Introduction to homomorphic encryption, encryption which allows computations on ciphertext. An overview of key aspects and the ideas that allow these schemes to work is given, as well as examples of how to apply it.
Christoph Matthies (@chrisma0), Hubert Hesse (@hubx), Robert Lehmann (@rlehmann)
Distributed Machine Learning with Apache MahoutSuneel Marthi
This document discusses Apache Mahout, an open source machine learning library. It provides examples of using Mahout for tasks like linear regression, dimensionality reduction, and data visualization. Key points covered include loading and manipulating distributed datasets, fitting regression models, evaluating predictions, and visualizing high-dimensional data in 2D and 3D plots.
1) EIRDH-P combines public key cryptography and steganography by encrypting images and embedding secret messages within the encrypted images.
2) It involves an Image Provider who encrypts a cover image using public key encryption. A Data Hider then embeds a secret message within the encrypted image.
3) The receiver decrypts the stego-image to extract the secret message and recover the original cover image using their private key.
The document provides examples for calculating derivatives and integrals of functions. It begins by defining the derivative and introducing notation. Several properties of derivatives are then listed, followed by common derivative formulas. The remainder of the document consists of 8 examples solving integrals using the properties of derivatives and integral formulas. Each example shows the steps to calculate the integral of a given function.
While porting 32-bit software to 64-bit systems there may appear some errors in the code of applications which were written in C++ language. The cause for these hides in the alteration of the base data types (to be more exact, in the relations between them) with the new hardware platform.
The document discusses program derivation and efficient programs. It covers topics like algorithm specification, correctness through verification, program construction through derivation and synthesis. It also covers concepts like foldr, foldl, list homomorphisms, and program fusion. Foldr and foldl are defined for recursively processing lists. Foldr processes the list from right to left, while foldl processes it from left to right. Program fusion techniques like map-fusion and foldr-fusion are discussed to improve efficiency by fusing together compositions of functions like map and foldr.
1) The document provides definitions and formulas for calculating derivatives, including the derivative of a function at a point, the derivative function, and common derivatives of basic functions like polynomials, exponentials, logarithms, trigonometric functions, and inverse trigonometric functions.
2) Examples are given of calculating derivatives using the definition of the derivative, for functions like f(x)=3x^2, f(x)=x+1, and f(x)=1/x.
3) Rules are listed for calculating the derivatives of sums, products, quotients of functions using properties of derivatives.
Distributed Machine Learning with Apache MahoutSuneel Marthi
This document discusses Apache Mahout, an open source machine learning library. It provides examples of using Mahout for tasks like linear regression, dimensionality reduction, and data visualization. Key points covered include loading and manipulating distributed datasets, fitting regression models, evaluating predictions, and visualizing high-dimensional data in 2D and 3D plots.
1) EIRDH-P combines public key cryptography and steganography by encrypting images and embedding secret messages within the encrypted images.
2) It involves an Image Provider who encrypts a cover image using public key encryption. A Data Hider then embeds a secret message within the encrypted image.
3) The receiver decrypts the stego-image to extract the secret message and recover the original cover image using their private key.
The document provides examples for calculating derivatives and integrals of functions. It begins by defining the derivative and introducing notation. Several properties of derivatives are then listed, followed by common derivative formulas. The remainder of the document consists of 8 examples solving integrals using the properties of derivatives and integral formulas. Each example shows the steps to calculate the integral of a given function.
While porting 32-bit software to 64-bit systems there may appear some errors in the code of applications which were written in C++ language. The cause for these hides in the alteration of the base data types (to be more exact, in the relations between them) with the new hardware platform.
The document discusses program derivation and efficient programs. It covers topics like algorithm specification, correctness through verification, program construction through derivation and synthesis. It also covers concepts like foldr, foldl, list homomorphisms, and program fusion. Foldr and foldl are defined for recursively processing lists. Foldr processes the list from right to left, while foldl processes it from left to right. Program fusion techniques like map-fusion and foldr-fusion are discussed to improve efficiency by fusing together compositions of functions like map and foldr.
1) The document provides definitions and formulas for calculating derivatives, including the derivative of a function at a point, the derivative function, and common derivatives of basic functions like polynomials, exponentials, logarithms, trigonometric functions, and inverse trigonometric functions.
2) Examples are given of calculating derivatives using the definition of the derivative, for functions like f(x)=3x^2, f(x)=x+1, and f(x)=1/x.
3) Rules are listed for calculating the derivatives of sums, products, quotients of functions using properties of derivatives.
This document summarizes the solution steps to determine the reactions and bending moments for a beam with a fixed edge at X=0 and a roller edge at X=L. It involves applying boundary conditions to determine constants C1 through C4 in the polynomial expression for deflection W(x). The constants are then used to calculate the bending moment M(X) and shear force S(X) expressions, and to determine the reactions and moments at the two edges.
ASFWS 2012 - Hash-flooding DoS reloaded: attacks and defenses par Jean-Philip...Cyber Security Alliance
This document discusses hash flooding denial of service (DoS) attacks and defenses. It presents the theory behind exploiting weaknesses in hash functions like MurmurHash2/3 through differential cryptanalysis. Specifically, it shows how to generate multicollision inputs that result in the same hash value. This allows an attacker to force worst-case insertion times into hash tables, overloading systems. The document notes that many systems using MurmurHash2/3 remain vulnerable. It then discusses potential real-world attacks against uses of hashes in applications like web frameworks. As an example, it demonstrates how to attack internal hash tables in Ruby on Rails, though default protections prevent attacks on request parameters.
This document provides formulas for integrals of common functions. It includes integrals of polynomials, rational functions, functions with roots, logarithms, exponentials, trigonometric functions, hyperbolic functions, and products of various functions. There are over 100 formulas presented in a table format with the function and integral provided.
(1) This document discusses random variables and stochastic processes. It defines key concepts such as random variables, probability mass functions, cumulative distribution functions, discrete and continuous random variables.
(2) It provides examples of defining random variables for experiments involving coin tosses and ball drawings. It illustrates how to determine the probability mass function and cumulative distribution function of discrete random variables.
(3) The document also discusses continuous random variables and their probability density functions. It introduces the concepts of joint probability distributions for two random variables and how to find marginal and conditional probabilities.
1) This document provides formulas for integrals of common functions including polynomials, rational functions, radicals, logarithms, trigonometric functions, exponentials, and hyperbolic functions.
2) The integrals are organized into sections based on the type of function, with the formula provided along with conditions on parameters.
3) There are over 100 integrals presented in the table spanning multiple pages of formulas.
This document provides formulas for integrals involving common functions including:
- Logarithms
- Roots
- Rational functions
- Trigonometric functions
- Exponentials
- Products of functions
It includes the basic forms for integrals with these functions as well as more complex integrals combining multiple functions. The integrals are grouped by function type for easy reference.
(i) The derivative of an exponential function with base e and variable x is the same exponential function multiplied by the derivative of x, which is 1.
(ii) To take the derivative of an exponential function raised to a power, use the power rule and multiply the derivative of the exponential by the power.
(iii) When adding exponential functions with the same base, the derivatives are added separately and the sums are multiplied by the common exponential term.
The document describes various probability distributions that can arise from combining Bernoulli random variables. It shows how a binomial distribution emerges from summing Bernoulli random variables, and how Poisson, normal, chi-squared, exponential, gamma, and inverse gamma distributions can approximate the binomial as the number of Bernoulli trials increases. Code examples in R are provided to simulate sampling from these distributions and compare the simulated distributions to their theoretical probability density functions.
This document discusses various techniques and optimizations from Apple's GameplayKit framework. It begins by introducing GameplayKit and explaining that it is used to develop gameplay mechanics rather than rendering. Several techniques are then presented as "Gems" including using GKRandomSource for shuffling arrays, GKRTree for performant visual searches, GKPerlinNoiseSource for natural randomness, and using GKObstacleGraph for pathfinding around obstacles. Links are provided at the end for further information on GameplayKit and related algorithms.
The document contains solutions to 5 problems related to computer and network security concepts:
1. It finds the greatest common divisor (GCD) of several pairs of numbers using Euclid's algorithm.
2. It calculates several numbers modulo other numbers.
3. It uses Fermat's theorem to calculate 3201 modulo 11.
4. It performs encryption and decryption of messages using the RSA algorithm with sample public and private keys.
5. Given a cipher text and public key, it decrypts the plain text message using the RSA algorithm.
The Bresenham's line drawing algorithm is an incremental scan conversion algorithm that uses only integer calculations. It works by calculating the difference between the ideal y value and the actual plotted pixel y value at each x value, and determining whether to plot the pixel above or below the line based on whether this difference is positive or negative. The algorithm takes the line endpoints as input, calculates the change in x and y per step, sets an initial decision parameter, and then iteratively plots pixels, updating the decision parameter to determine whether to plot above or below the line at each step.
This document contains problems related to Boolean algebra and logic gates. It asks the reader to:
- Convert between binary, decimal, hexadecimal, and octal number systems
- Derive truth tables for logic gates and Boolean functions
- Use Boolean algebra to simplify and prove equivalences between Boolean functions
- Express Boolean functions in sum of products and product of sums form
- Write Boolean functions in canonical form using minterms and maxterms
F# is well-suited for data analysis tasks due to its capabilities in data access, manipulation, visualization and integration with other tools. The document outlines several F# libraries and techniques for:
1. Accessing data from various sources using FSharp.Data and type providers.
2. Visualizing data with libraries like FSharp.Charting.
3. Manipulating and transforming data using techniques like Deedle frames, Math.NET for statistics, and calling R from F#.
4. Leveraging parallelism through {m}brace for distributed computing.
The document provides instructions for solving an ordinary differential equation using the finite element method. Specifically, it asks to:
1. Discretize the given differential equation over 7 equally spaced subintervals between 0 and 4.
2. Assemble the matrix equation from the discretized problem and calculate the load vector.
3. Solve the matrix equation to find the approximated solution at each node.
It then provides the details for constructing the stiffness matrix based on the given differential equation and basis functions over each subinterval.
This document discusses binary and BCD adders and subtractors, including half-adders, full-adders, 4-bit binary adders, BCD adders, half/full subtractors, and multiplexers. It also discusses instruction set architecture (ISA), comparing RISC and CISC architectures, and the Intel x86 programming model.
This document provides 98 examples of functions and their derivatives. The functions include polynomials, trigonometric functions like sine, cosine, tangent, inverse trigonometric functions, exponential functions, logarithmic functions, and combinations of these functions.
This document provides formulas for integrals of common functions including polynomials, rational functions, radicals, logarithms, exponentials, and trigonometric functions. It includes basic integral formulas like the integral of x^n dx as well as more complex integrals involving combinations of functions. There are over 100 formulas presented in a table format organized by function type.
This document provides formulas for integrals of common functions including polynomials, rational functions, radicals, logarithms, exponentials, and trigonometric functions. It includes basic integral formulas like the integral of x^n dx as well as more complex integrals involving combinations of functions. There are over 100 formulas presented in a table format organized by function type.
This document provides an introduction to machine learning concepts including linear regression, neural networks, and model evaluation. It discusses using machine learning for tasks like image recognition, text translation, and medical applications. Linear regression is demonstrated for predicting housing prices based on area. Neural networks are explained for classification problems with examples of predicting a developer type based on experience. The document outlines model training, calculating costs, tuning hyperparameters, and evaluating models on test vs. cross-validation data to avoid overfitting. Caveats are noted about omitted math details.
This week, Luke Pearson (Polychain Capital) and Joshua Fitzgerald (Anoma) present their work on Plonkup, a protocol that combines Plookup and PLONK into a single, efficient protocol. The protocol relies on a new hash function, called Reinforced Concrete, written by Dmitry Khovratovich. The three of them will present their work together at this week's edition of zkStudyClub!
Slides:
---
To Follow the Zero Knowledge Podcast us at https://www.zeroknowledge.fm
To the listeners of Zero Knowledge Podcast, if you like what we do:
- Follow us on Twitter - @zeroknowledgefm
- Join us on Telegram - https://t.me/joinchat/TORo7aknkYNLHmCM
- Support our Gitcoin Grant - https://gitcoin.co/grants/329/zero-knowledge-podcast-2
- Support us on Patreon - https://www.patreon.com/zeroknowledge
Cryptography: way to Arkham - Andriy SavchenkoRuby Meditation
This document discusses cryptography concepts including one-way hash functions, symmetric encryption using the Vigenère cipher, and asymmetric encryption using a simple RSA example. It provides sample code to demonstrate encrypting and decrypting messages using a basic public/private key pair. The document also briefly outlines the Secure Remote Password protocol and some considerations for implementing cryptography protocols including using the correct algorithms, versions, and avoiding partial implementations.
This document summarizes the solution steps to determine the reactions and bending moments for a beam with a fixed edge at X=0 and a roller edge at X=L. It involves applying boundary conditions to determine constants C1 through C4 in the polynomial expression for deflection W(x). The constants are then used to calculate the bending moment M(X) and shear force S(X) expressions, and to determine the reactions and moments at the two edges.
ASFWS 2012 - Hash-flooding DoS reloaded: attacks and defenses par Jean-Philip...Cyber Security Alliance
This document discusses hash flooding denial of service (DoS) attacks and defenses. It presents the theory behind exploiting weaknesses in hash functions like MurmurHash2/3 through differential cryptanalysis. Specifically, it shows how to generate multicollision inputs that result in the same hash value. This allows an attacker to force worst-case insertion times into hash tables, overloading systems. The document notes that many systems using MurmurHash2/3 remain vulnerable. It then discusses potential real-world attacks against uses of hashes in applications like web frameworks. As an example, it demonstrates how to attack internal hash tables in Ruby on Rails, though default protections prevent attacks on request parameters.
This document provides formulas for integrals of common functions. It includes integrals of polynomials, rational functions, functions with roots, logarithms, exponentials, trigonometric functions, hyperbolic functions, and products of various functions. There are over 100 formulas presented in a table format with the function and integral provided.
(1) This document discusses random variables and stochastic processes. It defines key concepts such as random variables, probability mass functions, cumulative distribution functions, discrete and continuous random variables.
(2) It provides examples of defining random variables for experiments involving coin tosses and ball drawings. It illustrates how to determine the probability mass function and cumulative distribution function of discrete random variables.
(3) The document also discusses continuous random variables and their probability density functions. It introduces the concepts of joint probability distributions for two random variables and how to find marginal and conditional probabilities.
1) This document provides formulas for integrals of common functions including polynomials, rational functions, radicals, logarithms, trigonometric functions, exponentials, and hyperbolic functions.
2) The integrals are organized into sections based on the type of function, with the formula provided along with conditions on parameters.
3) There are over 100 integrals presented in the table spanning multiple pages of formulas.
This document provides formulas for integrals involving common functions including:
- Logarithms
- Roots
- Rational functions
- Trigonometric functions
- Exponentials
- Products of functions
It includes the basic forms for integrals with these functions as well as more complex integrals combining multiple functions. The integrals are grouped by function type for easy reference.
(i) The derivative of an exponential function with base e and variable x is the same exponential function multiplied by the derivative of x, which is 1.
(ii) To take the derivative of an exponential function raised to a power, use the power rule and multiply the derivative of the exponential by the power.
(iii) When adding exponential functions with the same base, the derivatives are added separately and the sums are multiplied by the common exponential term.
The document describes various probability distributions that can arise from combining Bernoulli random variables. It shows how a binomial distribution emerges from summing Bernoulli random variables, and how Poisson, normal, chi-squared, exponential, gamma, and inverse gamma distributions can approximate the binomial as the number of Bernoulli trials increases. Code examples in R are provided to simulate sampling from these distributions and compare the simulated distributions to their theoretical probability density functions.
This document discusses various techniques and optimizations from Apple's GameplayKit framework. It begins by introducing GameplayKit and explaining that it is used to develop gameplay mechanics rather than rendering. Several techniques are then presented as "Gems" including using GKRandomSource for shuffling arrays, GKRTree for performant visual searches, GKPerlinNoiseSource for natural randomness, and using GKObstacleGraph for pathfinding around obstacles. Links are provided at the end for further information on GameplayKit and related algorithms.
The document contains solutions to 5 problems related to computer and network security concepts:
1. It finds the greatest common divisor (GCD) of several pairs of numbers using Euclid's algorithm.
2. It calculates several numbers modulo other numbers.
3. It uses Fermat's theorem to calculate 3201 modulo 11.
4. It performs encryption and decryption of messages using the RSA algorithm with sample public and private keys.
5. Given a cipher text and public key, it decrypts the plain text message using the RSA algorithm.
The Bresenham's line drawing algorithm is an incremental scan conversion algorithm that uses only integer calculations. It works by calculating the difference between the ideal y value and the actual plotted pixel y value at each x value, and determining whether to plot the pixel above or below the line based on whether this difference is positive or negative. The algorithm takes the line endpoints as input, calculates the change in x and y per step, sets an initial decision parameter, and then iteratively plots pixels, updating the decision parameter to determine whether to plot above or below the line at each step.
This document contains problems related to Boolean algebra and logic gates. It asks the reader to:
- Convert between binary, decimal, hexadecimal, and octal number systems
- Derive truth tables for logic gates and Boolean functions
- Use Boolean algebra to simplify and prove equivalences between Boolean functions
- Express Boolean functions in sum of products and product of sums form
- Write Boolean functions in canonical form using minterms and maxterms
F# is well-suited for data analysis tasks due to its capabilities in data access, manipulation, visualization and integration with other tools. The document outlines several F# libraries and techniques for:
1. Accessing data from various sources using FSharp.Data and type providers.
2. Visualizing data with libraries like FSharp.Charting.
3. Manipulating and transforming data using techniques like Deedle frames, Math.NET for statistics, and calling R from F#.
4. Leveraging parallelism through {m}brace for distributed computing.
The document provides instructions for solving an ordinary differential equation using the finite element method. Specifically, it asks to:
1. Discretize the given differential equation over 7 equally spaced subintervals between 0 and 4.
2. Assemble the matrix equation from the discretized problem and calculate the load vector.
3. Solve the matrix equation to find the approximated solution at each node.
It then provides the details for constructing the stiffness matrix based on the given differential equation and basis functions over each subinterval.
This document discusses binary and BCD adders and subtractors, including half-adders, full-adders, 4-bit binary adders, BCD adders, half/full subtractors, and multiplexers. It also discusses instruction set architecture (ISA), comparing RISC and CISC architectures, and the Intel x86 programming model.
This document provides 98 examples of functions and their derivatives. The functions include polynomials, trigonometric functions like sine, cosine, tangent, inverse trigonometric functions, exponential functions, logarithmic functions, and combinations of these functions.
This document provides formulas for integrals of common functions including polynomials, rational functions, radicals, logarithms, exponentials, and trigonometric functions. It includes basic integral formulas like the integral of x^n dx as well as more complex integrals involving combinations of functions. There are over 100 formulas presented in a table format organized by function type.
This document provides formulas for integrals of common functions including polynomials, rational functions, radicals, logarithms, exponentials, and trigonometric functions. It includes basic integral formulas like the integral of x^n dx as well as more complex integrals involving combinations of functions. There are over 100 formulas presented in a table format organized by function type.
This document provides an introduction to machine learning concepts including linear regression, neural networks, and model evaluation. It discusses using machine learning for tasks like image recognition, text translation, and medical applications. Linear regression is demonstrated for predicting housing prices based on area. Neural networks are explained for classification problems with examples of predicting a developer type based on experience. The document outlines model training, calculating costs, tuning hyperparameters, and evaluating models on test vs. cross-validation data to avoid overfitting. Caveats are noted about omitted math details.
This week, Luke Pearson (Polychain Capital) and Joshua Fitzgerald (Anoma) present their work on Plonkup, a protocol that combines Plookup and PLONK into a single, efficient protocol. The protocol relies on a new hash function, called Reinforced Concrete, written by Dmitry Khovratovich. The three of them will present their work together at this week's edition of zkStudyClub!
Slides:
---
To Follow the Zero Knowledge Podcast us at https://www.zeroknowledge.fm
To the listeners of Zero Knowledge Podcast, if you like what we do:
- Follow us on Twitter - @zeroknowledgefm
- Join us on Telegram - https://t.me/joinchat/TORo7aknkYNLHmCM
- Support our Gitcoin Grant - https://gitcoin.co/grants/329/zero-knowledge-podcast-2
- Support us on Patreon - https://www.patreon.com/zeroknowledge
Cryptography: way to Arkham - Andriy SavchenkoRuby Meditation
This document discusses cryptography concepts including one-way hash functions, symmetric encryption using the Vigenère cipher, and asymmetric encryption using a simple RSA example. It provides sample code to demonstrate encrypting and decrypting messages using a basic public/private key pair. The document also briefly outlines the Secure Remote Password protocol and some considerations for implementing cryptography protocols including using the correct algorithms, versions, and avoiding partial implementations.
Homomorphic encryption allows computations to be carried out on encrypted data without decrypting it first. This summary discusses Craig Gentry's scheme for fully homomorphic encryption based on ideal lattices. The scheme works by encrypting bits as ciphertexts with small noise that grows with computations. A bootstrapping procedure called re-crypt reduces the noise to keep ciphertexts decryptable. While promising for applications like cloud computing, the scheme has high computational costs that scale poorly with security level. Current research aims to make homomorphic encryption more efficient and practical.
This document contains a practice set of multiple choice questions related to curve sketching and analyzing functions based on their derivatives. There are questions about determining critical points, intervals of increasing/decreasing behavior, locating extrema, and classifying concavity. The document tests skills in analyzing functions through their derivatives to sketch curves and determine properties of the functions.
This document discusses cryptography and attacks on cryptosystems. It begins with an introduction to classical ciphers like the Caesar cipher and transposition cipher. It then covers the mathematics behind public key cryptography schemes like RSA, including number theory concepts like modulo arithmetic, discrete logarithms, and the Chinese Remainder Theorem. The document discusses the computational basis for RSA security in factoring large numbers and discusses different types of attacks on RSA like timing attacks, implementation attacks, and mathematical attacks using lattice basis reduction. It concludes with recommendations for building a secure RSA system, such as using large random paddings, large secret exponents, and generating strong prime numbers.
Lecture on 18 December 2018
Role of Cryptography in Blockchain
RSA and SHA
Blockchain for Beginners
Elective course from the Faculty of Information Technology, Thai - Nichi Institute of Technology, Bangkok for undergraduate students.
#BlockchainTNI2018
Elliptic curve cryptography and zero knowledge proofNimish Joseph
This document discusses elliptic curve cryptography and zero knowledge proofs. It begins by establishing the mathematical foundations needed for cryptography, including groups, rings, fields, and the discrete logarithm problem. It then explains how elliptic curves can be used in public key cryptography applications like Diffie-Hellman key exchange and ElGamal encryption. It also covers zero knowledge proofs, their properties, examples of uses, and the Fiat-Shamir identification protocol. Throughout, it provides examples to illustrate key concepts in elliptic curve cryptography and zero knowledge proofs.
Elliptic Curve Cryptography and Zero Knowledge ProofArunanand Ta
Elliptic Curve Cryptography and Zero Knowledge Proof
Presentation by Nimish Joseph, at College of Engineering Cherthala, Kerala, India, during Faculty Development Program, on 06-Nov-2013
This document contains an exercise set with 46 problems involving real numbers, intervals, and inequalities. The problems cover topics such as determining whether numbers are rational or irrational, solving equations, graphing inequalities on number lines, factoring polynomials, and solving compound inequalities.
Digital Signatures: Reassessing security of randomizable signaturesPriyanka Aash
The document summarizes research on differential attacks against deterministic digital signatures like EdDSA. It finds that removing randomness from signature generation does not eliminate all attack vectors, identifying 8 fault attacks and 1 side-channel attack. Fully compliant countermeasures per the EdDSA specification have significant performance impacts. Alternatively, introducing high-quality randomness where possible allows cheaper countermeasures without affecting key generation or verification. The research aims to inform standardization bodies on defining new digital signature algorithms.
Signyourd digital signature certificate providerKishankant Yadav
a digital code (generated and authenticated by public key encryption) which is attached to an electronically transmitted document to verify its contents and the sender's identity.
This definition explains how digital signatures work and what they are used for. Learn about the mathematical underpinnings of digital signature technology
A digital signature is basically a way to ensure that an electronic document (e-mail, spreadsheet, text file, etc.) is authentic. Authentic means that you know who created the document and you know that it has not been altered in any way since that person created it.
https://signyourdoc.com/
Pythran: Static compiler for high performance by Mehdi Amini PyData SV 2014PyData
Pythran is a an ahead of time compiler that turns modules written in a large subset of Python into C++ meta-programs that can be compiled into efficient native modules. It targets mainly compute intensive part of the code, hence it comes as no surprise that it focuses on scientific applications that makes extensive use of Numpy. Under the hood, Pythran inter-procedurally analyses the program and performs high level optimizations and parallel code generation. Parallelism can be found implicitly in Python intrinsics or Numpy operations, or explicitly specified by the programmer using OpenMP directives directly in the Python source code. Either way, the input code remains fully compatible with the Python interpreter. While the idea is similar to Parakeet or Numba, the approach differs significantly: the code generation is not performed at runtime but offline. Pythran generates C++11 heavily templated code that makes use of the NT2 meta-programming library and relies on any standard-compliant compiler to generate the binary code. We propose to walk through some examples and benchmarks, exposing the current state of what Pythran provides as well as the limit of the approach.
The document summarizes a presentation titled "Yoyak" given by Heejong Lee at ScalaDays 2015. The presentation introduces Yoyak, a static analysis framework developed by the speaker. It covers the following topics:
- Static analysis and abstract interpretation theory
- Implementation highlights of the Yoyak framework
- Experiences using Scala in developing Yoyak
- The roadmap for future development of Yoyak
Engineering Fast Indexes for Big-Data Applications: Spark Summit East talk by...Spark Summit
Contemporary computing hardware offers massive new performance opportunities. Yet high-performance programming remains a daunting challenge.
We present some of the lessons learned while designing faster indexes, with a particular emphasis on compressed bitmap indexes. Compressed bitmap indexes accelerate queries in popular systems such as Apache Spark, Git, Elastic, Druid and Apache Kylin.
Sasha Romijn - Everything I always wanted to know about crypto, but never tho...Codemotion
For many years, I had entirely given up on ever understanding the anything about cryptography. However, I’ve since learned it’s not nearly as hard as I thought to understand many of the important concepts. In this talk, I’ll take you through some of the underlying principles of modern applications of cryptography. We’ll talk about our goals, the parts are involved, and how to prevent and understand common vulnerabilities. This’ll help you to make better choices when you implement crypto in your products, and will improve your understanding of how crypto is applied to things you already use.
Introduction to Elliptic Curve CryptographyDavid Evans
This document summarizes a class on elliptic curve cryptography and bitcoin. It discusses elliptic curves over finite fields, including the field GF(2256 - 232 - 29 - 28 - 27 - 26 - 24 - 1) used in bitcoin. It explains how addition works on elliptic curves via line intersections. The document also notes that finding the discrete logarithm of points on an elliptic curve is considered a hard problem, and this property is important for bitcoin. Students are assigned to investigate the bitcoin they received, complete Project 1 by January 30th, and read materials on bitcoin and elliptic curves.
The document discusses extreme values (maximums and minimums) of functions. It defines local and absolute extrema and notes that not all functions have extrema. Critical points, where the derivative is zero or undefined, are discussed. The relationship between critical points and extrema is explained by Fermat's Theorem. Methods for finding extrema on closed intervals using critical points and endpoints are presented, along with an example. Rolle's Theorem relating critical points to functions with equal values at endpoints is also introduced.
https://telecombcn-dl.github.io/2017-dlsl/
Winter School on Deep Learning for Speech and Language. UPC BarcelonaTech ETSETB TelecomBCN.
The aim of this course is to train students in methods of deep learning for speech and language. Recurrent Neural Networks (RNN) will be presented and analyzed in detail to understand the potential of these state of the art tools for time series processing. Engineering tips and scalability issues will be addressed to solve tasks such as machine translation, speech recognition, speech synthesis or question answering. Hands-on sessions will provide development skills so that attendees can become competent in contemporary data anlytics tools.
Best 20 SEO Techniques To Improve Website Visibility In SERPPixlogix Infotech
Boost your website's visibility with proven SEO techniques! Our latest blog dives into essential strategies to enhance your online presence, increase traffic, and rank higher on search engines. From keyword optimization to quality content creation, learn how to make your site stand out in the crowded digital landscape. Discover actionable tips and expert insights to elevate your SEO game.
Communications Mining Series - Zero to Hero - Session 1DianaGray10
This session provides introduction to UiPath Communication Mining, importance and platform overview. You will acquire a good understand of the phases in Communication Mining as we go over the platform with you. Topics covered:
• Communication Mining Overview
• Why is it important?
• How can it help today’s business and the benefits
• Phases in Communication Mining
• Demo on Platform overview
• Q/A
TrustArc Webinar - 2024 Global Privacy SurveyTrustArc
How does your privacy program stack up against your peers? What challenges are privacy teams tackling and prioritizing in 2024?
In the fifth annual Global Privacy Benchmarks Survey, we asked over 1,800 global privacy professionals and business executives to share their perspectives on the current state of privacy inside and outside of their organizations. This year’s report focused on emerging areas of importance for privacy and compliance professionals, including considerations and implications of Artificial Intelligence (AI) technologies, building brand trust, and different approaches for achieving higher privacy competence scores.
See how organizational priorities and strategic approaches to data security and privacy are evolving around the globe.
This webinar will review:
- The top 10 privacy insights from the fifth annual Global Privacy Benchmarks Survey
- The top challenges for privacy leaders, practitioners, and organizations in 2024
- Key themes to consider in developing and maintaining your privacy program
Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...SOFTTECHHUB
The choice of an operating system plays a pivotal role in shaping our computing experience. For decades, Microsoft's Windows has dominated the market, offering a familiar and widely adopted platform for personal and professional use. However, as technological advancements continue to push the boundaries of innovation, alternative operating systems have emerged, challenging the status quo and offering users a fresh perspective on computing.
One such alternative that has garnered significant attention and acclaim is Nitrux Linux 3.5.0, a sleek, powerful, and user-friendly Linux distribution that promises to redefine the way we interact with our devices. With its focus on performance, security, and customization, Nitrux Linux presents a compelling case for those seeking to break free from the constraints of proprietary software and embrace the freedom and flexibility of open-source computing.
Building Production Ready Search Pipelines with Spark and MilvusZilliz
Spark is the widely used ETL tool for processing, indexing and ingesting data to serving stack for search. Milvus is the production-ready open-source vector database. In this talk we will show how to use Spark to process unstructured data to extract vector representations, and push the vectors to Milvus vector database for search serving.
GraphRAG for Life Science to increase LLM accuracyTomaz Bratanic
GraphRAG for life science domain, where you retriever information from biomedical knowledge graphs using LLMs to increase the accuracy and performance of generated answers
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5. July 2013:
Change in "De-Mail-Gesetz" defining De-Mail as
secure [1]
● Needs to be decrypted by
provider to "check for viruses"
● (Secret) key on server of provider
○ Server becomes juicy target
● Homomorphic encryption
○ Can check without decryption
[1] http://www.spiegel.de/netzwelt/netzpolitik/de-mail-bundestag-erklaert-bundes-mail-per-gesetz-als-sicher-a-895361.html
Current context
5
6. ● Medical records
○ Analyze disease / treatment without disclosing them
○ Search for DNA markers without revealing DNA
○ "Digitale Krankenakte"
● Spam filtering
○ Blacklisting encrypted mails
○ Third parties can scan your PGP traffic
Use cases
Doing something without knowing what6
7. Homomorphism
groups (P, ⊕) and (C, ⊗)
relation f : P → C
f is a group homomorphism in P and C, if:
∀ a,b ∈ P: f(a ⊕ b) = f(a) ⊗ f(b)
Especially:
∀ a,b ∈ P: a ⊕ b = f-1
( f(a) ⊗ f(b) )
7
8. be aware, mapping from one operation to another
Examples
groups (R, +) and (R*
, ×)
function: R → R
exp(x+y) = exp(x) × exp(y)
10x+y
= 10x
× 10y
ln(a×b) = ln(a) + ln(b)
8
28. ● Operations on ciphertext accumulate "noise"
○ Addition adds noise, multiplication multiplies it
○ Noise gets too high → decryption fails
● These "limited" algebra
homomorphism schemes:
Somewhat Homomorphic Encryption Schemes
(simplified)Pollution
28 Bob August, flickr (CC BY-NC-SA 2.0)
29. ● Using small N in RSA and large inputs
○ When output larger than RSA-modulus, decryption fails
Pollution
Calculate area of
square using RSA
10*15=150
Encryption:
c_w ≡ 1023
mod 143
≡ 43
c_h = 1523
mod 143
= 20
c_a = 43*20 = 860
Decryption:
a ≡ 86047
mod 143
(≡ 150 mod 143)
≡ 7
7 ≠ 150 ⚡
Example
15
10
29
30. Beyond + and ×
Every program can be expressed in
terms of a digital circuit.
*
* referentially transparent, ie. w/o side effects, today() is not ref. transparent
30 Tristan Nitot, flickr (CC BY-NC-SA 2.0)
31. Beyond + and ×
Every digital circuit can be expressed
in terms of AND, OR, and NOT.
31
32. Beyond + and ×
Every digital circuit can be expressed
in terms of AND, OR, and NOT.
(remember Disjunctive Normal Forms?)
32
33. Beyond + and ×
Every digital circuit can be expressed
in terms of AND, OR, and XOR.
XOR(x, 1) = NOT(x)
NOT(AND(NOT(x), NOT(y))) = !(!x & !y) = OR(x, y)
33
34. With ∧ and ⊕ we can
represent any operation
Fully homomorphic encryptionFully homomorphic encryption
34 Duane Romanell, flickr (CC BY-NC-ND 2.0)Duane Romanell, flickr (CC BY-NC-ND 2.0)
35. Circuit Encryption
● Assume homomorphic enc:
○ 0-bits → even ints
○ 1-bits → odd ints
○ ⊕ → +
○ ∧ → ×
○ Define: ∘ = (a + b) + ( a x b) (Logical OR)
⊕
{ OR = (a ∧ b) ∧ (a ⊕ b) }
(+ random r * secret p mod p!)
{ simple truth tables }
35
36. Circuit Encryption
● Single Bit Adder
○ A,B: inputs, Cin
: carry-in, S: sum, Cout
: carry-out
Toy example
S = ((A ⊕ B) ⊕ C)
Cout
= (A ∧ B) v ((A ⊕ B) ∧ Cin
)36
37. S = ((A ⊕ B) ⊕ C)
Cout
= (A ∧ B) v ((A ⊕ B) ∧ Cin
)
S = ((A + B) + C)
Cout
= (A × B) ∘ ((A+B) × Cin
)
Circuit Encryption
Toy example
map
operators
37
38. A B Cin
S Cout
1 0 1 0 1
3 4 7 ? ?encrypted
Circuit Encryption
Toy example - calc. S
S = ((A + B) + C)
S = ((3 + 4) + 7) = ?
apply
38
39. A B Cin
S Cout
1 0 1 0 1
3 4 7 14 ?encrypted
Circuit Encryption
Toy example - calc. S
S = ((A + B) + C)
S = ((3 + 4) + 7) = 14 ≙ 0
39
40. A B Cin
S Cout
1 0 1 0 1
3 4 7 14 649
Circuit Encryption
Toy example - calc. Cout
Cout
= (A × B) ∘ ((A + B) × Cin
)
Cout
= (3 × 4) ∘ ((3 + 4) × 7)
= 12 ∘ 49
= (12 + 49) + (12 * 49)
= 61 + 588 = 649 ≙ 1
∘ = (a + b) + (a x b)
apply
40
41. Circuit Encryption
● Assume homomorphic enc:
○ 0-bits → even ints
○ 1-bits → odd ints
○ ⊕ → +
○ ∧ → ×
○ Define: ∘ = (a + b) + ( a x b) (Logical OR)
⊕
{ OR = (a ∧ b) ∧ (a ⊕ b) }
(actually mod a secret p)
{ simple truth tables }
41
42. Circuit Enc.
● Encrypted Memory Access
●
Example
¬ao
∧ ¬a1
∧ m0
ao
∧ ¬a1
∧ m1
¬ao
∧ a1
∧ m2
ao
∧ a1
∧ m3
m0
m1
m2
m3
a0
a1
1 x x x 0 0
x 1 x x 1 0
x x 1 x 0 1
x x x 1 1 1
42
43. Encrypted Memory Access
●
row3
= ao
∧ a1
∧ m3
row2
= ¬ao
∧ a1
∧ m2
row1
= ao
∧ ¬a1
∧ m1
row0
= ¬ao
∧ ¬a1
∧ m0
c = row0
∨row1
∨row2
∨row3
[1] M Brenner, J Wiebelitz, G von Voigt. Secret program execution in the cloud applying homomorphic encryption. 201143
44. ●
row3
= ao
∧ a1
∧ m3
row2
= ¬ao
∧ a1
∧ m2
row1
= ao
∧ ¬a1
∧ m1
row0
= ¬ao
∧ ¬a1
∧ m0
c = row0
∨row1
∨row2
∨row3
m = {1, 0, 1, 0} a = 01
Encrypted Memory Access
44
45. ●
row3
= ao
∧ a1
∧ m3
row2
= ¬ao
∧ a1
∧ m2
row1
= ao
∧ ¬a1
∧ m1
row0
= ¬ao
∧ ¬a1
∧ m0
c = row0
∨row1
∨row2
∨row3
m = {1, 0, 1, 0} a = 01
Encrypted Memory Access
45
46. ●
row3
= ao
∧ a1
∧ 0
row2
= ¬ao
∧ a1
∧ 1
row1
= ao
∧ ¬a1
∧ 0
row0
= ¬ao
∧ ¬a1
∧ 1
c = row0
∨row1
∨row2
∨row3
m = {1, 0, 1, 0} a = 01
Encrypted Memory Access
46
47. ●
row3
= ao
∧ a1
∧ 0
row2
= ¬ao
∧ a1
∧ 1
row1
= ao
∧ ¬a1
∧ 0
row0
= ¬ao
∧ ¬a1
∧ 1
c = row0
∨row1
∨row2
∨row3
m = {1, 0, 1, 0} a = 01
Encrypted Memory Access
47
56. Fully homomorphic encryption
● "Holy Grail" of cryptography
● First proposed within a year of RSA
development
○ 1979
○ Idea due to weird homomorphic property of RSA
● for more than 30 years:
unclear whether FHE even possible
○ During that time: best one = Boneh-Goh-Nissim
(remember the area solver example)
(the one where only one multiplication was possible)
56
58. Gentry's approach
● 2009: Craig Gentry shows fully homomorphic
encryption in his doctoral thesis
● Employs somewhat homomorphic encryption
scheme using ideal lattices
● Scheme is bootstrappable
○ can evaluate its own decryption circuit
● Through recursive self-embedding, leads to
FHE
○ ciphertexts are reencrypted, eliminating noise
(based on "shortest lattice vector" problem used in cryptography, which is NP-hard)
58
61. [...] a simple string search using
homomorphic encryption is about a trillion
times slower than without encryption. [1]
Issues
1 000 000 000 000x
61 [1] CryptDB: A practical encrypted relational DBMS, RA Popa, N Zeldovich, H Balakrishnan, 2011
63. Fully hom. enc. IRL
● HELib by Shai Halevi (2013)
○ Implementation of Brakerski-Gentry-Vaikuntanathan[1]
scheme
○ Using many optimizations in literature[2][3] for speed
○ Does not implement bootstrapping (yet)
[1] Zvika Brakerski, Craig Gentry, Vinod Vaikuntanathan: (Leveled) fully homomorphic encryption without bootstrapping. ITCS 201
[2] Nigel P. Smart, Frederik Vercauteren: Fully Homomorphic SIMD Operations. IACR Cryptology ePrint Archive 2011: 133 (2011)
[3] Craig Gentry and Shai Halevi and Nigel P. Smart Homomorphic Evaluation of the AES Circuit, CRYPTO 2012
Performance
Modulus Time for addition (ms) Time for multiplication
(ms)
257 0.7 39
8209 0.7 38
65537 2.9 177
Even numbers < 65537,
80 Bits of security
63
64. Visions of a fully homomorphic cryptosystem
have been dancing in cryptographers' heads for
thirty years. [...] It will be years before a
sufficient number of cryptographers examine
the algorithm that we can have any confidence
that the scheme is secure. [1]
—Bruce Schneier, cryptographer, April 2013
Criticism
“ “
64
[1] Homomorphic Encryption Breakthrough, Schneier on Security, Bruce Schneier https://www.schneier.
com/blog/archives/2009/07/homomorphic_enc.html