There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The increasing volume of data in modern business and science calls for more complex and sophisticated tools. Although advances in data mining technology have made extensive data collection much easier, it's still always evolving and there is a constant need for new techniques and tools that can help us transform this data into useful information and knowledge. Since the previous edition's publication, great advances have been made in the field of data mining. Not only does the third of edition of Data Mining: Concepts and Techniques continue the tradition of equipping you with an understanding and application of the theory and practice of discovering patterns hidden in large data sets, it also focuses on new, important topics in the field: data warehouses and data cube technology, mining stream, mining social networks, and mining spatial, multimedia and other complex data. Each chapter is a stand-alone guide to a critical topic, presenting proven algorithms and sound implementations ready to be used directly or with strategic modification against live data. This is the resource you need if you want to apply today's most powerful data mining techniques to meet real business challenges. * Presents dozens of algorithms and implementation examples, all in pseudo-code and suitable for use in real-world, large-scale data mining projects. * Addresses advanced topics such as mining object-relational databases, spatial databases, multimedia databases, time-series databases, text databases, the World Wide Web, and applications in several fields. *Provides a comprehensive, practical look at the concepts and techniques you need to get the most out of real business data

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Data Mining: Concepts and Techniques

We propose a novel paradigm for defining security of cryptographic protocols, called universally composable security. The salient property of universally composable definitions of security is that they guarantee security even when a secure protocol is composed of an arbitrary set of protocols, or more generally when the protocol is used as a component of an arbitrary system. This is an essential property for maintaining security of cryptographic protocols in complex and unpredictable environments such as the Internet. In particular, universally composable definitions guarantee security even when an unbounded number of protocol instances are executed concurrently in an adversarially controlled manner, they guarantee non-malleability with respect to arbitrary protocols, and more. We show how to formulate universally composable definitions of security for practically any cryptographic task. Furthermore, we demonstrate that practically any such definition can be realized using known techniques, as long as only a minority of the participants are corrupted. We then proceed to formulate universally composable definitions of a wide array of cryptographic tasks, including authenticated and secure communication, key-exchange, public-key encryption, signature, commitment, oblivious transfer, zero knowledge and more. We also make initial steps towards studying the realizability of the proposed definitions in various settings.

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Universally composable security: a new paradigm for cryptographic protocols

Machine learning techniques based on neural networks are achieving remarkable results in a wide variety of domains. Often, the training of models requires large, representative datasets, which may be crowdsourced and contain sensitive information. The models should not expose private information in these datasets. Addressing this goal, we develop new algorithmic techniques for learning and a refined analysis of privacy costs within the framework of differential privacy. Our implementation and experiments demonstrate that we can train deep neural networks with non-convex objectives, under a modest privacy budget, and at a manageable cost in software complexity, training efficiency, and model quality.

Deep Learning with Differential Privacy

Today’s artificial intelligence still faces two major challenges. One is that, in most industries, data exists in the form of isolated islands. The other is the strengthening of data privacy and security. We propose a possible solution to these challenges: secure federated learning. Beyond the federated-learning framework first proposed by Google in 2016, we introduce a comprehensive secure federated-learning framework, which includes horizontal federated learning, vertical federated learning, and federated transfer learning. We provide definitions, architectures, and applications for the federated-learning framework, and provide a comprehensive survey of existing works on this subject. In addition, we propose building data networks among organizations based on federated mechanisms as an effective solution to allowing knowledge to be shared without compromising user privacy.

Federated Machine Learning: Concept and Applications

Preface I. Introduction and Classical Cryptography Introduction Cryptography and Modern Cryptography The Setting of Private-Key Encryption Historical Ciphers and Their Cryptanalysis Principles of Modern Cryptography Principle 1 - Formal Definitions Principle 2 - Precise Assumptions Principle 3 - Proofs of Security Provable Security and Real-World Security References and Additional Reading Exercises Perfectly Secret Encryption Definitions The One-Time Pad Limitations of Perfect Secrecy Shannon's Theorem References and Additional Reading Exercises II. Private-Key (Symmetric) Cryptography Private-Key Encryption Computational Security The Concrete Approach The Asymptotic Approach Defining Computationally Secure Encryption The Basic Definition of Security Semantic Security Constructing Secure Encryption Schemes Pseudorandom Generators and Stream Ciphers Proofs by Reduction A Secure Fixed-Length Encryption Scheme Stronger Security Notions Security for Multiple Encryptions Chosen-Plaintext Attacks and CPA-Security Constructing CPA-Secure Encryption Schemes Pseudorandom Functions and Block Ciphers CPA-Secure Encryption from Pseudorandom Functions Modes of Operation Stream-Cipher Modes of Operation Block-Cipher Modes of Operation Chosen-Ciphertext Attacks Defining CCA-Security Padding-Oracle Attacks References and Additional Reading Exercises Message Authentication Codes Message Integrity Secrecy vs. Integrity Encryption vs. Message Authentication Message Authentication Codes - Definitions Constructing Secure Message Authentication Codes A Fixed-Length MAC Domain Extension for MACs CBC-MAC The Basic Construction Proof of Security Authenticated Encryption Definitions Generic Constructions Secure Communication Sessions CCA-Secure Encryption Information-Theoretic MACs Constructing Information-Theoretic MACs Limitations on Information-Theoretic MACs References and Additional Reading Exercises Hash Functions and Applications Definitions Collision Resistance Weaker Notions of Security Domain Extension: The Merkle-Damgard Transform Message Authentication Using Hash Functions Hash-and-MAC HMAC Generic Attacks on Hash Functions Birthday Attacks for Finding Collisions Small-Space Birthday Attacks Time/Space Tradeoffs for Inverting Functions The Random-Oracle Model The Random-Oracle Model in Detail Is the Random-Oracle Methodology Sound? Additional Applications of Hash Functions Fingerprinting and Deduplication Merkle Trees Password Hashing Key Derivation Commitment Schemes References and Additional Reading Exercises Practical Constructions of Symmetric-Key Primitives Stream Ciphers Linear-Feedback Shift Registers Adding Nonlinearity Trivium RC4 Block Ciphers Substitution-Permutation Networks Feistel Networks DES - The Data Encryption Standard 3DES: Increasing the Key Length of a Block Cipher AES - The Advanced Encryption Standard Differential and Linear Cryptanalysis Hash Functions Hash Functions from Block Ciphers MD5 SHA-0, SHA-1, and SHA-2 SHA-3 (Keccak) References and Additional Reading Exercises Theoretical Constructions of Symmetric-Key Primitives One-Way Functions Definitions Candidate One-Way Functions Hard-Core Predicates From One-Way Functions to Pseudorandomness Hard-Core Predicates from One-Way Functions A Simple Case A More Involved Case The Full Proof Constructing Pseudorandom Generators Pseudorandom Generators with Minimal Expansion Increasing the Expansion Factor Constructing Pseudorandom Functions Constructing (Strong) Pseudorandom Permutations Assumptions for Private-Key Cryptography Computational Indistinguishability References and Additional Reading Exercises III. Public-Key (Asymmetric) Cryptography Number Theory and Cryptographic Hardness Assumptions Preliminaries and Basic Group Theory Primes and Divisibility Modular Arithmetic Groups The Group ZN Isomorphisms and the Chinese Remainder Theorem Primes, Factoring, and RSA Generating Random Primes Primality Testing The Factoring Assumption The RSA Assumption Relating the RSA and Factoring Assumptions Cryptographic Assumptions in Cyclic Groups Cyclic Groups and Generators The Discrete-Logarithm/Diffie-Hellman Assumptions Working in (Subgroups of) Zp Elliptic Curves Cryptographic Applications One-Way Functions and Permutations Constructing Collision-Resistant Hash Functions References and Additional Reading Exercises Algorithms for Factoring and Computing Discrete Logarithms Algorithms for Factoring Pollard's p - 1 Algorithm Pollard's Rho Algorithm The Quadratic Sieve Algorithm Algorithms for Computing Discrete Logarithms The Pohlig-Hellman Algorithm The Baby-Step/Giant-Step Algorithm Discrete Logarithms from Collisions The Index Calculus Algorithm Recommended Key Lengths References and Additional Reading Exercises Key Management and the Public-Key Revolution Key Distribution and Key Management A Partial Solution: Key-Distribution Centers Key Exchange and the Diffie-Hellman Protocol The Public-Key Revolution References and Additional Reading Exercises Public-Key Encryption Public-Key Encryption - An Overview Definitions Security against Chosen-Plaintext Attacks Multiple Encryptions Security against Chosen-Ciphertext Attacks Hybrid Encryption and the KEM/DEM Paradigm CPA-Security CCA-Security CDH/DDH-Based Encryption El Gamal Encryption DDH-Based Key Encapsulation A CDH-Based KEM in the Random-Oracle Model Chosen-Ciphertext Security and DHIES/ECIES RSA Encryption Plain RSA Padded RSA and PKCS #1 v1.5 CPA-Secure Encryption without Random Oracles OAEP and RSA PKCS #1 v A CCA-Secure KEM in the Random-Oracle Model RSA Implementation Issues and Pitfalls References and Additional Reading Exercises Digital Signature Schemes Digital Signatures - An Overview Definitions The Hash-and-Sign Paradigm RSA Signatures Plain RSA RSA-FDH and PKCS #1 v Signatures from the Discrete-Logarithm Problem The Schnorr Signature Scheme DSA and ECDSA Signatures from Hash Functions Lamport's Signature Scheme Chain-Based Signatures Tree-Based Signatures Certificates and Public-Key Infrastructures Putting It All Together - SSL/TLS Signcryption References and Additional Reading Exercises Advanced Topics in Public-Key Encryption Public-Key Encryption from Trapdoor Permutations Trapdoor Permutations Public-Key Encryption from Trapdoor Permutations The Paillier Encryption Scheme The Structure of ZN2 The Paillier Encryption Scheme Homomorphic Encryption Secret Sharing and Threshold Encryption Secret Sharing Verifiable Secret Sharing Threshold Encryption and Electronic Voting The Goldwasser-Micali Encryption Scheme Quadratic Residues Modulo a Prime Quadratic Residues Modulo a Composite The Quadratic Residuosity Assumption The Goldwasser-Micali Encryption Scheme The Rabin Encryption Scheme Computing Modular Square Roots A Trapdoor Permutation Based on Factoring The Rabin Encryption Scheme References and Additional Reading Exercises Index of Common Notation Appendix A: Mathematical Background Identities and Inequalities Asymptotic Notation Basic Probability The "Birthday" Problem Finite Fields Appendix B: Basic Algorithmic Number Theory Integer Arithmetic Basic Operations The Euclidean and Extended Euclidean Algorithms Modular Arithmetic Basic Operations Computing Modular Inverses Modular Exponentiation Montgomery Multiplication Choosing a Uniform Group Element Finding a Generator of a Cyclic Group Group-Theoretic Background Efficient Algorithms References and Additional Reading Exercises References Index

Introduction to Modern Cryptography

In this paper we introduce the concept of privacy preserving data mining. In our model, two parties owning confidential databases wish to run a data mining algorithm on the union of their databases, without revealing any unnecessary information. This problem has many practical and important applications, such as in medical research with confidential patient records.

Data mining algorithms are usually complex, especially as the size of the input is measured in megabytes, if not gigabytes. A generic secure multi-party computation solution, based on evaluation of a circuit computing the algorithm on the entire input, is therefore of no practical use. We focus on the problem of decision tree learning and use ID3, a popular and widely used algorithm for this problem. We present a solution that is considerably more efficient than generic solutions. It demands very few rounds of communication and reasonable bandwidth. In our solution, each party performs by itself a computation of the same order as computing the ID3 algorithm for its own database. The results are then combined using efficient cryptographic protocols, whose overhead is only logarithmic in the number of transactions in the databases. We feel that our result is a substantial contribution, demonstrating that secure multi-party computation can be made practical, even for complex problems and large inputs.

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Privacy Preserving Data Mining

In the mid 1980s, Yao presented a constant-round protocol for securely computing any two-party functionality in the presence of semi-honest adversaries (FOCS 1986). In this paper, we provide a complete description of Yao’s protocol, along with a rigorous proof of security. Despite the importance of Yao’s protocol to the theory of cryptography and in particular to the field of secure computation, to the best of our knowledge, this is the first time that an explicit proof of security has been published.

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A Proof of Security of Yao’s Protocol for Two-Party Computation

We show how to securely realize any multi-party functionality in a universally composable way, regardless of the number of corrupted participants. That is, we consider a multi-party network with open communication and an adversary that can adaptively corrupt as many parties as it wishes. In this setting, our protocols allow any subset of the parties (with pairs of parties being a special case) to securely realize any desired functionality of their local inputs, and be guaranteed that security is preserved regardless of the activity in the rest of the network. This implies that security is preserved under concurrent composition of an unbounded number of protocol executions, it implies non-malleability with respect to arbitrary protocols, and more. Our constructions are in the common reference string model and make general intractability assumptions.

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Universally composable two-party and multi-party secure computation

In this paper we introduce the concept of privacy preserving data mining. In our model, two parties owning confidential databases wish to run a data mining algorithm on the union of their databases, without revealing any unnecessary information. This problem has many practical and important applications, such as in medical research with confidential patient records. Data mining algorithms are usually complex, especially as the size of the input is measured in megabytes, if not gigabytes. A generic secure multi-party computation solution, based on evaluation of a circuit computing the algorithm on the entire input, is therefore of no practical use. We focus on the problem of decision tree learning and use ID3, a popular and widely used algorithm for this problem. We present a solution that is considerably more efficient than generic solutions. It demands very few rounds of communication and reasonable bandwidth. In our solution, each party performs by itself a computation of the same order as computing the ID3 algorithm for its own database. The results are then combined using efficient cryptographic protocols, whose overhead is only logarithmic in the number of transactions in the databases. We feel that our result is a substantial contribution, demonstrating that secure multi-party computation can be made practical, even for complex problems and large inputs.

Yehuda Lindell

Papers

Introduction to Modern Cryptography

Privacy Preserving Data Mining

A Proof of Security of Yao’s Protocol for Two-Party Computation

Universally composable two-party and multi-party secure computation

Privacy preserving data mining