After two decades of research and development, elliptic curve cryptography now has widespread exposure and acceptance. Industry, banking, and government standards are in place to facilitate extensive deployment of this efficient public-key mechanism. Anchored by a comprehensive treatment of the practical aspects of elliptic curve cryptography (ECC), this guide explains the basic mathematics, describes state-of-the-art implementation methods, and presents standardized protocols for public-key encryption, digital signatures, and key establishment. In addition, the book addresses some issues that arise in software and hardware implementation, as well as side-channel attacks and countermeasures. Readers receive the theoretical fundamentals as an underpinning for a wealth of practical and accessible knowledge about efficient application. Features & Benefits: * Breadth of coverage and unified, integrated approach to elliptic curve cryptosystems * Describes important industry and government protocols, such as the FIPS 186-2 standard from the U.S. National Institute for Standards and Technology * Provides full exposition on techniques for efficiently implementing finite-field and elliptic curve arithmetic* Distills complex mathematics and algorithms for easy understanding* Includes useful literature references, a list of algorithms, and appendices on sample parameters, ECC standards, and software toolsThis comprehensive, highly focused reference is a useful and indispensable resource for practitioners, professionals, or researchers in computer science, computer engineering, network design, and network data security.

https://cdn.preterhuman.net/texts/cryptography/Hankerson,%20Menezes,%20Vanstone.%20Guide%20to%20elliptic%20curve%20cryptography%20(Springer,%202004)(ISBN%20038795273X)(332s)_CsCr_.pdf

Guide to Elliptic Curve Cryptography

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

We quantitatively investigate how machine learning models leak information about the individual data records on which they were trained. We focus on the basic membership inference attack: given a data record and black-box access to a model, determine if the record was in the model's training dataset. To perform membership inference against a target model, we make adversarial use of machine learning and train our own inference model to recognize differences in the target model's predictions on the inputs that it trained on versus the inputs that it did not train on. We empirically evaluate our inference techniques on classification models trained by commercial "machine learning as a service" providers such as Google and Amazon. Using realistic datasets and classification tasks, including a hospital discharge dataset whose membership is sensitive from the privacy perspective, we show that these models can be vulnerable to membership inference attacks. We then investigate the factors that influence this leakage and evaluate mitigation strategies.

/pdf/membership-inference-attacks-against-machine-learning-models-2tzchejf91.pdf

Membership Inference Attacks Against Machine Learning Models

인공고관절의 세라믹 볼 헤드의 기계적 안정성 평가를 위한 3 차원 유한요소 해석

We present a novel approach to fully homomorphic encryption (FHE) that dramatically improves performance and bases security on weaker assumptions. A central conceptual contribution in our work is a new way of constructing leveled fully homomorphic encryption schemes (capable of evaluating arbitrary polynomial-size circuits), without Gentry's bootstrapping procedure.Specifically, we offer a choice of FHE schemes based on the learning with error (LWE) or ring-LWE (RLWE) problems that have 2λ security against known attacks. For RLWE, we have:• A leveled FHE scheme that can evaluate L-level arithmetic circuits with O(λ · L3) per-gate computation -- i.e., computation quasi-linear in the security parameter. Security is based on RLWE for an approximation factor exponential in L. This construction does not use the bootstrapping procedure.• A leveled FHE scheme that uses bootstrapping as an optimization, where the per-gate computation (which includes the bootstrapping procedure) is O(λ2), independent of L. Security is based on the hardness of RLWE for quasi-polynomial factors (as opposed to the sub-exponential factors needed in previous schemes).We obtain similar results to the above for LWE, but with worse performance.Based on the Ring LWE assumption, we introduce a number of further optimizations to our schemes. As an example, for circuits of large width -- e.g., where a constant fraction of levels have width at least λ -- we can reduce the per-gate computation of the bootstrapped version to O(λ), independent of L, by batching the bootstrapping operation. Previous FHE schemes all required Ω(λ3.5) computation per gate.At the core of our construction is a much more effective approach for managing the noise level of lattice-based ciphertexts as homomorphic operations are performed, using some new techniques recently introduced by Brakerski and Vaikuntanathan (FOCS 2011).

/pdf/leveled-fully-homomorphic-encryption-without-bootstrapping-f85icd2a59.pdf

Leveled) fully homomorphic encryption without bootstrapping

We demonstrate that, by using a recently proposed leveled homomorphic encryption scheme, it is possible to delegate the execution of a machine learning algorithm to a computing service while retaining confidentiality of the training and test data. Since the computational complexity of the homomorphic encryption scheme depends primarily on the number of levels of multiplications to be carried out on the encrypted data, we define a new class of machine learning algorithms in which the algorithm's predictions, viewed as functions of the input data, can be expressed as polynomials of bounded degree. We propose confidential algorithms for binary classification based on polynomial approximations to least-squares solutions obtained by a small number of gradient descent steps. We present experimental validation of the confidential machine learning pipeline and discuss the trade-offs regarding computational complexity, prediction accuracy and cryptographic security.

/pdf/ml-confidential-machine-learning-on-encrypted-data-3fsuwg3wzg.pdf

ML confidential: machine learning on encrypted data

This article provides an overview of elliptic curves and their use in cryptography. The focus is on the performance advantages to be obtained in the wireless environment by using elliptic curve cryptography instead of a traditional cryptosystem like RSA. Specific applications to secure messaging and identity-based encryption are discussed.

The advantages of elliptic curve cryptography for wireless security

In 1996, Hoffstein, Pipher and Silverman introduced an efficient lattice based encryption scheme dubbed NTRUEncrypt . Unfortunately, this scheme lacks a proof of security. However, in 2011, Stehle and Steinfeld showed how to modify NTRUEncrypt to reduce security to standard problems in ideal lattices. In 2012, Lopez-Alt, Tromer and Vaikuntanathan proposed a fully homomorphic scheme based on this modified system. However, to allow homomorphic operations and prove security, a non-standard assumption is required. In this paper, we show how to remove this non-standard assumption via techniques introduced by Brakerski and construct a new fully homomorphic encryption scheme from the Stehle and Steinfeld version based on standard lattice assumptions and a circular security assumption. The scheme is scale-invariant and therefore avoids modulus switching and the size of ciphertexts is one ring element. Moreover, we present a practical variant of our scheme, which is secure under stronger assumptions, along with parameter recommendations and promising implementation results. Finally, we present an approach for encrypting larger input sizes by extending ciphertexts to several ring elements via the CRT on the message space.

/pdf/improved-security-for-a-ring-based-fully-homomorphic-ejw001fkd0.pdf

Improved Security for a Ring-Based Fully Homomorphic Encryption Scheme

We propose constructing provable collision resistant hash functions from expander graphs in which finding cycles is hard. As examples, we investigate two specific families of optimal expander graphs for provable collision resistant hash function constructions: the families of Ramanujan graphs constructed by Lubotzky-Phillips-Sarnak and Pizer respectively. When the hash function is constructed from one of Pizers Ramanujan graphs, (the set of supersingular elliptic curves over with l-isogenies, l a prime different from p), then collision resistance follows from hardness of computing isogenies between supersingular elliptic curves. For the LPS graphs, the underlying hard problem is a representation problem in group theory. Constructing our hash functions from optimal expander graphs implies that the outputs closely approximate the uniform distribution. This property is useful for arguing that the output is indistinguishable from random sequences of bits. We estimate the cost per bit to compute these hash functions, and we implement our hash function for several members of the Pizer and LPS graph families and give actual timings.

/pdf/cryptographic-hash-functions-from-expander-graphs-4qzkjdgj1b.pdf

Cryptographic Hash Functions from Expander Graphs

https://cryptosith.org/papers/biopredict-20141125.pdf

Kristin E. Lauter

Papers

ML confidential: machine learning on encrypted data

The advantages of elliptic curve cryptography for wireless security

Improved Security for a Ring-Based Fully Homomorphic Encryption Scheme

Cryptographic Hash Functions from Expander Graphs

Private predictive analysis on encrypted medical data