Towards Append-Only Authenticated Dictionaries. Vivek Bhupatiraju, CS-PRIMES 2017
|
|
|
- Kory Martin
- 5 years ago
- Views:
Transcription
1 Towards Append-Only Authenticated Dictionaries Vivek Bhupatiraju, CS-PRIMES 27
2 Public-key Cryptography PK M e(m, PK SK
3 Secure Channels - Having secure channels is becoming more and more necessary - Many of these systems based around public-key cryptography - Essential to accurately distribute and access these public-keys - Let s use a directory!
4 3 Directory sends Robert PK J 2 Directory Directory stores PK J under John s name John publishes his public key, PK J Robert MS R e(ms R, PK J John PK J + SK J 4 5 Robert encrypts MS R with PK J John decrypts with SK J => MS R
5 3 Directory sends Robert PK M 2 Directory John publishes his public key, PK J Directory stores PK M under John s name, sends PK J to Mark Robert MS R e(ms R, PK M Mark e(ms R, PK J John PK J + SK J Robert encrypts Mark now knows MS R with PK M MS R - no secrecy John decrypts with SK J => MS R
6 Detecting Impersonation! (NON-MEMBERSHIP Directory Needs to check that directory is not hiding a PK M under his name John = PK J Alin = PK A 2 Sends cryptographic proof that this IS the case John PK J + SK J
7 Detecting Impersonation! (CONSISTENCY Directory John = PK MJ Needs to check that directory is not hiding a PK M under his name Alin = PK A 2 Sends cryptographic proof that this IS the case John PK J + SK J
8 Detecting Impersonation! (MEMBERSHIP Sends Robert PK M when he asks for John s PK Directory Robert MS R 2 Asks for proof that PK M is in the directory under John s name John = PK J Alin = PK A
9 Append-Only Dictionaries (Key-value pairs - NON-MEMBERSHIP - Proof that no values exist for key n other than the ones in the tree - CONSISTENCY - Proof that all data in version i of the dictionary is also in version j of the dictionary, where i j - MEMBERSHIP - Proof that (n, v n is in dictionary
10 Attempts at a Full AAD == number of key-value pairs in AAD / Server Membership Non-membership Consistency History Tree Prefix Tree Quadratic Prefix Forest
11 Merkle Tree H(L + R = Ω (Merkle Root H(H(A H(B = L H(H(C H(D = R H(A H(B H(C H(D A = (a, v a B = (b, v b C = (c, v c D = (d, v d
12 History Tree - Just a merkle tree that grows as key-value pairs are added to it (a, v a (b, v b (a, v a (b, v b (c, v c (a, v a (b, v b (c, v c (d, v d
13 History Tree (MEMBERSHIP Merkle Root: Ω o =? Ω c Space/Time Complexity (a, v a (b, v b (c, v c (d, v d
14 History Tree (NON-MEMBERSHIP Space/Time Complexity (j, v j (a, v a (j, v j (k, v k
15 History Tree (CONSISTENCY Space/Time Complexity: (a, v a (b, v b (a, v a (b, v b (c, v c (d, v d version i version j
16 Prefix Tree Tree defined by hashes: HASH( a = HASH( b = HASH( c = b a HASH( d = Also a merkle tree! c a - Each node is a hash of its children d b
17 Prefix Tree (MEMBERSHIP Space/Time Complexity (c, v c (a, v a (d, v d (b, v b
18 Prefix Tree (NON-MEMBERSHIP HASH( e = Space/Time Complexity (c, v c (a, v a (d, v d (b, v b
19 Prefix Tree (CONSISTENCY - Server has to send all key-value pairs added between versions OR membership proofs - Both linear in complexity, O(m
20 Quadratic Prefix Forest a tree of size n 2 c a d b U of Forest, Size U 2 of Forest, Size 4 U n of Forest, Size n 2
21 Quadratic Prefix Forest - Say there are trees in the forest - If there are total key-value pairs
22 Q Prefix Forests (MEMBERSHIP a c a tree of size n 2 d b # of Trees: Space / Time Complexity:
23 Q Prefix Forests (NON-MEMBERSHIP a c a tree of size n 2 d b # of Trees: Space / Time Complexity:
24 Q Prefix Forests (CONSISTENCY - Keep each of the Merkle roots of each prefix tree in a larger history tree - Merkle roots of each prefix tree should never change - Can check (via membership proofs the roots of the prefix tree against those stored in the history tree - Space/time complexity of
25 Q Prefix Forests (USABILITY - Each tree s size is a square number - At m =,, - Next tree will need ~, new key-value pairs - Sacrificing usability for better complexities in other operations
26 Future Work - Algebraic Hashing - H(a, b = L * a + R * b - Bilinear Accumulators - Accumulating sets into small digests - Incorporating NON-MEMBERSHIP into history trees - Coding up trees to test viability - Exploring new data structures
27 Acknowledgements I would like to thank: - Alin Tomescu, my mentor - Srini Devadas, coordinator of CS-PRIMES - My parents and family - MIT-PRIMES program
28 Thank you! Ask me questions!
Intro to Public Key Cryptography Diffie & Hellman Key Exchange
Introduction to Modern Cryptography Lecture 5 Number Theory: 1. Quadratic residues. 2. The discrete log problem. Intro to Public Key Cryptography Diffie & Hellman Key Exchange Course Summary - Math Part
Optimal Verification of Operations on Dynamic Sets
Optimal Verification of Operations on Dynamic Sets Charalampos Papamanthou Brown University Providence RI Roberto Tamassia Brown University Providence RI Nikos Triandopoulos RSA Laboratories Cambridge
Lecture 11: Hash Functions, Merkle-Damgaard, Random Oracle
CS 7880 Graduate Cryptography October 20, 2015 Lecture 11: Hash Functions, Merkle-Damgaard, Random Oracle Lecturer: Daniel Wichs Scribe: Tanay Mehta 1 Topics Covered Review Collision-Resistant Hash Functions
Cryptographic Solutions for Data Integrity in the Cloud
Cryptographic Solutions for Stanford University, USA Stanford Computer Forum 2 April 2012 Homomorphic Encryption Homomorphic encryption allows users to delegate computation while ensuring secrecy. Homomorphic
Quantum Wireless Sensor Networks
Quantum Wireless Sensor Networks School of Computing Queen s University Canada ntional Computation Vienna, August 2008 Main Result Quantum cryptography can solve the problem of security in sensor networks.
Question 1. The Chinese University of Hong Kong, Spring 2018
CSCI 5440: Cryptography The Chinese University of Hong Kong, Spring 2018 Homework 2 Solutions Question 1 Consider the following encryption algorithm based on the shortlwe assumption. The secret key is
Hashes and Message Digests Alex X. Liu & Haipeng Dai
Hashes and Message Digests Alex X. Liu & Haipeng Dai haipengdai@nju.edu.cn 313 CS Building Department of Computer Science and Technology Nanjing University Integrity vs. Secrecy Integrity: attacker cannot
Verifiable Set Operations over Outsourced Databases
Verifiable Set Operations over Outsourced Databases Ran Canetti Omer Paneth Dimitrios Papadopoulos Nikos Triandopoulos Abstract We study the problem of verifiable delegation of computation over outsourced
Non-Interactive Zero-Knowledge Proofs of Non-Membership
Non-Interactive Zero-Knowledge Proofs of Non-Membership O. Blazy, C. Chevalier, D. Vergnaud XLim / Université Paris II / ENS O. Blazy (XLim) Negative-NIZK CT-RSA 2015 1 / 22 1 Brief Overview 2 Building
CPSC 467: Cryptography and Computer Security
CPSC 467: Cryptography and Computer Security Michael J. Fischer Lecture 11 October 7, 2015 CPSC 467, Lecture 11 1/37 Digital Signature Algorithms Signatures from commutative cryptosystems Signatures from
Lecture 18: Message Authentication Codes & Digital Signa
Lecture 18: Message Authentication Codes & Digital Signatures MACs and Signatures Both are used to assert that a message has indeed been generated by a party MAC is the private-key version and Signatures
Cryptographical Security in the Quantum Random Oracle Model
Cryptographical Security in the Quantum Random Oracle Model Center for Advanced Security Research Darmstadt (CASED) - TU Darmstadt, Germany June, 21st, 2012 This work is licensed under a Creative Commons
SIGNATURE SCHEMES & CRYPTOGRAPHIC HASH FUNCTIONS. CIS 400/628 Spring 2005 Introduction to Cryptography
SIGNATURE SCHEMES & CRYPTOGRAPHIC HASH FUNCTIONS CIS 400/628 Spring 2005 Introduction to Cryptography This is based on Chapter 8 of Trappe and Washington DIGITAL SIGNATURES message sig 1. How do we bind
Outline. The Game-based Methodology for Computational Security Proofs. Public-Key Cryptography. Outline. Introduction Provable Security
The Game-based Methodology for Computational s David Pointcheval Ecole normale supérieure, CNRS & INRIA Computational and Symbolic Proofs of Security Atagawa Heights Japan April 6th, 2009 1/39 2/39 Public-Key
Lecture 1: Introduction to Public key cryptography
Lecture 1: Introduction to Public key cryptography Thomas Johansson T. Johansson (Lund University) 1 / 44 Key distribution Symmetric key cryptography: Alice and Bob share a common secret key. Some means
Lecture 19: Public-key Cryptography (Diffie-Hellman Key Exchange & ElGamal Encryption) Public-key Cryptography
Lecture 19: (Diffie-Hellman Key Exchange & ElGamal Encryption) Recall In private-key cryptography the secret-key sk is always established ahead of time The secrecy of the private-key cryptography relies
CIS 6930/4930 Computer and Network Security. Topic 5.2 Public Key Cryptography
CIS 6930/4930 Computer and Network Security Topic 5.2 Public Key Cryptography 1 Diffie-Hellman Key Exchange 2 Diffie-Hellman Protocol For negotiating a shared secret key using only public communication
Hash-based signatures & Hash-and-sign without collision-resistance
Hash-based signatures & Hash-and-sign without collision-resistance Andreas Hülsing 22.12.2016 Hash-based Signature Schemes [Mer89] Post quantum Only secure hash function Security well understood Fast 22-12-2016
Revisiting Cryptographic Accumulators, Additional Properties and Relations to other Primitives
S C I E N C E P A S S I O N T E C H N O L O G Y Revisiting Cryptographic Accumulators, Additional Properties and Relations to other Primitives David Derler, Christian Hanser, and Daniel Slamanig, IAIK,
1 Number Theory Basics
ECS 289M (Franklin), Winter 2010, Crypto Review 1 Number Theory Basics This section has some basic facts about number theory, mostly taken (or adapted) from Dan Boneh s number theory fact sheets for his
Applied cryptography
Applied cryptography Identity-based Cryptography Andreas Hülsing 19 November 2015 1 / 37 The public key problem How to obtain the correct public key of a user? How to check its authenticity? General answer:
Foundations of Network and Computer Security
Foundations of Network and Computer Security John Black Lecture #6 Sep 8 th 2005 CSCI 6268/TLEN 5831, Fall 2005 Announcements Quiz #1 later today Still some have not signed up for class mailing list Perhaps
L7. Diffie-Hellman (Key Exchange) Protocol. Rocky K. C. Chang, 5 March 2015
L7. Diffie-Hellman (Key Exchange) Protocol Rocky K. C. Chang, 5 March 2015 1 Outline The basic foundation: multiplicative group modulo prime The basic Diffie-Hellman (DH) protocol The discrete logarithm
Attribute-Based Encryption Optimized for Cloud Computing
ttribute-based Encryption Optimized for Cloud Computing Máté Horváth 27 January 1 / 17 Roadmap 1 Encryption in the Cloud 2 User Revocation 3 Background 4 The Proposed Scheme 5 Conclusion 2 / 17 Traditional
ECS 189A Final Cryptography Spring 2011
ECS 127: Cryptography Handout F UC Davis Phillip Rogaway June 9, 2011 ECS 189A Final Cryptography Spring 2011 Hints for success: Good luck on the exam. I don t think it s all that hard (I do believe I
Lecture 28: Public-key Cryptography. Public-key Cryptography
Lecture 28: Recall In private-key cryptography the secret-key sk is always established ahead of time The secrecy of the private-key cryptography relies on the fact that the adversary does not have access
Lecture Notes 20: Zero-Knowledge Proofs
CS 127/CSCI E-127: Introduction to Cryptography Prof. Salil Vadhan Fall 2013 Lecture Notes 20: Zero-Knowledge Proofs Reading. Katz-Lindell Ÿ14.6.0-14.6.4,14.7 1 Interactive Proofs Motivation: how can parties
Encuentro de tesistas - 13 of november 2012 Valparaiso. Predicate Preserving Collision-Resistant Hashing. Philippe Camacho
Encuentro de tesistas - 13 of november 2012 Valparaiso Predicate Preserving Collision-Resistant Hashing Philippe Camacho Motivation I need to outsource my database for scaling reasons How can I be sure
Notes for Lecture A can repeat step 3 as many times as it wishes. We will charge A one unit of time for every time it repeats step 3.
COS 533: Advanced Cryptography Lecture 2 (September 18, 2017) Lecturer: Mark Zhandry Princeton University Scribe: Mark Zhandry Notes for Lecture 2 1 Last Time Last time, we defined formally what an encryption
Introduction to Cybersecurity Cryptography (Part 4)
Introduction to Cybersecurity Cryptography (Part 4) Review of Last Lecture Blockciphers Review of DES Attacks on Blockciphers Advanced Encryption Standard (AES) Modes of Operation MACs and Hashes Message
Quiz 1 Solutions. (a) f 1 (n) = 8 n, f 2 (n) = , f 3 (n) = ( 3) lg n. f 2 (n), f 1 (n), f 3 (n) Solution: (b)
Introduction to Algorithms October 14, 2009 Massachusetts Institute of Technology 6.006 Spring 2009 Professors Srini Devadas and Constantinos (Costis) Daskalakis Quiz 1 Solutions Quiz 1 Solutions Problem
Katz, Lindell Introduction to Modern Cryptrography
Katz, Lindell Introduction to Modern Cryptrography Slides Chapter 12 Markus Bläser, Saarland University Digital signature schemes Goal: integrity of messages Signer signs a message using a private key
Post-quantum security models for authenticated encryption
Post-quantum security models for authenticated encryption Vladimir Soukharev David R. Cheriton School of Computer Science February 24, 2016 Introduction Bellare and Namprempre in 2008, have shown that
Introduction to Cybersecurity Cryptography (Part 4)
Introduction to Cybersecurity Cryptography (Part 4) Review of Last Lecture Blockciphers Review of DES Attacks on Blockciphers Advanced Encryption Standard (AES) Modes of Operation MACs and Hashes Message
Introduction to Cybersecurity Cryptography (Part 5)
Introduction to Cybersecurity Cryptography (Part 5) Prof. Dr. Michael Backes 13.01.2017 February 17 th Special Lecture! 45 Minutes Your Choice 1. Automotive Security 2. Smartphone Security 3. Side Channel
Public Key Cryptography
Public Key Cryptography Introduction Public Key Cryptography Unlike symmetric key, there is no need for Alice and Bob to share a common secret Alice can convey her public key to Bob in a public communication:
Entity Authentication
Entity Authentication Sven Laur swen@math.ut.ee University of Tartu Formal Syntax Entity authentication pk (sk, pk) Gen α 1 β 1 β i V pk (α 1,...,α i 1 ) α i P sk (β 1,...,β i 1 ) Is it Charlie? α k The
SPHINCS: practical stateless hash-based signatures
SPHINCS: practical stateless hash-based signatures D. J. Bernstein, D. Hopwood, A. Hülsing, T. Lange, R. Niederhagen, L. Papachristodoulou, P. Schwabe, and Z. Wilcox O'Hearn Digital Signatures are Important!
Chapter 7: Signature Schemes. COMP Lih-Yuan Deng
Chapter 7: Signature Schemes COMP 7120-8120 Lih-Yuan Deng lihdeng@memphis.edu Overview Introduction Security requirements for signature schemes ElGamal signature scheme Variants of ElGamal signature scheme
A New Knapsack Public-Key Cryptosystem Based on Permutation Combination Algorithm
A New Knapsack Public-Key Cryptosystem Based on Permutation Combination Algorithm Min-Shiang Hwang Cheng-Chi Lee Shiang-Feng Tzeng Department of Management Information System National Chung Hsing University
Introduction to Cryptography. Lecture 8
Introduction to Cryptography Lecture 8 Benny Pinkas page 1 1 Groups we will use Multiplication modulo a prime number p (G, ) = ({1,2,,p-1}, ) E.g., Z 7* = ( {1,2,3,4,5,6}, ) Z p * Z N * Multiplication
SPCS Cryptography Homework 13
1 1.1 PRP For this homework, use the ollowing PRP: E(k, m) : {0, 1} 3 {0, 1} 3 {0, 1} 3 000 001 010 011 100 101 110 111 m 000 011 001 111 010 000 101 110 100 001 101 110 010 000 111 100 001 011 010 001
Practice Exam Winter 2018, CS 485/585 Crypto March 14, 2018
Practice Exam Name: Winter 2018, CS 485/585 Crypto March 14, 2018 Portland State University Prof. Fang Song Instructions This exam contains 8 pages (including this cover page) and 5 questions. Total of
March 19: Zero-Knowledge (cont.) and Signatures
March 19: Zero-Knowledge (cont.) and Signatures March 26, 2013 1 Zero-Knowledge (review) 1.1 Review Alice has y, g, p and claims to know x such that y = g x mod p. Alice proves knowledge of x to Bob w/o
An Introduction. Dr Nick Papanikolaou. Seminar on The Future of Cryptography The British Computer Society 17 September 2009
An Dr Nick Papanikolaou Research Fellow, e-security Group International Digital Laboratory University of Warwick http://go.warwick.ac.uk/nikos Seminar on The Future of Cryptography The British Computer
Notes for Lecture 9. 1 Combining Encryption and Authentication
U.C. Berkeley CS276: Cryptography Handout N9 Luca Trevisan February 17, 2009 Notes for Lecture 9 Notes scribed by Joel Weinberger, posted March 1, 2009 Summary Last time, we showed that combining a CPA-secure
Cryptanalysis and improvement of an ID-based ad-hoc anonymous identification scheme at CT-RSA 05
Cryptanalysis and improvement of an ID-based ad-hoc anonymous identification scheme at CT-RSA 05 Fangguo Zhang 1 and Xiaofeng Chen 2 1 Department of Electronics and Communication Engineering, Sun Yat-sen
CS-E4320 Cryptography and Data Security Lecture 11: Key Management, Secret Sharing
Lecture 11: Key Management, Secret Sharing Céline Blondeau Email: celine.blondeau@aalto.fi Department of Computer Science Aalto University, School of Science Key Management Secret Sharing Shamir s Threshold
Notes on Zero Knowledge
U.C. Berkeley CS172: Automata, Computability and Complexity Handout 9 Professor Luca Trevisan 4/21/2015 Notes on Zero Knowledge These notes on zero knowledge protocols for quadratic residuosity are based
Authentication. Chapter Message Authentication
Chapter 5 Authentication 5.1 Message Authentication Suppose Bob receives a message addressed from Alice. How does Bob ensure that the message received is the same as the message sent by Alice? For example,
Elliptic curves: Theory and Applications. Day 4: The discrete logarithm problem.
Elliptic curves: Theory and Applications. Day 4: The discrete logarithm problem. Elisa Lorenzo García Université de Rennes 1 14-09-2017 Elisa Lorenzo García (Rennes 1) Elliptic Curves 4 14-09-2017 1 /
A Framework for Password-Based Authenticated Key Exchange
A Framework for Password-Based Authenticated Key Exchange Extended Abstract Rosario Gennaro and Yehuda Lindell IBM T.J. Watson Research Center Yorktown Heights, NY 10528, USA. {rosario,lindell}@us.ibm.com
Public Key Algorithms
Public Key Algorithms Raj Jain Washington University in Saint Louis Saint Louis, MO 63130 Jain@cse.wustl.edu Audio/Video recordings of this lecture are available at: http://www.cse.wustl.edu/~jain/cse571-09/
5199/IOC5063 Theory of Cryptology, 2014 Fall
5199/IOC5063 Theory of Cryptology, 2014 Fall Homework 2 Reference Solution 1. This is about the RSA common modulus problem. Consider that two users A and B use the same modulus n = 146171 for the RSA encryption.
Crypto math II. Alin Tomescu May 27, Abstract A quick overview on group theory from Ron Rivest s course in Spring 2015.
Crypto math II Alin Tomescu alinush@mit.edu May 7, 015 Abstract A quick overview on group theory from Ron Rivest s 6.857 course in Spring 015. 1 Overview Group theory review Diffie-Hellman (DH) key exchange
Improving Helios with Everlasting Privacy Towards the Public Denise Demirel, Jeroen van de Graaf, Roberto Araújo
Improving Helios with Everlasting Privacy Towards the Public Denise Demirel, Jeroen van de Graaf, Roberto Araúo 15.08.2012 Fachbereich 20 CDC Denise Demirel 1 Helios Introduced 2008 by Ben Adida Web application
Computer Science A Cryptography and Data Security. Claude Crépeau
Computer Science 308-547A Cryptography and Data Security Claude Crépeau These notes are, largely, transcriptions by Anton Stiglic of class notes from the former course Cryptography and Data Security (308-647A)
Lecture 1: Perfect Secrecy and Statistical Authentication. 2 Introduction - Historical vs Modern Cryptography
CS 7880 Graduate Cryptography September 10, 2015 Lecture 1: Perfect Secrecy and Statistical Authentication Lecturer: Daniel Wichs Scribe: Matthew Dippel 1 Topic Covered Definition of perfect secrecy One-time
The k-bdh Assumption Family: Bilinear Cryptography from Progressively Weaker Assumptions
The k-bdh Assumption Family: Bilinear Cryptography from Progressively Weaker Assumptions Karyn Benson (UCSD) Hovav Shacham (UCSD) Brent Waters (UT-Austin) Provable Security How to show your cryptosystem
2. Cryptography 2.5. ElGamal cryptosystems and Discrete logarithms
CRYPTOGRAPHY 19 Cryptography 5 ElGamal cryptosystems and Discrete logarithms Definition Let G be a cyclic group of order n and let α be a generator of G For each A G there exists an uniue 0 a n 1 such
Leftovers from Lecture 3
Leftovers from Lecture 3 Implementing GF(2^k) Multiplication: Polynomial multiplication, and then remainder modulo the defining polynomial f(x): (1,1,0,1,1) *(0,1,0,1,1) = (1,1,0,0,1) For small size finite
New Preimage Attack on MDC-4
New Preimage Attack on MDC-4 Deukjo Hong and Daesung Kwon Abstract In this paper, we provide some cryptanalytic results for double-blocklength (DBL) hash modes of block ciphers, MDC-4. Our preimage attacks
CRYPTANALYSIS OF COMPACT-LWE
SESSION ID: CRYP-T10 CRYPTANALYSIS OF COMPACT-LWE Jonathan Bootle, Mehdi Tibouchi, Keita Xagawa Background Information Lattice-based cryptographic assumption Based on the learning-with-errors (LWE) assumption
Introduction to Cryptography Lecture 4
Data Integrity, Message Authentication Introduction to Cryptography Lecture 4 Message authentication Hash functions Benny Pinas Ris: an active adversary might change messages exchanged between and M M
Cryptography CS 555. Topic 23: Zero-Knowledge Proof and Cryptographic Commitment. CS555 Topic 23 1
Cryptography CS 555 Topic 23: Zero-Knowledge Proof and Cryptographic Commitment CS555 Topic 23 1 Outline and Readings Outline Zero-knowledge proof Fiat-Shamir protocol Schnorr protocol Commitment schemes
Lecture 18 - Secret Sharing, Visual Cryptography, Distributed Signatures
Lecture 18 - Secret Sharing, Visual Cryptography, Distributed Signatures Boaz Barak November 27, 2007 Quick review of homework 7 Existence of a CPA-secure public key encryption scheme such that oracle
On the Impossibility of Batch Update for Cryptographic Accumulators
for Philippe Camacho (pcamacho@dcc.uchile.cl) Alejandro Hevia (ahevia@dcc.uchile.cl) FMCrypto Workshop: Formal Methods in Cryptography University of Chile March 24, 2010 Introduction This work is about
Lecture 10: HMAC and Number Theory
CS 6903 Modern Cryptography April 15, 2010 Lecture 10: HMAC and Number Theory Instructor: Nitesh Saxena Scribes: Anand Bidla, Samiksha Saxena,Varun Sanghvi 1 HMAC A Hash-based Message Authentication Code
Chapter 8 Public-key Cryptography and Digital Signatures
Chapter 8 Public-key Cryptography and Digital Signatures v 1. Introduction to Public-key Cryptography 2. Example of Public-key Algorithm: Diffie- Hellman Key Exchange Scheme 3. RSA Encryption and Digital
Basics in Cryptology. Outline. II Distributed Cryptography. Key Management. Outline. David Pointcheval. ENS Paris 2018
Basics in Cryptology II Distributed Cryptography David Pointcheval Ecole normale supérieure, CNRS & INRIA ENS Paris 2018 NS/CNRS/INRIA Cascade David Pointcheval 1/26ENS/CNRS/INRIA Cascade David Pointcheval
Definition: For a positive integer n, if 0<a<n and gcd(a,n)=1, a is relatively prime to n. Ahmet Burak Can Hacettepe University
Number Theory, Public Key Cryptography, RSA Ahmet Burak Can Hacettepe University abc@hacettepe.edu.tr The Euler Phi Function For a positive integer n, if 0
Carmen s Core Concepts (Math 135)
Carmen s Core Concepts (Math 135) Carmen Bruni University of Waterloo Week 8 1 The following are equivalent (TFAE) 2 Inverses 3 More on Multiplicative Inverses 4 Linear Congruence Theorem 2 [LCT2] 5 Fermat
during transmission safeguard information Cryptography: used to CRYPTOGRAPHY BACKGROUND OF THE MATHEMATICAL
THE MATHEMATICAL BACKGROUND OF CRYPTOGRAPHY Cryptography: used to safeguard information during transmission (e.g., credit card number for internet shopping) as opposed to Coding Theory: used to transmit
REU 2015: Complexity Across Disciplines. Introduction to Cryptography
REU 2015: Complexity Across Disciplines Introduction to Cryptography Symmetric Key Cryptosystems Iterated Block Ciphers Definition Let KS : K K s be a function that produces a set of subkeys k i K, 1 i
Converting Pairing-Based Cryptosystems from Composite-Order Groups to Prime-Order Groups
Converting Pairing-Based Cryptosystems from Composite-Order Groups to Prime-Order Groups David Mandell Freeman Stanford University, USA Eurocrypt 2010 Monaco, Monaco 31 May 2010 David Mandell Freeman (Stanford)
Lecture 7: ElGamal and Discrete Logarithms
Lecture 7: ElGamal and Discrete Logarithms Johan Håstad, transcribed by Johan Linde 2006-02-07 1 The discrete logarithm problem Recall that a generator g of a group G is an element of order n such that
ASYMMETRIC ENCRYPTION
ASYMMETRIC ENCRYPTION 1 / 1 Recommended Book Steven Levy. Crypto. Penguin books. 2001. A non-technical account of the history of public-key cryptography and the colorful characters involved. 2 / 1 Recall
CRYPTOGRAPHY AND NUMBER THEORY
CRYPTOGRAPHY AND NUMBER THEORY XINYU SHI Abstract. In this paper, we will discuss a few examples of cryptographic systems, categorized into two different types: symmetric and asymmetric cryptography. We
CSC 774 Advanced Network Security
CSC 774 Advanced Network Security Topic 2.6 ID Based Cryptography #2 Slides by An Liu Outline Applications Elliptic Curve Group over real number and F p Weil Pairing BasicIdent FullIdent Extensions Escrow
Public Key Cryptography
Public Key Cryptography Spotlight on Science J. Robert Buchanan Department of Mathematics 2011 What is Cryptography? cryptography: study of methods for sending messages in a form that only be understood
Public-key cryptography and the Discrete-Logarithm Problem. Tanja Lange Technische Universiteit Eindhoven. with some slides by Daniel J.
Public-key cryptography and the Discrete-Logarithm Problem Tanja Lange Technische Universiteit Eindhoven with some slides by Daniel J. Bernstein Cryptography Let s understand what our browsers do. Schoolbook
CSC 774 Advanced Network Security
CSC 774 Advanced Network Security Topic 2.6 ID Based Cryptography #2 Slides by An Liu Outline Applications Elliptic Curve Group over real number and F p Weil Pairing BasicIdent FullIdent Extensions Escrow
Breaking H 2 -MAC Using Birthday Paradox
Breaking H 2 -MAC Using Birthday Paradox Fanbao Liu 1,2, Tao Xie 1 and Changxiang Shen 2 1 School of Computer, National University of Defense Technology, Changsha, 410073, Hunan, P. R. China 2 School of
The Random Oracle Paradigm. Mike Reiter. Random oracle is a formalism to model such uses of hash functions that abound in practical cryptography
1 The Random Oracle Paradigm Mike Reiter Based on Random Oracles are Practical: A Paradigm for Designing Efficient Protocols by M. Bellare and P. Rogaway Random Oracles 2 Random oracle is a formalism to
Vector Commitments and their Applications
Vector Commitments and their Applications Dario Catalano 1 and Dario Fiore 2 1 Dipartimento di Matematica e Informatica, Università di Catania, Italy. catalano@dmi.unict.it 2 Max Planck Institute for Software
Lattice-Based Cryptography
Liljana Babinkostova Department of Mathematics Computing Colloquium Series Detecting Sensor-hijack Attacks in Wearable Medical Systems Krishna Venkatasubramanian Worcester Polytechnic Institute Quantum
Lattice Cryptography
CSE 206A: Lattice Algorithms and Applications Winter 2016 Lattice Cryptography Instructor: Daniele Micciancio UCSD CSE Lattice cryptography studies the construction of cryptographic functions whose security
Practice Final Exam Winter 2017, CS 485/585 Crypto March 14, 2017
Practice Final Exam Name: Winter 2017, CS 485/585 Crypto March 14, 2017 Portland State University Prof. Fang Song Instructions This exam contains 7 pages (including this cover page) and 5 questions. Total
CHAPTER 6: OTHER CRYPTOSYSTEMS, PSEUDO-RANDOM NUMBER GENERATORS and HASH FUNCTIONS. Part VI
CHAPTER 6: OTHER CRYPTOSYSTEMS, PSEUDO-RANDOM NUMER GENERATORS and HASH FUNCTIONS Part VI Public-key cryptosystems, II. Other cryptosystems, security, PRG, hash functions A large number of interesting
Algorithmic Number Theory and Public-key Cryptography
Algorithmic Number Theory and Public-key Cryptography Course 3 University of Luxembourg March 22, 2018 The RSA algorithm The RSA algorithm is the most widely-used public-key encryption algorithm Invented
Lecture 4 Chiu Yuen Koo Nikolai Yakovenko. 1 Summary. 2 Hybrid Encryption. CMSC 858K Advanced Topics in Cryptography February 5, 2004
CMSC 858K Advanced Topics in Cryptography February 5, 2004 Lecturer: Jonathan Katz Lecture 4 Scribe(s): Chiu Yuen Koo Nikolai Yakovenko Jeffrey Blank 1 Summary The focus of this lecture is efficient public-key
Lecture 10: NMAC, HMAC and Number Theory
CS 6903 Modern Cryptography April 13, 2011 Lecture 10: NMAC, HMAC and Number Theory Instructor: Nitesh Saxena Scribes: Anand Desai,Manav Singh Dahiya,Amol Bhavekar 1 Recap 1.1 MACs A Message Authentication
CPSC 467b: Cryptography and Computer Security
Outline Authentication CPSC 467b: Cryptography and Computer Security Lecture 18 Michael J. Fischer Department of Computer Science Yale University March 29, 2010 Michael J. Fischer CPSC 467b, Lecture 18
Question: Total Points: Score:
University of California, Irvine COMPSCI 134: Elements of Cryptography and Computer and Network Security Midterm Exam (Fall 2016) Duration: 90 minutes November 2, 2016, 7pm-8:30pm Name (First, Last): Please
A Knapsack Cryptosystem Based on The Discrete Logarithm Problem
A Knapsack Cryptosystem Based on The Discrete Logarithm Problem By K.H. Rahouma Electrical Technology Department Technical College in Riyadh Riyadh, Kingdom of Saudi Arabia E-mail: kamel_rahouma@yahoo.com
CS 4770: Cryptography. CS 6750: Cryptography and Communication Security. Alina Oprea Associate Professor, CCIS Northeastern University
CS 4770: Cryptography CS 6750: Cryptography and Communication Security Alina Oprea Associate Professor, CCIS Northeastern University March 26 2017 Outline RSA encryption in practice Transform RSA trapdoor
Pseudorandom Generators
Principles of Construction and Usage of Pseudorandom Generators Alexander Vakhitov June 13, 2005 Abstract In this report we try to talk about the main concepts and tools needed in pseudorandom generators
McBits: Fast code-based cryptography
McBits: Fast code-based cryptography Peter Schwabe Radboud University Nijmegen, The Netherlands Joint work with Daniel Bernstein, Tung Chou December 17, 2013 IMA International Conference on Cryptography
A survey on quantum-secure cryptographic systems
A survey on quantum-secure cryptographic systems Tomoka Kan May 24, 2018 1 Abstract Post-quantum cryptography refers to the search for classical cryptosystems which remain secure in the presence of a quantum
How to Use Short Basis : Trapdoors for Hard Lattices and new Cryptographic Constructions
Presentation Article presentation, for the ENS Lattice Based Crypto Workgroup http://www.di.ens.fr/~pnguyen/lbc.html, 30 September 2009 How to Use Short Basis : Trapdoors for http://www.cc.gatech.edu/~cpeikert/pubs/trap_lattice.pdf