degree of Master of Liberal Arts in Extension Studies Harvard University November 2019 Copyright 2019 [Fuk Yeung] Abstract The recent growth of blockchain technology and its usage has increased the size of cryptocurrency networks. However, this increase has come at the cost of high energy consumption due to the processing power needed to maintain large cryptocurrency networks. In the largest networks, this processing power is attributed to wasted computations centered around solving a Proof of Work algorithm. There have been several attempts to address this problem and it is an area of continuing improvement. We will present a summary of proposed solutions as well as an in-depth look at a promising alternative algorithm known as Proof of Useful Work. This solution will redirect wasted computation towards useful work. We will show that this is a viable alternative to Proof of Work. Dedication Thank you to everyone who has supported me throughout the process of writing this piece. -
Piecework: Generalized Outsourcing Control for Proofs of Work
(Short Paper): PieceWork: Generalized Outsourcing Control for Proofs of Work Philip Daian1, Ittay Eyal1, Ari Juels2, and Emin G¨unSirer1 1 Department of Computer Science, Cornell University, [email protected],[email protected],[email protected] 2 Jacobs Technion-Cornell Institute, Cornell Tech [email protected] Abstract. Most prominent cryptocurrencies utilize proof of work (PoW) to secure their operation, yet PoW suffers from two key undesirable prop- erties. First, the work done is generally wasted, not useful for anything but the gleaned security of the cryptocurrency. Second, PoW is natu- rally outsourceable, leading to inegalitarian concentration of power in the hands of few so-called pools that command large portions of the system's computation power. We introduce a general approach to constructing PoW called PieceWork that tackles both issues. In essence, PieceWork allows for a configurable fraction of PoW computation to be outsourced to workers. Its controlled outsourcing allows for reusing the work towards additional goals such as spam prevention and DoS mitigation, thereby reducing PoW waste. Meanwhile, PieceWork can be tuned to prevent excessive outsourcing. Doing so causes pool operation to be significantly more costly than today. This disincentivizes aggregation of work in mining pools. 1 Introduction Distributed cryptocurrencies such as Bitcoin [18] rely on the equivalence \com- putation = money." To generate a batch of coins, clients in a distributed cryp- tocurrency system perform an operation called mining. Mining requires solving a computationally intensive problem involving repeated cryptographic hashing. Such problem and its solution is called a Proof of Work (PoW) [11]. As currently designed, nearly all PoWs suffer from one of two drawbacks (or both, as in Bitcoin). -
Alternative Mining Puzzles
Cryptocurrency Technologies Alternative Mining Puzzles Alternative Mining Puzzles • Essential Puzzle Requirements • ASIC-Resistant Puzzles • Proof-of-Useful-Work • Non-outsourceable Puzzles • Proof-of-Stake “Virtual Mining” Puzzles (recap) Incentive system steers participants Basic features of Bitcoin’s puzzle The puzzle is difficult to solve, so attacks are costly … but not too hard, so honest miners are compensated Q: What other features could a puzzle have? 1 Cryptocurrency Technologies Alternative Mining Puzzles On today’s menu . Alternative puzzle designs Used in practice, and speculative Variety of possible goals ASIC resistance, pool resistance, intrinsic benefits, etc. Essential security requirements Alternative Mining Puzzles • Essential Puzzle Requirements • ASIC-Resistant Puzzles • Proof-of-Useful-Work • Non-outsourceable Puzzles • Proof-of-Stake “Virtual Mining” 2 Cryptocurrency Technologies Alternative Mining Puzzles Puzzle Requirements A puzzle should ... – be cheap to verify – have adjustable difficulty – <other requirements> – have a chance of winning that is proportional to hashpower • Large player get only proportional advantage • Even small players get proportional compensation Bad Puzzle: a sequential Puzzle Consider a puzzle that takes N steps to solve a “Sequential” Proof of Work N Solution Found! 3 Cryptocurrency Technologies Alternative Mining Puzzles Bad Puzzle: a sequential Puzzle Problem: fastest miner always wins the race! Solution Found! Good Puzzle => Weighted Sample This property is sometimes called progress free. 4 Cryptocurrency Technologies Alternative Mining Puzzles Alternative Mining Puzzles • Essential Puzzle Requirements • ASIC-Resistant Puzzles • Proof-of-Useful-Work • Non-outsourceable Puzzles • Proof-of-Stake “Virtual Mining” ASIC Resistance – Why?! Goal: Ordinary people with idle laptops, PCs, or even mobile phones can mine! Lower barrier to entry! Approach: Reduce the gap between custom hardware and general purpose equipment. -
ON PRIME CHAINS 3 Can Be Found in Many Elementary Number Theory Texts, for Example [8]
ON PRIME CHAINS DOUGLAS S. STONES Abstract. Let b be an odd integer such that b ≡ ±1 (mod 8) and let q be a prime with primitive root 2 such that q does not divide b. We show q−2 that if (pk)k=0 is a sequence of odd primes such that pk = 2pk−1 + b for all 1 ≤ k ≤ q − 2, then either (a) q divides p0 + b, (b) p0 = q or (c) p1 = q. λ−1 For integers a,b with a ≥ 1, a sequence of primes (pk)k=0 such that pk = apk−1+b for all 1 ≤ k ≤ λ − 1 is called a prime chain of length λ based on the pair (a,b). This follows the terminology of Lehmer [7]. The value of pk is given by k k (a − 1) (1) p = a p0 + b k (a − 1) for all 0 ≤ k ≤ λ − 1. For prime chains based on the pair (2, +1), Cunningham [2, p. 241] listed three prime chains of length 6 and identified some congruences satisfied by the primes within prime chains of length at least 4. Prime chains based on the pair (2, +1) are now called Cunningham chains of the first kind, which we will call C+1 chains, for short. Prime chains based on the pair (2, −1) are called Cunningham chains of the second kind, which we will call C−1 chains. We begin with the following theorem which has ramifications on the maximum length of a prime chain; it is a simple corollary of Fermat’s Little Theorem. -
Arxiv:Math/0412262V2 [Math.NT] 8 Aug 2012 Etrgae Tgte Ihm)O Atnscnetr and Conjecture fie ‘Artin’S Number on of Cojoc Me) Domains’
ARTIN’S PRIMITIVE ROOT CONJECTURE - a survey - PIETER MOREE (with contributions by A.C. Cojocaru, W. Gajda and H. Graves) To the memory of John L. Selfridge (1927-2010) Abstract. One of the first concepts one meets in elementary number theory is that of the multiplicative order. We give a survey of the lit- erature on this topic emphasizing the Artin primitive root conjecture (1927). The first part of the survey is intended for a rather general audience and rather colloquial, whereas the second part is intended for number theorists and ends with several open problems. The contribu- tions in the survey on ‘elliptic Artin’ are due to Alina Cojocaru. Woj- ciec Gajda wrote a section on ‘Artin for K-theory of number fields’, and Hester Graves (together with me) on ‘Artin’s conjecture and Euclidean domains’. Contents 1. Introduction 2 2. Naive heuristic approach 5 3. Algebraic number theory 5 3.1. Analytic algebraic number theory 6 4. Artin’s heuristic approach 8 5. Modified heuristic approach (`ala Artin) 9 6. Hooley’s work 10 6.1. Unconditional results 12 7. Probabilistic model 13 8. The indicator function 17 arXiv:math/0412262v2 [math.NT] 8 Aug 2012 8.1. The indicator function and probabilistic models 17 8.2. The indicator function in the function field setting 18 9. Some variations of Artin’s problem 20 9.1. Elliptic Artin (by A.C. Cojocaru) 20 9.2. Even order 22 9.3. Order in a prescribed arithmetic progression 24 9.4. Divisors of second order recurrences 25 9.5. Lenstra’s work 29 9.6. -
Cryptocurrency and the Blockchain: Technical Overview and Potential Impact on Commercial Child Sexual Exploitation
Cryptocurrency and the BlockChain: Technical Overview and Potential Impact on Commercial Child Sexual Exploitation Prepared for the Financial Coalition Against Child Pornography (FCACP) and the International Centre for Missing & Exploited Children (ICMEC) by Eric Olson and Jonathan Tomek, May 2017 Foreword The International Centre for Missing & Exploited Children (ICMEC) advocates, trains and collaborates to eradicate child abduction, sexual abuse and exploitation around the globe. Collaboration – one of the pillars of our work – is uniquely demonstrated by the Financial Coalition Against Child Pornography (FCACP), which was launched in 2006 by ICMEC and the National Center for Missing & Exploited Children. The FCACP was created when it became evident that people were using their credit cards to buy images of children being sexually abused online. Working alongside law enforcement, the FCACP followed the money to disrupt the economics of the child pornography business, resulting in the virtual elimination of the use of credit cards in the United States for the purchase of child sexual abuse content online. And while that is a stunning accomplishment, ICMEC and the FCACP are mindful of the need to stay vigilant and continue to fight those who seek to profit from the sexual exploitation of children. It is with this in mind that we sought to research cryptocurrencies and the role they play in commercial sexual exploitation of children. This paper examines several cryptocurrencies, including Bitcoin, and the Blockchain architecture that supports them. It provides a summary of the underground and illicit uses of the currencies, as well as the ramifications for law enforcement and industry. ICMEC is extremely grateful to the authors of this paper – Eric Olson and Jonathan Tomek of LookingGlass Cyber Solutions. -
Survey on Surging Technology: Cryptocurrency
International Journal of Engineering &Technology, 7 (3.12) (2018) 296-299 International Journal of Engineering & Technology Website: www.sciencepubco.com/index.php/IJET Research paper Survey on Surging Technology: Cryptocurrency Swathi Singh1, Suguna R2, Divya Satish3, Ranjith Kumar MV4 1Research Scholar, 2, 3Professor, 4Assistant Professor 1,2,3,4Department of Computer Science and Engineering, 1,3SKR Engineering College, Chennai, India, 2Vel Tech Rangarajan Dr.Sagunthala Institute of Science and Technology, Chennai, India 4SRM Institute of Science and Technology, Kattankulathur, Chennai. *Corresponding Author Email: [email protected] Abstract The paper gives an insight on cryptography within digital money used in electronic commerce. The combination of digital currencies with cryptography is named as cryptocurrencies or cryptocoins. Though this technique came into existence years ago, it is bound to have a great future due to its flexibility and very less or nil transaction costs. The concept of cryptocurrency is not new in digital world and is already gaining subtle importance in electronic commerce market. This technology can bring down various risks that may have occurred in usage of physical currencies. The transaction of cryptocurrencies are protected with strong cryptographic hash functions that ensure the safe sending and receiving of assets within the transaction chain or blockchain in a Peer-to-Peer network. The paper discusses the merits and demerits of this technology with a wide range of applications that use cryptocurrency. Index Terms: Blockchain, Cryptocurrency. However, the first implementation of Bitcoin protocol routed 1. Introduction many other cryptocurrencies to exist. Bitcoin is a self-regulatory system that is not supported by government or any organization. -
A Survey on Consensus Mechanisms and Mining Strategy Management
1 A Survey on Consensus Mechanisms and Mining Strategy Management in Blockchain Networks Wenbo Wang, Member, IEEE, Dinh Thai Hoang, Member, IEEE, Peizhao Hu, Member, IEEE, Zehui Xiong, Student Member, IEEE, Dusit Niyato, Fellow, IEEE, Ping Wang, Senior Member, IEEE Yonggang Wen, Senior Member, IEEE and Dong In Kim, Fellow, IEEE Abstract—The past decade has witnessed the rapid evolution digital tokens between Peer-to-Peer (P2P) users. Blockchain in blockchain technologies, which has attracted tremendous networks, especially those adopting open-access policies, are interests from both the research communities and industries. The distinguished by their inherent characteristics of disinterme- blockchain network was originated from the Internet financial sector as a decentralized, immutable ledger system for transac- diation, public accessibility of network functionalities (e.g., tional data ordering. Nowadays, it is envisioned as a powerful data transparency) and tamper-resilience [2]. Therefore, they backbone/framework for decentralized data processing and data- have been hailed as the foundation of various spotlight Fin- driven self-organization in flat, open-access networks. In partic- Tech applications that impose critical requirement on data ular, the plausible characteristics of decentralization, immutabil- security and integrity (e.g., cryptocurrencies [3], [4]). Further- ity and self-organization are primarily owing to the unique decentralized consensus mechanisms introduced by blockchain more, with the distributed consensus provided by blockchain networks. This survey is motivated by the lack of a comprehensive networks, blockchains are fundamental to orchestrating the literature review on the development of decentralized consensus global state machine1 for general-purpose bytecode execution. mechanisms in blockchain networks. In this survey, we provide a Therefore, blockchains are also envisaged as the backbone systematic vision of the organization of blockchain networks. -
A Polynomial Recursion for Prime Constellations 1
A POLYNOMIAL RECURSION FOR PRIME CONSTELLATIONS SCOTT B. GUTHERY Abstract. An algorithm for recursively generating the sequence of solutions of a prime constellation is described. The algorithm is based on a polynomial equation formed from the first n elements of the constellation. A root of this equation is the next element of the sequence. 1. Introduction Hypothesis H is one of the few mathematics conjectures that is distinguished by having its own Wikipedia page. The hypothesis, proposed independently by Schinzel-Sierpinski [1] and Bateman-Horn [2], describes a pattern of integers and then hypothesizes that there is an instance of the pattern such that all the integers in the pattern are prime numbers. It is a small step to conjecture that there are an infinite number of such occurrences. The twin prime pattern, n; n + 2, is one of the forms characterized Hypothesis H but the hypothesis also subsumes the conjectures of de Polignac [3], Bunyakovskii [4], Hardy-Littlewood [5], Dickson [6], Shanks [7], and many others regarding the infinitude and density of patterns of primes. Hypothesis H. Let m be a positive integer and let F = ff1(x); f2(x); : : : ; fm(x)g be a set of irreducible polynomials with integral coefficients and positive leading coefficients such that there is not a prime p which divides the product Ym f1(n) · f2(n) · ::: · fi(n) = fi(n) (1) i=1 for every integer n. Then there exists an integer q such that f1(q); f2(q); : : : ; fm(q) are all prime numbers. A sequence of functions F which satisfies Hypothesis H is traditionally called a prime constellation. -
Discussion of "Mobile Collateral Versus Immobile Collateral"
Discussion of Mobile Collateral versus Immobile Collateral by Gary Gorton and Tyler Muir Andrei Kirilenko MIT Sloan School of Management Main points of the paper “In the thirty years prior to the 2007-2008 financial crisis, the global financial system evolved away from a system of immobile collateral into a system of mobile collateral.” “Since the financial crisis of 2007-2008, regulatory initiatives have been aimed at making collateral once again immobile.” “There is a cost to making this collateral immobile because it ties up safe debt.” Instead of providing the benefit of making the system safer, “other forms of bank debt increase when safe collateral becomes immobile, possibly making the system riskier.” Argument: BIS LCR Era is “structurally similar” to the U.S. National Banking Era The National Banking Era The Rise of National Banks National Banks in Operation, 1864-1913 Source: Annual Report of the Comptroller of the Currency (1914, Table 6) and Weber (2015) National Banks Were Given An Advantage « National banks had to pay 1 percent (o.5 percent from 1900) tax on their national bank notes in circulation. « State banks had to pay a 10 percent tax on their notes in circulation. « National banks can take the full value of their capital, invest it in government bonds, deposit bonds with the Comptroller of the Currency, get 90 percent (100 percent after 1900) of that value in national bank notes and loan the notes out. « State banks can only loan out the notes that they issued backed by their capital. To Make the Payment System Cheaper and the Banking System Safer and Deeper « National bank are accepted as legal tender in states other than those in which they are issued. -
BLOCKCHAIN TECHNOLOGIES Spring 2021
CS 5594: BLOCKCHAIN TECHNOLOGIES Spring 2021 THANG HOANG, PhD VIRTUAL MINING Some slides attributed to the authors of “Bitcoin and Cryptocurrency Technologies” Overview Proof of Work (Recap) Proof of Useful Work Proof of Stake Proof of Authority Proof of Elapsed Time Proof of Burn … Proof of Work (Recap) First consensus algorithm in blockchain Miners compete against each other to update the blockchain Solving hash puzzle Purely depending on raw computational power PoW Issues Reward and voting power proportional to mining power Miners with better equipment get more reward Power usage and resource wasteful!!! Need high computation power Incur high energy consumption Bitcoin devours more electricity than many other countries! Image credited to https://digiconomist.net/bitcoin- energy-consumption/ Proof of Useful Work Spending computing resource to solve hash puzzle is wasteful Can we recycle this to do something more meaningful? Protein folding? Find a low energy configuration Search for aliens? Find anomalies in radio signals Break crypto? Challenges Randomly chosen instances must be hard! Project Founded Goal Impact Great Internet 1996 Finding large Mersenne Found new largest prime number twelve Mersenne Prime Search primes straight times, including 2^57885161 -1 Distributed.net 1997 Crypto brute-force demo First successful public brute force of a 64- bit crypto Key SETI@home 1999 Identifying signs of 5 mil. Participants extraterrestrial life Folding@home 2000 Atomic-level simulation 118 scientific papers of protein folding Primecoin Find -
Blockchains: Distributed Consensus Protocols
Blockchains: Distributed Consensus Protocols Abstract Blockchains are expected to provide disruptive innovations through the radical dis- intermediation of trust from distributed consensus. However, the different protocols for distributed consensus in blockchains have yet to be exhaustively documented and critically compared. We identify, define and compare the different protocols of distributed consensus for blockchains. We first define Distributed Consensus Blockchains (DCBs) as distributed ledgers in which the order of transactions is peer-validated by computationally-mediated distributed consensus. We then identify and define the different protocols of distributed consensus for blockchains. We then compare the different protocols for distributed con- sensus in terms of resources utilisation for determining consensus, energy use, and block time for transaction validation. We then discuss the difficulty of future proofing protocols against resource centralisation, given the development of Application-Specific Integrated Circuits (ASICs) for the Proof-of-Work (PoW) protocol of the Bitcoin DCB. We suggest that the Proof-of-Capacity (PoC) protocol can be future proofed, better than the alternative protocols, against resource centralisation. We conclude by suggesting future work into the transparency implications for DCBs, and their potential for disrupting business models. Keywords: blockchains; distributed consensus; protocol 1 Introduction Since the first implementation of a blockchain in 2009, as part of the Bitcoin currency, more than seven hundred blockchains have been created at the time of writing this paper [1]. We consider the most significant property of blockchains, distinguishing them from other forms of distributed computing, is the use of distributed consensus. Based upon this distributed consensus blockchains are expected to be as significant as automation, computing, robots and the Internet, in contributing immensely to cultures [2].