Security & Cryptography
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RSA: Encryption, Decryption
Data Communications & Networks Session 11 – Main Theme Network Security Dr. Jean-Claude Franchitti New York University Computer Science Department Courant Institute of Mathematical Sciences Adapted from course textbook resources Computer Networking: A Top-Down Approach, 5/E Copyright 1996-2009 J.F. Kurose and K.W. Ross, All Rights Reserved 1 Agenda 1 Session Overview 2 Network Security 3 Summary and Conclusion 2 What is the class about? .Course description and syllabus: »http://www.nyu.edu/classes/jcf/CSCI-GA.2262-001/ »http://www.cs.nyu.edu/courses/spring15/CSCI- GA.2262-001/index.html .Textbooks: » Computer Networking: A Top-Down Approach (5th Edition) James F. Kurose, Keith W. Ross Addison Wesley ISBN-10: 0136079679, ISBN-13: 978-0136079675, 5th Edition (03/09) 3 Course Overview . Computer Networks and the Internet . Application Layer . Fundamental Data Structures: queues, ring buffers, finite state machines . Data Encoding and Transmission . Local Area Networks and Data Link Control . Wireless Communications . Packet Switching . OSI and Internet Protocol Architecture . Congestion Control and Flow Control Methods . Internet Protocols (IP, ARP, UDP, TCP) . Network (packet) Routing Algorithms (OSPF, Distance Vector) . IP Multicast . Sockets 4 Course Approach . Introduction to Basic Networking Concepts (Network Stack) . Origins of Naming, Addressing, and Routing (TCP, IP, DNS) . Physical Communication Layer . MAC Layer (Ethernet, Bridging) . Routing Protocols (Link State, Distance Vector) . Internet Routing (BGP, OSPF, Programmable Routers) . TCP Basics (Reliable/Unreliable) . Congestion Control . QoS, Fair Queuing, and Queuing Theory . Network Services – Multicast and Unicast . Extensions to Internet Architecture (NATs, IPv6, Proxies) . Network Hardware and Software (How to Build Networks, Routers) . Overlay Networks and Services (How to Implement Network Services) . -
Secret Sharing and Shared Digital Signature Using Elliptic Curves
ANALELE S»TIINT»IFICE ALE UNIVERSITAT»II¸ \AL.I. CUZA" DIN IAS»I (S.N.) MATEMATICA,¸ Tomul LV, 2009, f.1 SECRET SHARING AND SHARED DIGITAL SIGNATURE USING ELLIPTIC CURVES BY RAZVAN¸ LIT»CANU* and SILVIA PALAS»CA¸ Abstract. This note is a short presentation of the elliptic curves cryptography. We illustrate this important aspect of the modern cryptography by a shared digital signature protocol, that adapts the classical elliptic curve digital signature scheme to a collective user and extends a distributed key generation protocol proposed by Tang [13]. Mathematics Subject Classi¯cation 2000: 14G50, 11T71, 11G07, 94A60. Key words: public key cryptography, elliptic curves, Edwards curves, digital signa- ture. 1. Introduction. Since the publication of the breakthrough article of Diffie and Hellman [2] in 1976, the public-key cryptography has gained the leading part in the theory and practice of the information security. Due to its strong points by respect to the classical symmetric cryptosystems, it became indispensable for secure communication in the Internet, for imple- menting smart cards etc. Moreover, the public key cryptography provides the foundation for secure digital signatures or key distribution for symmet- ric cryptosystems. Nevertheless, an important disadvantage of the public key algorithms by respect to the classical ones is the dimension of the keys by respect to those of classical cryptosystems, for reaching a similar security level. The dimension of the keys requires, on one hand, larger memory, and more time for computations on the other hand. Finding public keys algorithms requiring smaller keys and being more e±cient has been an important re- search challenge in this area. -
Semi-Quantum Communication: Protocols for Key Agreement, Controlled Secure Direct Communication and Dialogue Arxiv:1702.07861V1
Semi-quantum communication: Protocols for key agreement, controlled secure direct communication and dialogue Chitra Shuklaa;,∗ Kishore Thapliyalb;,y Anirban Pathakb;z aGraduate School of Information Science, Nagoya University, Furo-cho 1, Chikusa-ku, Nagoya, 464-8601, Japan bJaypee Institute of Information Technology, A-10, Sector-62, Noida, UP-201307, India February 28, 2017 Abstract Semi-quantum protocols that allow some of the users to remain classical are proposed for a large class of problems associated with secure communication and secure multiparty computation. Specif- ically, first time semi-quantum protocols are proposed for key agreement, controlled deterministic secure communication and dialogue, and it is shown that the semi-quantum protocols for controlled deterministic secure communication and dialogue can be reduced to semi-quantum protocols for e- commerce and private comparison (socialist millionaire problem), respectively. Complementing with the earlier proposed semi-quantum schemes for key distribution, secret sharing and deterministic secure communication, set of schemes proposed here and subsequent discussions have established that almost every secure communication and computation tasks that can be performed using fully quantum protocols can also be performed in semi-quantum manner. Further, it addresses a funda- mental question in context of a large number problems- how much quantumness is (how many quan- tum parties are) required to perform a specific secure communication task? Some of the proposed schemes are completely orthogonal-state-based, and thus, fundamentally different from the existing semi-quantum schemes that are conjugate-coding-based. Security, efficiency and applicability of the proposed schemes have been discussed with appropriate importance. arXiv:1702.07861v1 [quant-ph] 25 Feb 2017 Keywords: Semi-quantum protocol, quantum communication, key agreement, quantum dialogue, deter- ministic secure quantum communication, secure direct quantum communication. -
CHURP: Dynamic-Committee Proactive Secret Sharing
CHURP: Dynamic-Committee Proactive Secret Sharing Sai Krishna Deepak Maram∗† Cornell Tech Fan Zhang∗† Lun Wang∗ Andrew Low∗ Cornell Tech UC Berkeley UC Berkeley Yupeng Zhang∗ Ari Juels∗ Dawn Song∗ Texas A&M Cornell Tech UC Berkeley ABSTRACT most important resources—money, identities [6], etc. Their loss has We introduce CHURP (CHUrn-Robust Proactive secret sharing). serious and often irreversible consequences. CHURP enables secure secret-sharing in dynamic settings, where the An estimated four million Bitcoin (today worth $14+ Billion) have committee of nodes storing a secret changes over time. Designed for vanished forever due to lost keys [69]. Many users thus store their blockchains, CHURP has lower communication complexity than pre- cryptocurrency with exchanges such as Coinbase, which holds at vious schemes: O¹nº on-chain and O¹n2º off-chain in the optimistic least 10% of all circulating Bitcoin [9]. Such centralized key storage case of no node failures. is also undesirable: It erodes the very decentralization that defines CHURP includes several technical innovations: An efficient new blockchain systems. proactivization scheme of independent interest, a technique (using An attractive alternative is secret sharing. In ¹t;nº-secret sharing, asymmetric bivariate polynomials) for efficiently changing secret- a committee of n nodes holds shares of a secret s—usually encoded sharing thresholds, and a hedge against setup failures in an efficient as P¹0º of a polynomial P¹xº [73]. An adversary must compromise polynomial commitment scheme. We also introduce a general new at least t +1 players to steal s, and at least n−t shares must be lost technique for inexpensive off-chain communication across the peer- to render s unrecoverable. -
Improved Threshold Signatures, Proactive Secret Sharing, and Input Certification from LSS Isomorphisms
Improved Threshold Signatures, Proactive Secret Sharing, and Input Certification from LSS Isomorphisms Diego F. Aranha1, Anders Dalskov2, Daniel Escudero1, and Claudio Orlandi1 1 Aarhus University, Denmark 2 Partisia, Denmark Abstract. In this paper we present a series of applications steming from a formal treatment of linear secret-sharing isomorphisms, which are linear transformations between different secret-sharing schemes defined over vector spaces over a field F and allow for efficient multiparty conversion from one secret-sharing scheme to the other. This concept generalizes the folklore idea that moving from a secret-sharing scheme over Fp to a secret sharing \in the exponent" can be done non-interactively by multiplying the share unto a generator of e.g., an elliptic curve group. We generalize this idea and show that it can also be used to compute arbitrary bilinear maps and in particular pairings over elliptic curves. We include the following practical applications originating from our framework: First we show how to securely realize the Pointcheval-Sanders signature scheme (CT-RSA 2016) in MPC. Second we present a construc- tion for dynamic proactive secret-sharing which outperforms the current state of the art from CCS 2019. Third we present a construction for MPC input certification using digital signatures that we show experimentally to outperform the previous best solution in this area. 1 Introduction A(t; n)-secure secret-sharing scheme allows a secret to be distributed into n shares in such a way that any set of at most t shares are independent of the secret, but any set of at least t + 1 shares together can completely reconstruct the secret. -
Practical Threshold Signatures with Linear Secret Sharing Schemes*
Practical Threshold Signatures with Linear Secret Sharing Schemes? Ilker_ Nadi Bozkurt, Kamer Kaya??, Ali Aydın Sel¸cuk Department of Computer Engineering Bilkent University Ankara, 06800, Turkey fbozkurti,kamer,[email protected] Abstract. Function sharing deals with the problem of distribution of the computation of a function (such as decryption or signature) among several parties. The necessary values for the computation are distributed to the participating parties using a secret sharing scheme (SSS). Several function sharing schemes have been proposed in the literature, with most of them using Shamir secret sharing as the underlying SSS. In this pa- per, we investigate how threshold cryptography can be conducted with any linear secret sharing scheme and present a function sharing scheme for the RSA cryptosystem. The challenge is that constructing the secret in a linear SSS requires the solution of a linear system which normally involves computing inverses, while computing an inverse modulo '(N) cannot be tolerated in a threshold RSA system in any way. Keywords: Linear secret sharing, threshold cryptography, function shar- ing 1 Introduction The secure storage of the private keys of a cryptosystem is an important problem. Possession of a highly sensitive key by an individual may not be desirable as the key can easily be lost or as the individual may not be fully trusted. Giving copies of the key to more than one individual increases the risk of compromise. A solution to this problem is to give shares of the key to several individuals, forcing them to cooperate to find the secret key. This not only reduces the risk of losing the key but also makes compromising the key more difficult. -
Lecture 12: Quantum Key Distribution. Secret Key. BB84, E91 and B92 Protocols. Continuous-Variable Protocols. 1. Secret Key. A
Lecture 12: Quantum key distribution. Secret key. BB84, E91 and B92 protocols. Continuous-variable protocols. 1. Secret key. According to the Vernam theorem, any message (for instance, consisting of binary symbols, 01010101010101), can be encoded in an absolutely secret way if the one uses a secret key of the same length. A key is also a sequence, for instance, 01110001010001. The encoding is done by adding the message and the key modulo 2: 00100100000100. The one who knows the key can decode the encoded message by adding the key to the message modulo 2. The important thing is that the key should be used only once. It is exactly this way that classical cryptography works. Therefore the only task of quantum cryptography is to distribute the secret key between just two users (conventionally called Alice and Bob). This is Quantum Key Distribution (QKD). 2. BB84 protocol, proposed in 1984 by Bennett and Brassard – that’s where the name comes from. The idea is to encode every bit of the secret key into the polarization state of a single photon. Because the polarization state of a single photon cannot be measured without destroying this photon, this information will be ‘fragile’ and not available to the eavesdropper. Any eavesdropper (called Eve) will have to detect the photon, and then she will either reveal herself or will have to re-send this photon. But then she will inevitably send a photon with a wrong polarization state. This will lead to errors, and again the eavesdropper will reveal herself. The protocol then runs as follows. -
Cryptography Knowledge Area (Draft for Comment)
CRYPTOGRAPHY KNOWLEDGE AREA (DRAFT FOR COMMENT) AUTHOR: Nigel Smart – KU Leuven EDITOR: George Danezis – University College London REVIEWERS: Dan Bogdanov - Cybernetica Kenny Patterson – Royal Holloway, University of London Liqun Chen – University of Surrey Cryptography Nigel P. Smart April 2018 INTRODUCTION The purpose of this chapter is to explain the various aspects of cryptography which we feel should be known to an expert in cyber-security. The presentation is at a level needed for an instructor in a module in cryptography; so they can select the depth needed in each topic. Whilst not all experts in cyber-security need be aware of all the technical aspects mentioned below, we feel they should be aware of all the overall topics and have an intuitive grasp as to what they mean, and what services they can provide. Our focus is mainly on primitives, schemes and protocols which are widely used, or which are suitably well studied that they could be used (or are currently being used) in specific application domains. Cryptography by its very nature is one of the more mathematical aspects of cyber-security; thus this chapter contains a lot more mathematics than one has in some of the other chapters. The overall presentation assumes a basic knowledge of either first-year undergraduate mathematics, or that found in a discrete mathematics course of an undergraduate Computer Science degree. The chapter is structured as follows: After a quick recap on some basic mathematical notation (Sec- tion 1), we then give an introduction to how security is defined in modern cryptography. This section (Section 2) forms the basis of our discussions in the other sections. -
Asynchronous Verifiable Secret Sharing and Proactive Cryptosystems
Asynchronous Verifiable Secret Sharing and Proactive Ý Cryptosystems£ Christian Cachin Klaus Kursawe Anna LysyanskayaÞ Reto Strobl IBM Research Zurich Research Laboratory CH-8803 R¨uschlikon, Switzerland {cca,kku,rts}@zurich.ibm.com ABSTRACT However, when a threshold cryptosystem operates over a longer Verifiable secret sharing is an important primitive in distributed time period, it may not be realistic to assume that an adversary cor- cryptography. With the growing interest in the deployment of rupts only Ø servers during the entire lifetime of the system. Proac- threshold cryptosystems in practice, the traditional assumption of tive cryptosystems address this problem by operating in phases; a synchronous network has to be reconsidered and generalized to they can tolerate the corruption of up to Ø different servers dur- an asynchronous model. This paper proposes the first practical ing every phase [18]. They rely on the assumption that servers may verifiable secret sharing protocol for asynchronous networks. The erase data and on a special reboot procedure to remove the adver- protocol creates a discrete logarithm-based sharing and uses only sary from a corrupted server. The idea is to proactively reboot all a quadratic number of messages in the number of participating servers at the beginning of every phase, and to subsequently refresh servers. It yields the first asynchronous Byzantine agreement pro- the secret key shares such that in any phase, knowledge of shares tocol in the standard model whose efficiency makes it suitable for from previous phases does not give the adversary an advantage. use in practice. Proactive cryptosystems are another important ap- Thus, proactive cryptosystems tolerate a mobile adversary [20], plication of verifiable secret sharing. -
A New Approach to the Secret Image Sharing with Steganography and Authentication
1 A new approach to the secret image sharing with steganography and authentication C-C Wua, M-S Hwang*b and S-J Kaoa aDepartment of Computer Science and Engineering, National Chung Hsing University, No. 250, Kuo Kuang Road, Taichung 402, Taiwan bDepartment of Management Information Systems, National Chung Hsing University, No. 250, Kuo Kuang Road, Taichung 402, Taiwan Abstract: Steganography can be viewed as cryptography. It includes a variety of secret communication methods that embed the existence of the message and makes it appear invisible. Both of them have been used to protect secret information. In 2004, Lin and Tsai proposed a novel secret image sharing method that was based on the (k, n)-threshold scheme with the additional capabilities of steganography and authentication. They protect a secret image by breaking it into n user-selected ordinary camouflage images. Besides, their methods also embed fragile watermark signals into the camouflage images by using parity bit checking. Recently, Yang et al. have shown three weaknesses in Lin–Tsai’s scheme and further proposed improvements in 2007. They not only improve authentication ability and image quality of stego- image, but also introduce a lossless version image sharing scheme for secret image. Unfortunately, there is a common drawback in Lin–Tsai’s and Yang et al.’s scheme: The enlargement size of the camouflage images and stego-images is 4 times of the secret image. However, the proposed scheme does only require 3.5 times enlargement. In addition, the experimental result of image quality analyzing shows that the proposed scheme has better image quality than other methods. -
Function Secret Sharing⋆
Function Secret Sharing? Elette Boyle1, Niv Gilboa2, and Yuval Ishai1 1 Computer Science Department, Technion [email protected], [email protected] 2 Dept. of Communication Systems Engineering, Ben Gurion University [email protected] Abstract. Motivated by the goal of securely searching and updating dis- tributed data, we introduce and study the notion of function secret shar- ing (FSS). This new notion is a natural generalization of distributed point functions (DPF), a primitive that was recently introduced by Gilboa and Ishai (Eurocrypt 2014). Given a positive integer p ≥ 2 and a class F of n functions f : f0; 1g ! G, where G is an Abelian group, a p-party FSS scheme for F allows one to split each f 2 F into p succinctly described n Pp functions fi : f0; 1g ! G, 1 ≤ i ≤ p, such that: (1) i=1 fi = f, and (2) any strict subset of the fi hides f. Thus, an FSS for F can be thought of as method for succinctly performing an \additive secret sharing" of functions from F. The original definition of DPF coincides with a two- party FSS for the class of point functions, namely the class of functions that have a nonzero output on at most one input. We present two types of results. First, we obtain efficiency improvements and extensions of the original DPF construction. Then, we initiate a sys- tematic study of general FSS, providing some constructions and estab- lishing relations with other cryptographic primitives. More concretely, we obtain the following main results: { Improved DPF. We present an improved (two-party) DPF con- struction from a pseudorandom generator (PRG), reducing the length log 3 of the key describing each fi from O(λ · n 2 ) to O(λn), where λ is the PRG seed length. -
Device-Independent Quantum Cryptography for Continuous Variables
Device-Independent Quantum Cryptography for Continuous Variables Kevin Marshall1, ∗ and Christian Weedbrook1, 2, y 1Department of Physics, University of Toronto, Toronto, M5S 3G4, Canada 2QKD Corp., 60 St. George St., Toronto, M5S 3G4, Canada (Dated: October 8, 2018) We present the first device-independent quantum cryptography protocol for continuous variables. Our scheme is based on the Gottesman-Kitaev-Preskill encoding scheme whereby a qubit is embedded in the infinite-dimensional space of a quantum harmonic oscillator. The novel application of discrete-variable device- independent quantum key distribution to this encoding enables a continuous-variable analogue. Since the se- curity of this protocol is based on discrete-variables we inherit by default security against collective attacks and, under certain memoryless assumptions, coherent attacks. We find that our protocol is valid over the same distances as its discrete-variable counterpart, except that we are able to take advantage of high efficiency com- mercially available detectors where, for the most part, only homodyne detection is required. This offers the potential of removing the difficulty in closing the loopholes associated with Bell inequalities. PACS numbers: 03.67.Dd, 03.67.Hk, 42.50.-p, 89.70.Cf I. INTRODUCTION parties may share a private key despite having no knowledge of the inner workings of their respective devices. Conversely, Quantum key distribution (QKD) [1,2] is a method by in conventional QKD protocols it is regularly assumed that which two parties, Alice and Bob, may generate a shared both parties have a high degree of control over both state secret key over an insecure quantum channel monitored by preparation as well as measurement.