1. The document discusses cryptography and the RSA algorithm. It provides definitions of encryption, decryption, symmetric and asymmetric cryptography.
2. RSA is described as an asymmetric cryptography algorithm invented by Rivest, Adleman and Shamir using the initials of their last names. It uses a public key for encryption and a private key for decryption.
3. An example is provided to demonstrate how RSA works by encrypting a message using a public key and decrypting it with a private key.
The presentation describes basics of cryptography and information security. It covers goals of cryptography, history of cipher symmetric and public key cryptography
The document discusses the Digital Signature Standard (DSS) and the Digital Signature Algorithm (DSA). It begins by explaining that the DSS standard requires federal agencies to use this standard for secure communication of non-classified information, and it is also available for private sector use. The DSS ensures secure algorithms for message transmission. It then describes how digital signatures work using public/private key pairs to verify identity and detect unauthorized modifications. The DSA is one of three algorithms specified in the DSS standard and generates signatures using cryptographic keys and a secure hash function. The document provides details on the parameters and processes used in DSA digital signature generation and verification.
The document discusses Diffie-Hellman key exchange, which is the first public key algorithm published in 1976. It allows two parties that have no prior knowledge of each other to jointly establish a shared secret key over an insecure communications channel. This key can then be used to encrypt subsequent communications using a symmetric key cipher. The security of the algorithm relies on the difficulty of solving the discrete logarithm problem in finite fields.
The document summarizes the RSA encryption algorithm. It begins by explaining that RSA was developed in 1977 by Rivest, Shamir and Adleman. It then provides an example to demonstrate how RSA works step-by-step, generating keys, encrypting a message and decrypting the ciphertext. Finally, it discusses some challenges with breaking RSA encryption, including brute force attacks and mathematical attacks based on factoring the encryption keys, as well as timing attacks that aim to deduce keys based on variations in processing time.
Modern block ciphers are widely used to provide encryption of quantities of information, and/or a cryptographic checksum to ensure the contents have not been altered. We continue to use block ciphers because they are comparatively fast, and because we know a fair amount about how to design them.
This document provides an overview of cryptography. It begins with basic definitions related to cryptography and a brief history of its use from ancient times to modern ciphers. It then describes different types of ciphers like stream ciphers, block ciphers, and public key cryptosystems. It also covers cryptography methods like symmetric and asymmetric algorithms. Common types of attacks on cryptosystems like brute force, chosen ciphertext, and frequency analysis are also discussed.
Public Key Cryptography and RSA algorithmIndra97065
Public Key Cryptography and RSA algorithm.Explanation and proof of RSA algorithm in details.it also describer the mathematics behind the RSA. Few mathematics theorem are given which are use in the RSA algorithm.
The presentation describes basics of cryptography and information security. It covers goals of cryptography, history of cipher symmetric and public key cryptography
The document discusses the Digital Signature Standard (DSS) and the Digital Signature Algorithm (DSA). It begins by explaining that the DSS standard requires federal agencies to use this standard for secure communication of non-classified information, and it is also available for private sector use. The DSS ensures secure algorithms for message transmission. It then describes how digital signatures work using public/private key pairs to verify identity and detect unauthorized modifications. The DSA is one of three algorithms specified in the DSS standard and generates signatures using cryptographic keys and a secure hash function. The document provides details on the parameters and processes used in DSA digital signature generation and verification.
The document discusses Diffie-Hellman key exchange, which is the first public key algorithm published in 1976. It allows two parties that have no prior knowledge of each other to jointly establish a shared secret key over an insecure communications channel. This key can then be used to encrypt subsequent communications using a symmetric key cipher. The security of the algorithm relies on the difficulty of solving the discrete logarithm problem in finite fields.
The document summarizes the RSA encryption algorithm. It begins by explaining that RSA was developed in 1977 by Rivest, Shamir and Adleman. It then provides an example to demonstrate how RSA works step-by-step, generating keys, encrypting a message and decrypting the ciphertext. Finally, it discusses some challenges with breaking RSA encryption, including brute force attacks and mathematical attacks based on factoring the encryption keys, as well as timing attacks that aim to deduce keys based on variations in processing time.
Modern block ciphers are widely used to provide encryption of quantities of information, and/or a cryptographic checksum to ensure the contents have not been altered. We continue to use block ciphers because they are comparatively fast, and because we know a fair amount about how to design them.
This document provides an overview of cryptography. It begins with basic definitions related to cryptography and a brief history of its use from ancient times to modern ciphers. It then describes different types of ciphers like stream ciphers, block ciphers, and public key cryptosystems. It also covers cryptography methods like symmetric and asymmetric algorithms. Common types of attacks on cryptosystems like brute force, chosen ciphertext, and frequency analysis are also discussed.
Public Key Cryptography and RSA algorithmIndra97065
Public Key Cryptography and RSA algorithm.Explanation and proof of RSA algorithm in details.it also describer the mathematics behind the RSA. Few mathematics theorem are given which are use in the RSA algorithm.
This document discusses data encryption methods. It defines encryption as hiding information so it can only be accessed by those with the key. There are two main types: symmetric encryption uses one key, while asymmetric encryption uses two different but related keys. Encryption works by scrambling data using techniques like transposition, which rearranges the order, and substitution, which replaces parts with other values. The document specifically describes the Data Encryption Standard (DES) algorithm and the public key cryptosystem, which introduced the innovative approach of using different keys for encryption and decryption.
MD5 is a cryptographic hash function that produces a 128-bit hash value for a message of any length. It was originally designed to provide authentication of digital signatures but is no longer considered reliable for cryptography due to techniques that can generate collisions. MD5 operates by padding the input, appending the length, dividing into blocks, initializing variables, processing blocks through 4 rounds of operations with different constants each round, and outputting the hash value. While it was intended to be difficult to find collisions or recover the input, MD5 is no longer considered cryptographically secure due to attacks demonstrating collisions.
In cryptography, a block cipher is a deterministic algorithm operating on ... Systems as a means to effectively improve security by combining simple operations such as .... Finally, the cipher should be easily cryptanalyzable, such that it can be ...
RSA is a public-key cryptosystem that uses both public and private keys for encryption and decryption. It was the first practical implementation of such a cryptosystem. The algorithm involves four main steps: 1) generation of the public and private keys, 2) encryption of messages using the public key, 3) decryption of encrypted messages using the private key, and 4) potential cracking of the encrypted message. It works by using two large prime numbers to generate the keys and performs exponentiation and modulo operations on messages to encrypt and decrypt them. There were some drawbacks to the original RSA algorithm related to redundant calculations and representing letters numerically that opened it up to easier hacking. Enhancements to RSA improved it by choosing
This presentation is based on the paper :
"A Method for Obtaining Digital Signatures and Public-Key Cryptosystems" by R.L. Rivest, A. Shamir, and L. Adleman
This document discusses message authentication codes (MACs). It explains that MACs use a shared symmetric key to authenticate messages, ensuring integrity and validating the sender. The document outlines the MAC generation and verification process, and notes that MACs provide authentication but not encryption. It then describes HMAC specifically, which applies a cryptographic hash function to the message and key to generate the MAC. The key steps of the HMAC process are detailed.
Key management: Introduction, How public key distribution done, Diffie Hellman Key Exchage Algorithm,Digital Certificate. Key Management using Digital certificate is done etc. wireshark screenshot showing digital cetificate.
Dijkstra's algorithm is used to find the shortest paths from a source node to all other nodes in a network. It works by marking all nodes as tentative with initial distances from the source set to 0 and others to infinity. It then extracts the closest node, adds it to the shortest path tree, and relaxes distances of its neighbors. This process repeats until all nodes are processed. When applied to the example network, Dijkstra's algorithm finds the shortest path from node A to all others to be A-B=4, A-C=6, A-D=8, A-E=7, A-F=7, A-G=7, and A-H=9.
Introduction to Public key Cryptosystems with block diagrams
Reference : Cryptography and Network Security Principles and Practice , Sixth Edition , William Stalling
This document provides an overview of cryptography including:
1. Cryptography is the process of encoding messages to protect information and ensure confidentiality, integrity, authentication and other security goals.
2. There are symmetric and asymmetric encryption algorithms that use the same or different keys for encryption and decryption. Examples include AES, RSA, and DES.
3. Other techniques discussed include digital signatures, visual cryptography, and ways to implement cryptography like error diffusion and halftone visual cryptography.
This presentation introduces Feistel encryption and decryption. It discusses the Feistel cipher structure which partitions the input block into two halves and processes them through multiple rounds of substitution and permutation. It shows diagrams of the Feistel encryption and decryption processes. It also covers the design features of Feistel networks such as block size, key size, number of rounds, and sub-key generation. Finally, it provides an example of the round function that performs a bitwise XOR of the left half and output of a function applied to the right half and sub-key.
cyber Security and Cryptography Elgamal Encryption Algorithm, Not-petya Case study all in one.
ElGamal encryption is a public-key cryptosystem
ElGamal Algo. uses asymmetric key encryption for communicating between two parties and encrypting the message.
This cryptosystem is based on the difficulty of finding discrete logarithm in a cyclic group
It is based on the Diffie–Hellman key exchange And It was described by Taher Elgamal in 1985.
Receiver Generates public and private keys.
Select Large Prime No. (P)
Select Decryption key/ private Key (D)
gcd(D,P)=1
Select Second part of Encryption key or public key (E1) & gcd(E1,P)=1
Third part of the encryption key or public key (E2)
E2 = E1D mod P
Public Key=(E1, E2, P) & Private key=D
In 2017 Maersk was impacted by Not-Petya ransomware attack and their network was down for a whole 9 days.
A total of 49,000 PCs and 7,000 servers were encrypted by Not-petya. Other companies that were impacted by the same attack are Merck, TNT express etc.
The tools used in Notpetya were EternalBlue and Mimikatz and hence the attack was very fast and devastating for victims.
It was The Most Devastating Cyber attack in History that’s
How a single piece of code crashed the world.
The presentation include:
-Diffie hellman key exchange algorithm
-Primitive roots
-Discrete logarithm and discrete logarithm problem
-Attacks on diffie hellman and their possible solution
-Key distribution center
Random Oracle Model & Hashing - Cryptography & Network SecurityMahbubur Rahman
This document discusses hashing and the random oracle model. It defines cryptographic hash functions as deterministic functions that map arbitrary strings to fixed-length outputs in a way that appears random. The random oracle model assumes an ideal hash function that behaves like a random function. The document discusses collision resistance, preimage resistance, and birthday attacks as they relate to finding collisions or preimages with a given hash function. It provides examples of calculating the number of messages an attacker would need to find collisions or preimages with different probabilities. The document concludes by listing some applications of cryptographic hash functions like password storage, file authenticity, and digital signatures.
Cryptography is the practice and study of techniques for conveying information security.
The goal of Cryptography is to allow the intended recipients of the message to receive the message securely.
The most famous algorithm used today is RSA algorithm
Public-Key Cryptography.pdfWrite the result of the following operation with t...FahmiOlayah
Write the result of the following operation with the correct number of significant figure of 0.248?Write the result of the following operation with the correct number of signi
This document discusses data encryption methods. It defines encryption as hiding information so it can only be accessed by those with the key. There are two main types: symmetric encryption uses one key, while asymmetric encryption uses two different but related keys. Encryption works by scrambling data using techniques like transposition, which rearranges the order, and substitution, which replaces parts with other values. The document specifically describes the Data Encryption Standard (DES) algorithm and the public key cryptosystem, which introduced the innovative approach of using different keys for encryption and decryption.
MD5 is a cryptographic hash function that produces a 128-bit hash value for a message of any length. It was originally designed to provide authentication of digital signatures but is no longer considered reliable for cryptography due to techniques that can generate collisions. MD5 operates by padding the input, appending the length, dividing into blocks, initializing variables, processing blocks through 4 rounds of operations with different constants each round, and outputting the hash value. While it was intended to be difficult to find collisions or recover the input, MD5 is no longer considered cryptographically secure due to attacks demonstrating collisions.
In cryptography, a block cipher is a deterministic algorithm operating on ... Systems as a means to effectively improve security by combining simple operations such as .... Finally, the cipher should be easily cryptanalyzable, such that it can be ...
RSA is a public-key cryptosystem that uses both public and private keys for encryption and decryption. It was the first practical implementation of such a cryptosystem. The algorithm involves four main steps: 1) generation of the public and private keys, 2) encryption of messages using the public key, 3) decryption of encrypted messages using the private key, and 4) potential cracking of the encrypted message. It works by using two large prime numbers to generate the keys and performs exponentiation and modulo operations on messages to encrypt and decrypt them. There were some drawbacks to the original RSA algorithm related to redundant calculations and representing letters numerically that opened it up to easier hacking. Enhancements to RSA improved it by choosing
This presentation is based on the paper :
"A Method for Obtaining Digital Signatures and Public-Key Cryptosystems" by R.L. Rivest, A. Shamir, and L. Adleman
This document discusses message authentication codes (MACs). It explains that MACs use a shared symmetric key to authenticate messages, ensuring integrity and validating the sender. The document outlines the MAC generation and verification process, and notes that MACs provide authentication but not encryption. It then describes HMAC specifically, which applies a cryptographic hash function to the message and key to generate the MAC. The key steps of the HMAC process are detailed.
Key management: Introduction, How public key distribution done, Diffie Hellman Key Exchage Algorithm,Digital Certificate. Key Management using Digital certificate is done etc. wireshark screenshot showing digital cetificate.
Dijkstra's algorithm is used to find the shortest paths from a source node to all other nodes in a network. It works by marking all nodes as tentative with initial distances from the source set to 0 and others to infinity. It then extracts the closest node, adds it to the shortest path tree, and relaxes distances of its neighbors. This process repeats until all nodes are processed. When applied to the example network, Dijkstra's algorithm finds the shortest path from node A to all others to be A-B=4, A-C=6, A-D=8, A-E=7, A-F=7, A-G=7, and A-H=9.
Introduction to Public key Cryptosystems with block diagrams
Reference : Cryptography and Network Security Principles and Practice , Sixth Edition , William Stalling
This document provides an overview of cryptography including:
1. Cryptography is the process of encoding messages to protect information and ensure confidentiality, integrity, authentication and other security goals.
2. There are symmetric and asymmetric encryption algorithms that use the same or different keys for encryption and decryption. Examples include AES, RSA, and DES.
3. Other techniques discussed include digital signatures, visual cryptography, and ways to implement cryptography like error diffusion and halftone visual cryptography.
This presentation introduces Feistel encryption and decryption. It discusses the Feistel cipher structure which partitions the input block into two halves and processes them through multiple rounds of substitution and permutation. It shows diagrams of the Feistel encryption and decryption processes. It also covers the design features of Feistel networks such as block size, key size, number of rounds, and sub-key generation. Finally, it provides an example of the round function that performs a bitwise XOR of the left half and output of a function applied to the right half and sub-key.
cyber Security and Cryptography Elgamal Encryption Algorithm, Not-petya Case study all in one.
ElGamal encryption is a public-key cryptosystem
ElGamal Algo. uses asymmetric key encryption for communicating between two parties and encrypting the message.
This cryptosystem is based on the difficulty of finding discrete logarithm in a cyclic group
It is based on the Diffie–Hellman key exchange And It was described by Taher Elgamal in 1985.
Receiver Generates public and private keys.
Select Large Prime No. (P)
Select Decryption key/ private Key (D)
gcd(D,P)=1
Select Second part of Encryption key or public key (E1) & gcd(E1,P)=1
Third part of the encryption key or public key (E2)
E2 = E1D mod P
Public Key=(E1, E2, P) & Private key=D
In 2017 Maersk was impacted by Not-Petya ransomware attack and their network was down for a whole 9 days.
A total of 49,000 PCs and 7,000 servers were encrypted by Not-petya. Other companies that were impacted by the same attack are Merck, TNT express etc.
The tools used in Notpetya were EternalBlue and Mimikatz and hence the attack was very fast and devastating for victims.
It was The Most Devastating Cyber attack in History that’s
How a single piece of code crashed the world.
The presentation include:
-Diffie hellman key exchange algorithm
-Primitive roots
-Discrete logarithm and discrete logarithm problem
-Attacks on diffie hellman and their possible solution
-Key distribution center
Random Oracle Model & Hashing - Cryptography & Network SecurityMahbubur Rahman
This document discusses hashing and the random oracle model. It defines cryptographic hash functions as deterministic functions that map arbitrary strings to fixed-length outputs in a way that appears random. The random oracle model assumes an ideal hash function that behaves like a random function. The document discusses collision resistance, preimage resistance, and birthday attacks as they relate to finding collisions or preimages with a given hash function. It provides examples of calculating the number of messages an attacker would need to find collisions or preimages with different probabilities. The document concludes by listing some applications of cryptographic hash functions like password storage, file authenticity, and digital signatures.
Cryptography is the practice and study of techniques for conveying information security.
The goal of Cryptography is to allow the intended recipients of the message to receive the message securely.
The most famous algorithm used today is RSA algorithm
Public-Key Cryptography.pdfWrite the result of the following operation with t...FahmiOlayah
Write the result of the following operation with the correct number of significant figure of 0.248?Write the result of the following operation with the correct number of signi
Public-key cryptography uses two keys, a public key that can be shared widely, and a private key that is kept secret. It allows for both encryption and digital signatures. The most widely used public-key cryptosystem is RSA, which relies on the difficulty of factoring large prime numbers. Diffie-Hellman key exchange allows two parties to securely exchange a secret key over an insecure channel without any prior secrets.
This document discusses public key cryptography and the RSA algorithm. It begins by explaining the differences between symmetric and asymmetric cryptosystems. It then describes the key components of public key cryptography, including public/private key pairs, certificates, and algorithms. The document goes on to explain the mathematical foundations of public key cryptography using concepts like Euler's totient function and the discrete logarithm problem. It provides details on the RSA algorithm, including key generation, encryption, and decryption. It also includes an example of RSA encryption and decryption. Finally, it discusses some attacks on RSA like brute force and timing attacks, as well as countermeasures.
This document provides an overview of number theory and its applications to asymmetric key cryptography. It begins with definitions of prime numbers, relatively prime numbers, and modular arithmetic. It then covers the Euclidean algorithm for finding the greatest common divisor of two numbers, Fermat's and Euler's theorems, and the Chinese Remainder Theorem. The document concludes with an introduction to public key cryptography, including the basic principles, requirements, and the RSA algorithm as a widely used example of an asymmetric encryption scheme.
Information and network security 33 rsa algorithmVaibhav Khanna
RSA algorithm is asymmetric cryptography algorithm. Asymmetric actually means that it works on two different keys i.e. Public Key and Private Key. As the name describes that the Public Key is given to everyone and Private key is kept private
This document summarizes a research paper that proposes a new public key cryptosystem based on the difficulty of inverting the function F(x) = (a × x)Mod(2p)Div(2q). The cryptosystem includes a key exchange algorithm, public key encryption algorithm, and digital signature algorithm. The document analyzes the efficiency and security of the cryptosystem, showing it has O(n) faster time complexity than RSA and Diffie-Hellman. It also reduces breaking the cryptosystem to solving difficult SAT instances or sets of multivariate polynomial equations over F(2). Python implementations of the key exchange and signature algorithms are provided in appendices.
RSA is a public-key cryptography algorithm used for encryption, digital signatures, and key exchange. It uses a public and private key pair based on the difficulty of factoring large prime numbers. To encrypt a message, it is encrypted with the recipient's public key. To decrypt, the recipient uses their private key. The security of RSA relies on the difficulty of determining the prime factors of a large number.
RSA is one of the most commonly used public-key encryption algorithms. It uses two keys, a public key to encrypt messages, and a private key to decrypt messages. The keys are generated based on the difficulty of factoring large prime numbers. To encrypt a message, it is converted to a number and then raised to the power of the public key modulo a composite number. Decryption involves raising the encrypted number to the power of the private key modulo the same composite number.
This project aims to evaluate and analyze the RSA algorithm as a security policy. The objective is to analyze conventional security policies, evaluate RSA, and perform performance analysis and measurement. The methodology uses random padding schemes as an outer layer of protection for the core RSA policy to make it unbreakable. It also aims to minimize computational complexity of RSA. The project implements RSA encryption and decryption in C++ and C# with a graphical user interface. It analyzes performance in Matlab and models the project using UML.
Rivest Shamir Adleman Algorithm and its variant : DRSA.pptxwerip98386
The document summarizes the RSA cryptosystem. It begins with an introduction to cryptography and the two types: symmetric and asymmetric. RSA is an asymmetric algorithm that uses a public and private key pair. The document provides an illustration of how RSA works and describes the key generation process where two prime numbers are multiplied to generate the modulus and keys. It also provides an example of encrypting a plaintext message using a public key and decrypting the ciphertext with a private key. Advantages of RSA include security while disadvantages are slower speed and large key sizes.
The RSA algorithm is a widely used public-key encryption technique developed in 1977. It uses a public and private key pair based on the difficulty of factoring large prime numbers. The encryption of a message m involves computing c = me mod n, where e is the public key exponent and n is the product of two large primes. Decryption gets the original message by computing m = cd mod n, where d is the private key exponent. For the encryption and decryption to be reversible, d is chosen such that ed = 1 mod φ(n), where φ is Euler's totient function.
RSA is an asymmetric encryption algorithm that uses a public key to encrypt messages, and a private key to decrypt them. It is based on the difficulty of factoring large prime numbers. To generate a key pair, two large prime numbers are randomly selected and multiplied together. The public key contains the result of this multiplication and an encryption exponent, while the private key contains a decryption exponent. A message encrypted with the public key can only be decrypted with the private key.
Public Key Cryptography uses two keys - a public key that can encrypt messages and verify signatures, and a private key that can decrypt messages and create signatures. The RSA algorithm, the most widely used public key algorithm, is based on the mathematical difficulty of factoring large prime numbers. It works by having users generate a public/private key pair using two large prime numbers and performing modular exponentiation. The security of RSA relies on the fact that it is computationally infeasible to derive the private key from the public key and modulus.
The document discusses the RSA algorithm for cryptography. It begins by explaining that RSA was created by Ron Rivest, Adi Shamir, and Leonard Adleman in 1977. It uses logarithmic functions to encrypt and decrypt data in a way that is difficult to break, even with powerful computers. RSA can encrypt generic data to enable secure sharing and can verify digital signatures. It works using a public key that encrypts data and a private key that decrypts it. The document then provides examples of how RSA encryption works step-by-step using prime numbers to generate keys. It discusses the security of RSA and how increasing the key size makes it more difficult to break through brute force attacks or factorization. Proper key management is
This document presents an improved asymmetric key encryption algorithm using MATLAB. It begins with an introduction to asymmetric key cryptography and the RSA cryptosystem. It then describes a modified RSA algorithm using multiple public and private keys to increase security. Next, it explains how to implement RSA using the Chinese Remainder Theorem to reduce computational time. The document implements the original, modified, and CRT-based RSA algorithms in MATLAB and analyzes computation time versus number of prime numbers. It concludes the modified and CRT-based approaches provide more security than the original RSA algorithm with reduced computational time.
Cupdf.com public key-cryptography-569692953829ajsk1950
This document provides an overview of public key cryptography. It discusses how public key cryptography uses asymmetric key pairs, with one key used for encryption and the other for decryption. One key is public and accessible, while the other is private. It also discusses how digital signatures use public key cryptography to authenticate the sender of a message. The document provides examples to illustrate how public key encryption and digital signatures work. It discusses issues like key management and risks associated with public key cryptography.
This document provides a summary of public key encryption and digital signatures. It begins by reviewing symmetric cryptography and its limitations in key distribution. It then introduces public key encryption, where each party has a public and private key pair. The document outlines the RSA algorithm and how it uses large prime number factorization problems to encrypt and decrypt messages. It also discusses how digital signatures can provide authentication, integrity, and non-repudiation for electronic messages and contracts using public key techniques like RSA.
The document discusses the RSA and MD5 algorithms. It provides an overview of how RSA works, including key generation, encryption, and decryption. It also explains the MD5 hashing algorithm and its use in ensuring data integrity. Both algorithms are commonly used in security and encryption applications.
Public-key cryptography uses two keys: a public key for encryption and digital signatures, and a private key for decryption and signature verification. RSA is the most widely used public-key cryptosystem, using large prime factorization and modular exponentiation. It allows secure communication without prior key exchange. While brute force attacks on RSA are infeasible due to large key sizes, its security relies on the difficulty of factoring large numbers.
The binding of cosmological structures by massless topological defectsSérgio Sacani
Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field
equations sourced by a topological defect, i.e. a singularity of a very specific form, the result is a localized gravitational
field capable of driving flat rotation (i.e. Keplerian circular orbits at a constant speed for all radii) of test masses on a thin
spherical shell without any underlying mass. Moreover, a large-scale structure which exploits this solution by assembling
concentrically a number of such topological defects can establish a flat stellar or galactic rotation curve, and can also deflect
light in the same manner as an equipotential (isothermal) sphere. Thus, the need for dark matter or modified gravity theory is
mitigated, at least in part.
ESA/ACT Science Coffee: Diego Blas - Gravitational wave detection with orbita...Advanced-Concepts-Team
Presentation in the Science Coffee of the Advanced Concepts Team of the European Space Agency on the 07.06.2024.
Speaker: Diego Blas (IFAE/ICREA)
Title: Gravitational wave detection with orbital motion of Moon and artificial
Abstract:
In this talk I will describe some recent ideas to find gravitational waves from supermassive black holes or of primordial origin by studying their secular effect on the orbital motion of the Moon or satellites that are laser ranged.
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...Sérgio Sacani
Context. With a mass exceeding several 104 M⊙ and a rich and dense population of massive stars, supermassive young star clusters
represent the most massive star-forming environment that is dominated by the feedback from massive stars and gravitational interactions
among stars.
Aims. In this paper we present the Extended Westerlund 1 and 2 Open Clusters Survey (EWOCS) project, which aims to investigate
the influence of the starburst environment on the formation of stars and planets, and on the evolution of both low and high mass stars.
The primary targets of this project are Westerlund 1 and 2, the closest supermassive star clusters to the Sun.
Methods. The project is based primarily on recent observations conducted with the Chandra and JWST observatories. Specifically,
the Chandra survey of Westerlund 1 consists of 36 new ACIS-I observations, nearly co-pointed, for a total exposure time of 1 Msec.
Additionally, we included 8 archival Chandra/ACIS-S observations. This paper presents the resulting catalog of X-ray sources within
and around Westerlund 1. Sources were detected by combining various existing methods, and photon extraction and source validation
were carried out using the ACIS-Extract software.
Results. The EWOCS X-ray catalog comprises 5963 validated sources out of the 9420 initially provided to ACIS-Extract, reaching a
photon flux threshold of approximately 2 × 10−8 photons cm−2
s
−1
. The X-ray sources exhibit a highly concentrated spatial distribution,
with 1075 sources located within the central 1 arcmin. We have successfully detected X-ray emissions from 126 out of the 166 known
massive stars of the cluster, and we have collected over 71 000 photons from the magnetar CXO J164710.20-455217.
(June 12, 2024) Webinar: Development of PET theranostics targeting the molecu...Scintica Instrumentation
Targeting Hsp90 and its pathogen Orthologs with Tethered Inhibitors as a Diagnostic and Therapeutic Strategy for cancer and infectious diseases with Dr. Timothy Haystead.
Travis Hills of MN is Making Clean Water Accessible to All Through High Flux ...Travis Hills MN
By harnessing the power of High Flux Vacuum Membrane Distillation, Travis Hills from MN envisions a future where clean and safe drinking water is accessible to all, regardless of geographical location or economic status.
Current Ms word generated power point presentation covers major details about the micronuclei test. It's significance and assays to conduct it. It is used to detect the micronuclei formation inside the cells of nearly every multicellular organism. It's formation takes place during chromosomal sepration at metaphase.
Mending Clothing to Support Sustainable Fashion_CIMaR 2024.pdfSelcen Ozturkcan
Ozturkcan, S., Berndt, A., & Angelakis, A. (2024). Mending clothing to support sustainable fashion. Presented at the 31st Annual Conference by the Consortium for International Marketing Research (CIMaR), 10-13 Jun 2024, University of Gävle, Sweden.
Basics of crystallography, crystal systems, classes and different forms
RSA-W7(rsa) d1-d2
1. Information Security I
By
Fahad Layth Malallah
Reference Books:
1. Introduction to Computer Security, by Matt Bishop.
2. Security in Computing, 4th Edition, by Charls P. Pfleeger.
3. Principle of Computer Security. 2nd edition, by Arthur.
4th grade, Computer Science
Cihan University
First Semester, 2014-2015.
Lecture-W7-D1-D2.
1
3. -Aim of this lecture:
Students will be familiar and able to secure information by using:
E- Asymmetric Cryptography (Public-Key Systems):
1-Basic on modular arithmetic, Number Theory.
2-Modular arithmetic inverse computation.
3- Al-Gamal Algorithm (ciphering & de-ciphering).
4-RSA Algorithm (ciphering & de-ciphering).
3
4. 4- RSA Algorithm (ciphering & de-ciphering).
• Three scientist have invented a security algorithm named it by
first character of their names:
• Adleman the mathematician.
• Rivest and Shamir the computer scientists.
– Alice must create a Public Key, which she can publish so that Bob (and
everyone else) can use it to encrypt messages to her. Because the
public key is a one way function, it must be virtually impossible for
anybody to reverse it and decrypt Alice’s message.
– However, Alice needs to decrypt the messages being sent to her. She
must therefore have a Private Key, which allows her to reverse the
effect of the Public Key.
– There is a mathematical relation between the Public Key and Private
Key, but if the Public Key is known the ability to find the Private Key is
zero, even if the mathematical relation is known!!!
4
5. Hard Mathematical Problem
• The concept HMP is best understood as a
mathematical problem which is computationally
infeasible to solve.
• The HMP is proven mathematically.
• Among the concepts that are HMP that we have
seen are:
– DLP (Discrete Logarithm Problem).
– Integer Factorization.
MCS 1413 - CRYPTOGRAPHY 5
6. RSA Algorithm:
6
Ali:
1-Alie encrypts M by
using public keys (e, n)as:
Bob:
1- chooses secret primes p and q and
computes n=pq .
2- chooses an exponent e as:
gcd( e, [p-1 ]. [q-1])= 1
3- then, computes d as :
de= 1 mod (p-1)(q-1)
4- Bob makes (p,q,d) public and keeps
(e,n) secret keys, then send only the
public to Ali….
5-Bob decrypts by computing .
Procedures is : Ali want to send a Secret message M to Bob. So , Ali
will encrypt a M and Bob will decrypt the message. Bob should
create a private key to decryption.
.
7. RSA numerical Example 1:
Part A wants to send a message M to Part B. encrypt the message
m=10 and decrypt the cipher c by using asymmetric cryptosystem
RSA. Let p = 7 and q = 13 be the two primes.
Solution:
1- Part B must select n= pq. and e where: gcd(e, [p-1][q-1])
n = pq = 91 and (p − 1)(q − 1) = 72.
To find e : gcd(e,72)=1 :
Choose e. Let’s look among the primes.
• Try e = 2. gcd(2, 72) = 2 (does not work)
• Try e = 3. gcd(3, 72) = 3 (does not work)
• Try e = 5. gcd(5, 72) = 1 (it works)
We choose e = 5. (e,n) is the public key
2- Part B also must find d (private key) next slides… 7
8. RSA numerical Example 1: Continue…
2- Part B also must find d (private key) by :
d.e = 1 mod (p-1) (q-1) d.e=1 mod (7-1) (13-1)
d. 5 = 1 mod (6 ) (12) d.5 = 1 mod 72
Now, we find multiplication inverse for 5 mod 72.
inverse equation: 1= ax + by a=5, b=72 1= 5x + 72 y.
1= (5*29) + (-2 * 72) correct.
Inverse(5)= 29.
29 = 1 mod 72
d=29.
Private key is 29. this should be kept with Part B for decryption. 8
9. RSA numerical Example 1: Continue…
3- Now, Part B sends the public key (e,n) and keeps the private key
(p,q,d).
4- Now, Part A encrypt the message m=10 as:
9
82
91mod10
mod
5
C
C
nMC e
5- Now , Part B will decrypt the C by using the private key 29
10
91mod82
mod
29
m
m
nCm d
11. -Exercises:
1-On which hard mathematical problem does RSA base its security?
2- Explain the ciphering and deciphering operations of RSA.
3-Compare between Al-Gamal and RSA .
4- In RSA, the cipher-text C = 9. The public key is given by n = 143 and
e = 23. In the following, we will try to crack the system and to
determine the original message M.
(i) What parameters comprises the public key and what parameters
the private key?.
(ii) What steps are necessary to determine the private key from the
public key?.
(iii) Determine the private key for the given system.
(iv) What is the original message M?.
5- Given p = 19, q = 29, N = pq and e = 17, compute the private key d
corresponding to the RSA system.
11
12. -Exercises:
6- Local Area Network uses a public key infrastructure based on RSA
with public key n =pq=55 and e=7.
(i) Find the private key d. For RSA we have de= 1 mod (p-1)(q-1)
(ii) Find the corresponding message M for a cipher C = 3.
7- Consider a RSA public-key system where the public key consists of
n = pq = 143 and e = 71.
A: Find a number d such that ed = 1 modulo (p-1)(q -1).
B: Give the decryption function for RSA.
C: Decrypt the cipher C = 12.
8-Alice has published her RSA public keys as <N; e> = <91;5>, where
N is the known public number and e is her public key. Accordingly,
Bob sent her the cipher text 81. Find the corresponding message.
12
13. -Exercises:
1-On which hard mathematical problem does RSA base its security?
1-discrete Logarithm Problem.
2- Number factorization.
2- Explain the ciphering and deciphering operations of RSA.
It is available in the lecture documents (slide 6).
3-Compare between Al-Gamal and RSA .
13
RSA Al-Gamal
Depend on DLP, Number factorization Depend on DLP
Cipher text size is the same as the message
size
Cipher text size is the double of message
size
Public key (n,e), private key= p,q, d. public key g,p,A private key: a
14. 4- In RSA, the cipher-text C = 9. The public key is given by n = 143 and
e = 23. In the following, we will try to crack the system and to
determine the original message M.
(i) What parameters comprises the public key and what parameters
the private key?.
(ii) What steps are necessary to determine the private key from the
public key?.
(iii) Determine the private key for the given system.
(iv) What is the original message M?.
Sol:
1-Public key : n=143, e= 23. private key is d. ( d.e= 1 mod (p-1)(q-1))
2- d.e= 1 mod (p-1) (q-1), how do we find p & q.
Divide n by sqrt(n). Sqrt(143)= 11.9
143/3
143/7
143/11= 13 ok. Now p=11, q= 13 14
15. Now p=11, q= 13
d.23 = 1 mod (11-1) (13-1) 23. d= 1 mod 120
Now compute the inverse as 1 =ax + by : a= 23, b= 120
X= 47, y= -9 , the inverse is 47, so d= 47.
3- Original message is M
http://www.cs.princeton.edu/~dsri/modular-inversion.html
5- Given p = 19, q = 29, N = pq and e = 17, compute the private key d
corresponding to the RSA system.
Sol:
d.e = 1 mod (p-1)( q-1) d. 17= 1 mod (19-1) (29-1)
15
46
143mod9
mod
47
M
M
nCM d
16. http://www.cs.princeton.edu/~dsri/modular-inversion.html
5- Given p = 19, q = 29, N = pq and e = 17, compute the private key d
corresponding to the RSA system.
Sol:
d.e = 1 mod (p-1)( q-1) d. 17= 1 mod (19-1) (29-1)
17. d = 1 mod 504
Now, compute the inverse of d as:
1 = ax + by : a= 17, b= 504.
1= 17 x + 504 y
Now, compute q from gcd (504,17), then compute x(s) and y(s).
Finally: x= 89, y= -3.
Accordingly, the inverse d = 89.
16
17. 6- Local Area Network uses a public key infrastructure based on RSA
with public key n =pq=55 and e=7.
(i) Find the private key d. For RSA we have de= 1 mod (p-1)(q-1)
(ii) Find the corresponding message M for a cipher C = 3.
Sol:
1- d.e= 1 mod (p-1) (q-1) we have to find p & q.
So p= 11, q=5.
-To compute d: d. 7 = 1 mod (11-1) (5-1) 7.d =1 mod 40
-to compute inverse : 1= ax + by as a = 7, b= 40
- Compute x & y , x=-17 ,y= 3 d= (-17*1 + 40) mod 40 d= 23 17
11555
3.18355
4.755
18. 6- Local Area Network uses a public key infrastructure based on RSA
with public key n =pq=55 and e=7.
(i) Find the private key d. For RSA we have de= 1 mod (p-1)(q-1)
(ii) Find the corresponding message M for a cipher C = 3.
Sol:
-Compute x & y , x=-17 ,y= 3 d= (-17*1 + 40) mod 40 d= 23
2-
18
27
55mod3
mod
23
M
M
nCM d
19. 7- Consider a RSA public-key system where the public key consists of
n = pq = 143 and e = 71.
A: Find a number d such that ed = 1 modulo (p-1)(q -1).
B: Give the decryption function for RSA.
C: Decrypt the cipher C = 12.
Sol:
A- n=143=pq=11.13 d ed=1 mod (p-1)(q-1)
71. d = 1 mod (11-1)(13-1). 71 d = 1 mod 120
to compute the inverse 1= ax + by: a=71, b=120
So, x= -49 , y= 29.
d= 1 * -49 mod 120 d=71.
B-
C-
19
nCM d
mod
73
143mod1271
M
M
20. 8-Alice has published her RSA public keys as <N; e> = <91;5>, where
N is the known public number and e is her public key. Accordingly,
Bob sent her the cipher text 81. Find the corresponding message.
Sol:
In order to find the message , we have to firstly find the private key
which is d.
d.e =1 mod (p-1) (q-1) now we have to find q & p from n where
n=pq.
91= 7 . 13= p.q.
d.5 = 1 mod (7-1) (13-1) 5.d = 1 mod 72 by finding the inverse
so: d=29.
Now, apply the decryption rule
20
5
91mod81
mod
29
M
M
nCM d
Editor's Notes
Model of security: policies of securities
Model of security: policies of securities
Factorization of big numbers Finding big prime numbers Multiplication of big prime numbers Exponentiation of big numbers Computing discrete logarithms.
Factorization of big numbers Finding big prime numbers Multiplication of big prime numbers Exponentiation of big numbers Computing discrete logarithms.