Diffie hellman key algorithm

Download as pptx, pdf

0 likes249 views

The Diffie-Hellman key agreement protocol allows two users to exchange a secret key over an insecure medium without any prior secrets. It uses two public parameters, a prime number p and an integer g that is primitive root modulo p. Each user selects a private random number and computes their public number using g and p. Both users can then compute the same shared secret key using each other's public numbers and their own private number. The security relies on the difficulty of calculating the shared secret key given only the public values. However, it is vulnerable to man-in-the-middle attacks without authentication. The document provides an example of how the algorithm works and discusses advantages like public key distribution and disadvantages like lack of authentication.

Technology

Most read

Introduction
• The Diffie-Hellman key agreement protocol was developed by
Diffie and Hellman in 1976.
• This protocol allows two users to exchange a secret key over an
insecure medium without any prior secrets.
• The protocol has two system parameters p and g.
• They are both public and may be used by all users in a system.
• Parameter p is a prime number and parameter g is an integer less
than p, with the following property:
– For every number n between 1 and p – 1 inclusive.
– There is a power k of g such that n = 𝑔𝑘
𝑚𝑜𝑑 𝑝.

Introduction
• The protocol depends on the discrete algorithm problem for its
security.
• It assumes that it is computationally infeasible to calculate the
shared secret key 𝑘 = 𝑔𝑎𝑏 𝑚𝑜𝑑 𝑝 given the two public values
𝑔𝑎 𝑚𝑜𝑑 𝑝 and 𝑔𝑏 𝑚𝑜𝑑 𝑝 when the prime p is sufficiently large.
• The Diffie – Hellman key exchange is vulnerable to a man-in-the-
middle attack.
• This vulnerability is present because Diffie-Hellman key exchange
does not authenticate the participants.
• Possible solutions include the use of digital signatures and other
protocol variants.

Algorithm
• Select two numbers:
1. Prime number 𝑞.
2. 𝛼 an integer that is a primitive root of 𝑞.
• Suppose the users A and B wish to exchange a key.
1. User A select a random integer 𝑋𝐴 < 𝑞 and computes
𝑌
𝐴 = 𝛼𝑋𝐴 𝑚𝑜𝑑 𝑞.
2. User A select a random integer 𝑋𝐵 < 𝑞 and computes
𝑌𝐵 = 𝛼𝑋𝐵 𝑚𝑜𝑑 𝑞.
3. Both side keeps the X value private and makes the Y
value available publicly to the other sides.
4. User A computes the key as 𝐾 = (𝑌𝐵)𝑋𝐴 𝑚𝑜𝑑 𝑞.
5. User B computes the key as 𝐾 = (𝑌𝐴)𝑋𝐵 𝑚𝑜𝑑 𝑞.

Algorithm
• Both side gets same results:
𝐾 = (𝑌𝐵)𝑋𝐴 𝑚𝑜𝑑 𝑞 = (𝛼𝑋𝐵 𝑚𝑜𝑑 𝑞)𝑋𝐴 𝑚𝑜𝑑 𝑞
= (𝛼𝑋𝐵)𝑋𝐴 𝑚𝑜𝑑 𝑞 = 𝛼𝑋𝐵𝑋𝐴𝑚𝑜𝑑 𝑞
= (𝛼𝑋𝐴 𝑚𝑜𝑑 𝑞)𝑋𝐵 𝑚𝑜𝑑 𝑞 = (𝑌𝐴)𝑋𝐵 𝑚𝑜𝑑 𝑞

Example
User A and User B use the Diffie-Hellman key exchange technique
with a common prime 𝑞 = 17 and a primitive root 𝛼 = 7.
a) If user A has private key 𝑋𝐴 = 5, what is A’s public key 𝑌
𝐴?
b) If user B has private key 𝑋𝐵 = 12, what is B’s public key 𝑌𝐵?
c) What is the shared secret key?
Solution:
a) A’s public key 𝒀𝑨
𝑌
𝐴 = 𝛼𝑋𝐴 𝑚𝑜𝑑 𝑞 = (7)5
𝑚𝑜𝑑 71 = 16807 mod 71 = 51
b) B’s public key 𝒀𝑩
𝑌𝐵 = 𝛼𝑋𝐵 𝑚𝑜𝑑 𝑞 = (7)12 𝑚𝑜𝑑 71 = 13841287201 mod 71 = 4
c) A’s public key 𝒀𝑨
𝐾 = (𝑌𝐵)𝑋𝐴 𝑚𝑜𝑑 𝑞 = (4)5 𝑚𝑜𝑑 71
= 1024 𝑚𝑜𝑑 71 = 30

Advantages
1. Any user can choose a random x and publish 𝑔𝑥 in a public
database such as a phone book.
2. Phone book must be maintained by a TTP.
3. Other users can look up the database and get the public key
for the individual and use it to encrypt the message.
4. Ideal for use with emails.

Disadvantages
1. Does not protect against man in middle attacks.
2. Even can intercept all traffic between Alice and Bob and
generate separate keys for communication with them.
3. If Alice sends an encrypted message for Bob with his public
key, Even simply forwards it.
4. For large prime 𝑝, 𝑝 − 1 is an even number and so 𝑍𝑝
∗ will
have an subgroup of order 2.

This document presents an overview of Kerberos authentication protocol. Kerberos was developed at MIT to provide strong authentication on insecure networks. It uses a centralized authentication server and relies on symmetric encryption. The document describes the requirements for Kerberos, differences between versions 4 and 5, key concepts like tickets and authenticators, and the message exchanges involved in the authentication process. The strengths of Kerberos are highlighted as mutual authentication between clients and servers without sending passwords in plain text across the network.

symmetric key encryption algorithmsRashmi Burugupalli

Symmetric Key Encryption Algorithms can be categorized as stream ciphers or block ciphers. Block ciphers like the Data Encryption Standard (DES) operate on fixed-length blocks of bits, while stream ciphers process messages bit-by-bit. DES is an example of a block cipher that encrypts 64-bit blocks using a 56-bit key. International Data Encryption Algorithm (IDEA) is another block cipher that uses a 128-bit key and 64-bit blocks, employing addition and multiplication instead of XOR like DES. IDEA consists of 8 encryption rounds followed by an output transformation to generate the ciphertext from the plaintext and key.

Information Security (Digital Signatures)Zara Nawaz

Digital signatures rely on encryption and authentication to verify the identity of a sender and ensure a document has not been altered. They use a mathematical technique that validates authenticity, integrity, and allows verification of author, date, and time. Digital signatures offer more security than traditional signatures by solving problems of tampering and impersonation. They are important for authentication, non-repudiation, and ensuring integrity of communications. Key generation and signing algorithms are used to create digital signatures, while verification algorithms are used to validate signatures.

Information and network security 13 playfair cipherVaibhav Khanna

The Playfair cipher, invented by Charles Wheatstone in 1854, improves encryption security by treating pairs of letters (digrams) in plaintext as single units, using a 5x5 key matrix. This method complicates frequency analysis due to the increased number of digrams compared to single letters, significantly enhancing security over monoalphabetic ciphers. However, despite its historical use by military forces, the Playfair cipher can still be broken with enough ciphertext as it retains some structure of the original language.

Unit 2KRAMANJANEYULU1

Block ciphers like DES encrypt data in blocks and use a symmetric key known to both the sender and receiver. The AES block cipher is commonly used today. It operates on 128-bit blocks and supports key sizes of 128, 192, or 256 bits. The AES algorithm consists of repeated rounds of substitutions, shifts, and XOR operations with a expanded key schedule. It was designed to improve upon DES by having stronger cryptography and being more computationally efficient.

MD5 ALGORITHM.pptxRajapriya82

The MD5 algorithm is a cryptographic hash function that generates a 128-bit digest from a message of any length. It works by first padding the message to a length that is a multiple of 512 bits, then appending the message length. It initializes buffers and processes the message in 512-bit blocks using four rounds of 16 operations each, applying different functions to update the buffers. The final buffer values become the MD5 digest. It is commonly used to verify file integrity but is now considered insecure due to possible hash collisions.

Diffie-hellman algorithmComputer_ at_home

The Diffie-Hellman algorithm, developed in 1976 by Whitfield Diffie and Martin Hellman, enables two parties to generate a shared cryptographic key for secure communication over an insecure channel without transferring the key itself. The process involves agreeing on a prime number and a primitive root, where each party computes their public key using a secret key and shares it to compute a final shared secret key. While this method allows secure key sharing and communication, it is slower and requires more processing power compared to symmetric encryption.

Symmetric and Asymmetric Encryption.pptHassanAli980906

Symmetric and asymmetric encryption methods are compared. Symmetric encryption uses a single shared key for encryption and decryption while asymmetric encryption uses two separate keys: a public key for encryption and a private key for decryption. The main advantages of symmetric encryption are that it is simple and fast but key distribution is insecure. Asymmetric encryption is more secure for key distribution since users only need to share public keys, but it is more complex computationally.

Message authenticationCAS

The document discusses computer security focusing on message authentication, highlighting the requirements for message integrity and sender validation. It covers methods such as symmetric and public-key encryption, hash functions, message authentication codes (MAC), and HMAC, explaining their roles in ensuring message security against various attacks. The content serves as an outline for effective communication protocol management in IT, emphasizing the importance of confidentiality and authentication mechanisms.

2. public key cryptography and RSADr.Florence Dayana

Public Key Cryptography (PKC) is an encryption method utilizing a pair of public and private keys for secure communications. The document explains the principles, requirements, and applications of PKC, including the RSA algorithm, which is widely used for encrypting messages and protecting confidentiality. Additionally, it covers various types of attacks on RSA and the use of Optimal Asymmetric Encryption Padding (OAEP) for enhanced security.

Public Key CryptosystemDevakumar Kp

Public-key cryptosystems emerged to address issues in symmetric encryption, specifically key distribution and digital signatures. Users generate a pair of keys, with one public and one private, enabling secure message encryption, decryption, and authentication. Requirements for effective public-key cryptography include easy key generation, efficient encryption and decryption processes, and strong resistance against adversaries attempting to derive private keys or original messages.

Diffie Hellman Key ExchangeSAURABHDHAGE6

The document presents an overview of the Diffie-Hellman key exchange method, detailing its origins, workings, advantages, and vulnerabilities such as the risk of man-in-the-middle attacks. It explains how users generate and exchange keys over an insecure channel, emphasizing the importance of using sufficiently large and random numbers for security. The Diffie-Hellman protocol is widely implemented in various security protocols including SSL/TLS and SSH.

13. Query Processing in DBMSkoolkampus

The document discusses various steps and algorithms for processing database queries. It covers parsing and optimizing queries, estimating query costs, and algorithms for operations like selection, sorting, and joins. Selection algorithms include linear scans, binary searches, and using indexes. Sorting can use indexes or external merge sort. Join algorithms include nested loops, merge join, and hash join.

DES (Data Encryption Standard) pressentationsarhadisoftengg

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.

Public Key CryptographyGopal Sakarkar

Public key cryptography uses two keys, a public key that can encrypt messages and a private key that decrypts messages. It has six components: plain text, encryption algorithm, public and private keys, ciphertext, and decryption algorithm. Some key characteristics are that it is computationally infeasible to determine the private key from the public key alone, and encryption/decryption is easy when the relevant key is known. The requirements of public key cryptography are that it is easy to generate a public-private key pair, easy to encrypt with the public key, easy for the recipient to decrypt with the private key, and infeasible to determine the private key from the public key or recover the plaintext from the ciphertext and public key alone

Email Security Pretty Good Privacy (PGP),Services Provided by PGP.pdfaryalmadhave123

The document discusses email security, focusing on Pretty Good Privacy (PGP) as a method for ensuring confidentiality, integrity, and authenticity of email communications. It outlines various security measures such as strong passwords, two-factor authentication, and encryption, while detailing the operational mechanisms of PGP, including authentication, confidentiality, compression, and segmentation. Additionally, it addresses challenges with PGP such as user complexity and compatibility with email clients.

Grasp patterns and its typesSyed Hassan Ali

The document discusses the GRASP (General Responsibility Assignment Software Principles) patterns and principles for assigning responsibilities in object-oriented design. It defines GRASP as helping to clearly outline which objects are responsible for which actions. There are nine GRASP principles covered: Creator, Controller, Information Expert, Low Coupling, High Cohesion, Indirection, Polymorphism, Protected Variations, and Pure Fabrication. These principles provide guidelines for assigning responsibilities to classes to achieve well-structured and maintainable code. The document then explains each principle in more detail using a chess game as an example domain.

Operator precedenceAkshaya Arunan

This document discusses operator precedence parsing. It describes operator grammars that can be parsed efficiently using an operator precedence parser. It explains how precedence relations are defined between terminal symbols and how these relations are used during the shift-reduce parsing process to determine whether to shift or reduce at each step. It also addresses handling unary minus operators and recovering from shift/reduce errors during parsing.

Hash Function ssuserdfb2da

This document discusses cryptographic hash functions including their applications in message authentication and digital signatures. It describes the requirements for hash functions to be secure including resistance to brute force attacks and cryptanalysis. The document outlines some simple hash functions and provides details on the Secure Hash Algorithm (SHA) family of cryptographic hash functions used in standards like SHA-512 which operates on 1024-bit blocks through 80 rounds. It also mentions NIST's selection of the Keccak algorithm as the new SHA-3 standard.

X.509 CertificatesSou Jana

block ciphersAsad Ali

The document discusses secret key cryptography, which involves using the same key for both encryption and decryption, and is classified into block and stream ciphers. It details the workings of various ciphers, particularly the Feistel cipher structure, including key generation, encryption, and decryption processes for the Data Encryption Standard (DES). Finally, it addresses the design principles, properties of good ciphers, and some controversies surrounding DES's key length and security.

Peephole optimization techniques in compiler designAnul Chaudhary

This document discusses various compiler optimization techniques, focusing on peephole optimization. It defines optimization as transforming code to run faster or use less memory without changing functionality. Optimization can be machine-independent, transforming code regardless of hardware, or machine-dependent, tailored to a specific architecture. Peephole optimization examines small blocks of code and replaces them with faster or smaller equivalents using techniques like constant folding, strength reduction, null sequence elimination, and algebraic laws. Common replacement rules aim to improve performance, reduce memory usage, and decrease code size.

Diffie Hellman.pptxSou Jana

The document summarizes the Diffie-Hellman key exchange algorithm. It was the first practical method for public key exchange proposed by Diffie and Hellman in 1976. It allows two parties to establish a shared secret key over an insecure channel. Each party generates a public/private key pair, and the secret key is derived from the exponentiation of each public key with the other party's private key. While it can securely establish a shared key, it is vulnerable to man-in-the-middle attacks without authentication of the participating identities.

Interconnection NetworkHeman Pathak

This document discusses different types of interconnection network topologies for parallel machines. It provides details on: 1) Linear array networks have nodes connected in a line, with diameter of n-1, node degree of 2, and bisection width of 1. 2) Mesh networks connect nodes in a grid, with diameter of 2(n-1), node degree of 4, and bisection width of n for an nXn mesh. 3) Hypercube networks have nodes connected by log2N routing functions, with diameter and node degree of log2N and bisection width of 2n-1 for a network with N nodes.

Digital signature schemesravik09783

This document discusses digital signature schemes. It begins by introducing cryptography and defining cryptosystems. It then describes private and public key cryptosystems. Digital signatures are introduced as a technique for non-repudiation based on public key cryptography. The properties and types of digital signatures are outlined, including direct and arbitrated signatures. Common digital signature standards like DSS, El Gamal, and RSA are then explained at a high level. The document concludes that digital signatures provide an effective mechanism for authenticity and non-repudiation of messages.

Information Security & CryptographyArun ACE

This document provides an overview of information security and cryptography. It discusses objectives of security like avoiding data threats. It also covers topics like password auditing, data security, authentication, encryption, decryption, public and private key cryptography, digital signatures, and the RSA algorithm. It demonstrates an example of encrypting a message using RSA and decrypting the cipher text. The conclusion emphasizes the importance of information security.

SCHEDULING ALGORITHMSDhaval Sakhiya

This document discusses different types of scheduling algorithms used by operating systems to determine which process or processes will run on the CPU. It describes preemptive and non-preemptive scheduling, and provides examples of common scheduling algorithms like first-come, first-served (FCFS), shortest job first (SJF), round robin, and priority-based scheduling. Formulas for calculating turnaround time and waiting time are also presented.

Substitution techniquesvinitha96

- Substitution techniques involve replacing the letters of plaintext with other letters, numbers or symbols. The main substitution techniques are Caesar cipher, monoalphabetic cipher, Playfair cipher and Hill cipher. - The Caesar cipher replaces each letter with the letter three positions down the alphabet. The monoalphabetic cipher uses a single alphabetic key for the entire message. The Playfair cipher encrypts pairs of letters based on a 5x5 grid generated from a keyword. The Hill cipher encrypts blocks of letters as numerical values using a matrix-based approach.

Rsa diffi-network security-ittrameshvvv

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.

Unit - 3.pptDHANABALSUBRAMANIAN

This document discusses key management and distribution in public-key cryptography. It covers several methods for distributing public keys including public announcement, directories, certificates. It also discusses using public keys to distribute secret keys, including Diffie-Hellman key exchange and hybrid encryption. Finally, it introduces elliptic curve cryptography as an alternative to systems like RSA that allows equivalent security with smaller key sizes.

More Related Content

What's hot (20)

Message authenticationCAS

2. public key cryptography and RSADr.Florence Dayana

Public Key CryptosystemDevakumar Kp

Diffie Hellman Key ExchangeSAURABHDHAGE6

13. Query Processing in DBMSkoolkampus

DES (Data Encryption Standard) pressentationsarhadisoftengg

Public Key CryptographyGopal Sakarkar

Email Security Pretty Good Privacy (PGP),Services Provided by PGP.pdfaryalmadhave123

Grasp patterns and its typesSyed Hassan Ali

Operator precedenceAkshaya Arunan

Hash Function ssuserdfb2da

X.509 CertificatesSou Jana

block ciphersAsad Ali

Peephole optimization techniques in compiler designAnul Chaudhary

Diffie Hellman.pptxSou Jana

Interconnection NetworkHeman Pathak

Digital signature schemesravik09783

Information Security & CryptographyArun ACE

SCHEDULING ALGORITHMSDhaval Sakhiya

Substitution techniquesvinitha96

Message authenticationCAS

2. public key cryptography and RSADr.Florence Dayana

Public Key CryptosystemDevakumar Kp

Diffie Hellman Key ExchangeSAURABHDHAGE6

13. Query Processing in DBMSkoolkampus

DES (Data Encryption Standard) pressentationsarhadisoftengg

Public Key CryptographyGopal Sakarkar

Email Security Pretty Good Privacy (PGP),Services Provided by PGP.pdfaryalmadhave123

Grasp patterns and its typesSyed Hassan Ali

Operator precedenceAkshaya Arunan

Hash Function ssuserdfb2da

X.509 CertificatesSou Jana

block ciphersAsad Ali

Peephole optimization techniques in compiler designAnul Chaudhary

Diffie Hellman.pptxSou Jana

Interconnection NetworkHeman Pathak

Digital signature schemesravik09783

Information Security & CryptographyArun ACE

SCHEDULING ALGORITHMSDhaval Sakhiya

Substitution techniquesvinitha96

Similar to Diffie hellman key algorithm (20)

Rsa diffi-network security-ittrameshvvv

Unit - 3.pptDHANABALSUBRAMANIAN

RSA - ALGORITHM by Muthugomathy and Meenakshi Shetti of GIT COLLEGE Qualcomm

The document provides an overview of public key cryptography, particularly the RSA encryption algorithm, detailing its principles, advantages, and disadvantages. It explains the roles of private and public keys, the process of prime factorization, and Euler's theorem in cryptography, as well as the popularity of PGP desktop as a practical application. Additionally, the document discusses the security implications of public key systems and references various sources for further reading.

international security system data threatsgacop74666

PRINCIPLES OF INFORMATION SYSTEM SECURITYgacop74666

Introduction: Information security is more and more important every day in the workplace. If we want to improve our information security, we need a solid understanding of the principles that will help us do that. This guide explores those principles and will guide you to building a more secure environment. Information Security Principles: There are three basic principles of information security, and all other practices are based on these three: * Confidentiality: Confidentiality is the basic tenet of information security. Confidentiality means that you don't share private or confidential information with anyone who shouldn't know it. As the name implies, you don't give out confidential information. * Availability: Availability means that you can access the information you need when you need it. You may not need access to everything all the time, but when you do, you want access quickly. You may need access to your bank account when you pay a bill. This is availability. * Integrity: If you make a change to something, it should be tracked and logged in a journal or log. That way, you can verify that no unauthorized changes were made to the original information, so we know that the information is genuine. In short, integrity means you can verify that the information hasn't been altered in any way. There are four key concepts that underpin the practice of information security. These concepts, when integrated and applied appropriately, enable security managers and practitioners to defend against and recover from attacks. The four key concepts are: * Confidentiality: Confidentiality refers to protecting information from unauthorized access, use, or disclosure. This includes both internal and external threats. Data encryption or access control lists are examples of confidentiality controls. * Integrity: Integrity refers to protecting the accuracy, completeness, and validity of information. This includes protecting data from being modified without authorization. Data hashing algorithms or message authentication codes are examples of integrity controls. * Availability: Availability refers to ensuring that information and systems are accessible to authorized users when they need them. This includes measures to prevent service outages or data loss due to natural disasters or accidental or intentional malicious activity. Redundant systems, data backups, and disaster recovery plans are examples of availability controls. * Accountability: Accountability involves tracing user actions to the identity of the user. If the user's identity is associated with a group, then the actions of the user are also associated with the group. Accountability mechanisms typically involve the use of logs, audit trails, and other monitoring techniques. Accountability controls are also used to identify and fix system weaknesses that could lead to unauthorized access or changes to data and systems. By following these basic principles, we can help protect our information fro

Rsa and diffie hellman algorithmsdaxesh chauhan

The document provides an overview of RSA and Diffie-Hellman algorithms. It defines key terms in cryptography like plain text, cipher text, and key. It then describes how RSA works by choosing prime numbers, computing keys, and encrypting/decrypting messages. Diffie-Hellman allows two parties to establish a shared secret key over an insecure channel by agreeing on a modulus and base, and exchanging values while keeping their secret integers private.

Parallel processing -open mpTanjilla Sarkar

parallelprocessing-openmp-181105062408.pdfbosdhoni7378

Ch10Joe Christensen

1. Public key distribution methods include public announcement, publicly available directories, public key authorities, and public key certificates. 2. Diffie-Hellman key exchange allows two parties to jointly establish a shared secret key over an insecure channel without any prior secrets. 3. Elliptic curve cryptography provides the same level of security as other public key systems like RSA but with smaller key sizes, reducing computational overhead.

Unit 3(1)Vinod Kumar Gorrepati

The document discusses principles of public-key cryptography and algorithms like RSA and Diffie-Hellman key exchange. It provides the following key points: 1. Public-key cryptography solves the key distribution problem of symmetric encryption by using different but mathematically-related public and private keys. 2. The RSA algorithm was one of the first practical public-key cryptosystems, using modular exponentiation with large prime numbers. 3. Diffie-Hellman key exchange allows two parties to jointly establish a shared secret over an insecure channel without any prior secrets. It is based on the difficulty of calculating discrete logarithms.

Information and Network SecurityMaulik Togadiya

The Diffie-Hellman key exchange algorithm allows two users to securely exchange a secret key over an insecure channel. It uses discrete logarithms over finite fields. Each user generates a public/private key pair, and the exchange of the public keys allows both to independently calculate a shared secret key. The security of the algorithm relies on the difficulty of solving the discrete logarithm problem.

Ch9Mahender Kumar

This document discusses public key cryptography and the RSA algorithm. It begins by outlining some misconceptions about public key encryption. It then provides an overview of the key concepts behind public key cryptosystems, including the use of public and private key pairs to enable encryption, digital signatures, and key exchange. The document goes on to provide detailed explanations of the RSA algorithm, including how it uses large prime numbers and modular arithmetic to encrypt and decrypt messages securely. It discusses the security of the RSA algorithm and analyzes approaches for attacking it, such as brute force key searching and mathematical attacks based on factoring the private key.

Information and network security 32 principles of public key cryptosystemsVaibhav Khanna

The document discusses the principles of public-key cryptosystems, highlighting their use for both confidentiality and authentication through the generation of public and private key pairs. It classifies applications of public-key systems into categories such as encryption/decryption, digital signatures, and key exchange, emphasizing the importance of computational infeasibility for security. Additionally, it notes the necessity of trapdoor one-way functions and the challenges that come with ensuring the security of public-key systems compared to private key schemes.

Unit 3(1)Vinod Kumar Gorrepati

The document discusses principles of public-key cryptography and the Diffie-Hellman key exchange algorithm. It begins by explaining the problems with symmetric encryption that public-key cryptography aims to address. It then provides an overview of public-key cryptosystems and their requirements. The document goes on to describe the RSA algorithm in detail and provide an example of how it works. It also explains the Diffie-Hellman key exchange algorithm, how it allows two parties to securely exchange a key without transmitting it, and provides a numerical example.

Asymmetric Ciphers in Networks and Security.pptxVivekanandaGN1

The document outlines key concepts related to asymmetric ciphers and public key cryptosystems, including the RSA algorithm, Diffie-Hellman key exchange, and the principles of digital signatures and encryption. It details the processes of generating public and private keys, encrypting and decrypting messages, as well as potential attacks such as the man-in-the-middle attack. Various examples and methods for key generation and encryption are provided to illustrate these concepts.

Module 2 of cryptography old scheme VTU pptMonaReddy12

This document discusses public-key cryptography, specifically the principles of public-key cryptosystems like RSA and the Diffie-Hellman key exchange method. It explains key concepts such as encryption and decryption algorithms, plain text, cipher text, and the roles of public and private keys. Additionally, it highlights the ElGamal cryptographic system, which is based on the Diffie-Hellman method and the difficulty of computing discrete logarithms.

engineering cryptography pptxmodule 4 rsa.pptxshaziasulthana2

Public key algorithmPrateek Pandey

Public key algorithms like RSA and ElGamal allow for secure encryption without a shared private key. RSA uses a public and private key pair generated from large prime numbers such that a message encrypted with the public key can only be decrypted by the corresponding private key. It is widely used due to its security being based on the difficulty of factoring large numbers, though it is less efficient than symmetric algorithms due to involving modular exponentiation. ElGamal also uses a public/private key approach and its security relies on the discrete logarithm problem.

KEY MGMT.pptRizwanBasha12

The document discusses key management and the Diffie-Hellman key exchange protocol. It begins by explaining public-key encryption helps address key distribution problems. It then describes different methods for distributing public keys including public announcement, publicly available directories, public-key authorities, and public-key certificates. It also explains how public-key encryption can be used to distribute secret keys, including Diffie-Hellman key exchange and hybrid key distribution. The document concludes by discussing elliptic curve cryptography as an alternative to methods using large integer arithmetic.

Cryptography 101Aditya Kamat

The document provides an extensive overview of cryptography, including definitions, key concepts, and various encryption techniques such as hashing, symmetric and asymmetric key encryption, and digital signatures. It also discusses real-world applications, mathematical foundations, and best practices for secure communication, particularly emphasizing the importance of confidentiality, integrity, and availability of data. Additionally, it highlights tools like PGP for email security and common pitfalls to avoid in cryptographic implementations.

Rsa diffi-network security-ittrameshvvv

Unit - 3.pptDHANABALSUBRAMANIAN

RSA - ALGORITHM by Muthugomathy and Meenakshi Shetti of GIT COLLEGE Qualcomm

international security system data threatsgacop74666

PRINCIPLES OF INFORMATION SYSTEM SECURITYgacop74666

Rsa and diffie hellman algorithmsdaxesh chauhan

Parallel processing -open mpTanjilla Sarkar

parallelprocessing-openmp-181105062408.pdfbosdhoni7378

Ch10Joe Christensen

Unit 3(1)Vinod Kumar Gorrepati

Information and Network SecurityMaulik Togadiya

Ch9Mahender Kumar

Information and network security 32 principles of public key cryptosystemsVaibhav Khanna

Unit 3(1)Vinod Kumar Gorrepati

Asymmetric Ciphers in Networks and Security.pptxVivekanandaGN1

Module 2 of cryptography old scheme VTU pptMonaReddy12

engineering cryptography pptxmodule 4 rsa.pptxshaziasulthana2

Public key algorithmPrateek Pandey

KEY MGMT.pptRizwanBasha12

Cryptography 101Aditya Kamat

More from ShaishavShah8 (19)

Constructor oopjShaishavShah8

Constructor is a special method in Java that is used to initialize an object. There are two types of constructors: default (no-arg) constructors that have no parameters, and parameterized constructors that allow passing parameters to set object attribute values. Constructors can be overloaded to support different initialization scenarios. They are invoked during object creation to construct and provide initial values for the object's attributes.

Clipping computer graphicsShaishavShah8

Clipping is the process of removing graphics that are outside the viewing area. There are different types of clipping including point, line, area/polygon, curve, and text clipping. Line clipping algorithms like Cohen-Sutherland and Liang-Barsky use line endpoints and intersection calculations to determine which portions of a line are inside the clip region. Polygon clipping algorithms like Sutherland-Hodgman and Weiler-Atherton process polygon vertices and edges to generate clipped polygon areas. Curve and text clipping also use bounding areas and intersection calculations to clip complex graphical elements.

Classification of debuggers spShaishavShah8

Debuggers are used to identify and fix problems in computer programs. There are several types of debuggers including static debuggers, which insert debugging code directly into the source program, and dynamic interactive debuggers, which can stop, examine, and continue an executing program. Dynamic interactive debuggers include breakpoint debuggers, which allow setting conditional or unconditional breakpoints, meta debuggers which can debug themselves, kernel debuggers for debugging operating systems, and tele-debuggers which execute on a separate computer. Debuggers can also be classified based on whether the debugger and debugged process run in the same or separate processes.

Parallel and perspective projection in 3 d cgShaishavShah8

This document discusses parallel and perspective projections in 3D computer graphics. It defines projection as mapping a 3D object onto a 2D view plane using projection lines. There are two main types of projection: parallel projection, where lines are parallel; and perspective projection, where lines converge at a vanishing point. Perspective projection creates a smaller image but is more realistic. The document describes one, two, and three-point perspective projections and provides examples of each. It concludes that advances in computer graphics allow for more complex projections than when early sci-fi films were made.

Asymptotic notations adaShaishavShah8

This document discusses different asymptotic notations used to represent the complexity of algorithms: - O(g(n)) represents asymptotic upper bound - function g(n) grows at least as fast as f(n) for large n. - Ω(g(n)) represents asymptotic lower bound - function g(n) grows no faster than f(n) for large n. - θ(g(n)) represents asymptotic tight bound - functions g(n) and f(n) grow at the same rate for large n. It also explains the differences between O and o notations, and between Ω and ω notations - where the former represents loose asymptotic bounds and the latter

Arrays in java oopjShaishavShah8

Classical cyphers python programmingShaishavShah8

- Classical ciphers like the Caesar cipher are simple encryption techniques that are fun to program and understand. The document discusses the Caesar cipher specifically. - The Caesar cipher replaces each letter in a message with another letter a fixed number of positions down the alphabet. For example, with a shift of 3, A would be replaced by D, B by E, etc. - In Python, the ord() and chr() functions are used to convert between characters and their Unicode numeric codes to perform the encryption and decryption calculations for the Caesar cipher. Mathematical formulas are provided for both the encryption and decryption processes.

Logics for non monotonic reasoning-aiShaishavShah8

Non-monotonic reasoning allows conclusions to be retracted when new information is introduced. It is used to model plausible reasoning where defaults may be overridden. For example, it is typically true that birds fly, so we could conclude that Tweety flies since Tweety is a bird. However, if we are later told Tweety is a penguin, we would retract the conclusion that Tweety flies since penguins do not fly despite being birds. Non-monotonic reasoning resolves inconsistencies by removing conclusions derived from default rules when specific countervailing information is received.

Rdd transformations bdaShaishavShah8

This document discusses RDD transformations in Spark. It defines RDD as a resilient distributed dataset, which are fault-tolerant collections of elements that can be operated on in parallel. There are two types of RDD operations: transformations and actions. Transformations are lazy operations that take an RDD as input and return one or more RDDs as output, without changing the original RDD. Transformations are either narrow, operating only on a single partition, or wide, taking data from multiple partitions and shuffling the data.

Introduction to data warehouse dmbiShaishavShah8

This document provides an introduction to data warehouses. It defines a data warehouse as a subject-oriented, integrated, time-variant and non-volatile collection of data to support management decision making. The key features of a data warehouse are that it is subject-oriented, integrated, time variant and non-volatile. It also distinguishes between operational databases used for transaction processing and data warehouses used for analytical processing and decision making.

Lan, wan, man mcwcShaishavShah8

The document discusses three types of computer networks: Local Area Networks (LANs), Wide Area Networks (WANs), and Metropolitan Area Networks (MANs). LANs connect computers within a single building or campus through a shared cable. WANs span large areas like countries and connect hosts through leased telephone lines or satellite links. MANs cover entire cities using cable television networks and similar technology to LANs but over a larger geographical range.

Introduction to xml, uses of xml wtShaishavShah8

This document introduces XML (eXtensible Markup Language) and discusses its uses. XML is a markup language that uses tags to provide extra information about a document's content. XML tags describe the meaning of data rather than how to display it like HTML tags. XML is commonly used to transfer data between systems, often over the Internet. Specific XML subsets have been designed for transferring things like news feeds, scientific data, and publishing information. XML has advantages like being text-based so it takes up less space than other formats and can be displayed differently depending on the media. XML documents can also be modularized by reusing parts of them. For an XML document to be valid, it must be "well-formed" by

Agile process seShaishavShah8

This document provides an overview of agile processes and extreme programming (XP). It defines agility as effective response to change through communication among stakeholders and involving customers on the development team. Principles of agile processes include customer involvement, embracing change, incremental delivery, simplicity, and valuing people over processes. Extreme programming is described as one of the most widely used agile methods, with planning beginning through user stories, estimating costs, grouping stories into deliverable increments, and committing to delivery dates.

Applications of huffman coding dcdrShaishavShah8

Cookie management using jsp a javaShaishavShah8

Cookies are text files stored on a client machine that are used to track information for various purposes. They are set in the HTTP header and stored by the browser if configured to do so until their expiry date. The document discusses cookie management in Java using various JSP methods like setDomain(), getDomain(), setMaxAge(), getMaxAge(), setValue(), getValue(), setPath(), getPath(), setSecure(), and setComment() and getComment(). It also outlines the steps to set up a cookie by creating a cookie object, setting the maximum age, and sending the cookie in the HTTP response headers.

The login control provides a user interface for user authentication on a website. It authenticates users based on a username and password. The login control allows restricting access to pages. It has various methods like CreateChildControls and properties like CreateUserIconUrl. Events like LoggedIn are raised during different stages of the login process like when the user logs in successfully or when there is a login error.

Rdd transformationsShaishavShah8

RDD stands for Resilient Distributed Dataset, which are fault-tolerant collections of elements that can be operated on in parallel in Spark. There are two ways to create RDDs: by parallelizing an existing collection or referencing a dataset in an external storage system. RDD operations include transformations, which take an RDD as input and output one or more RDDs lazily without changing the original, and actions, which trigger computation. Transformations are either narrow, originating from a single partition, or wide, taking data from multiple partitions requiring a shuffle.

LAN, WAN, MANShaishavShah8

Introduction to data warehouseShaishavShah8

Data warehouses are subject-oriented collections of integrated and non-volatile data designed to support management decision making. They integrate data from multiple sources and apply data cleaning and integration techniques to ensure consistency. In contrast to operational databases focused on current transactions, data warehouses have a longer time horizon of historical data over many years. They are physically separate from operational systems and do not require transaction processing, but rather support analysis and decision making.

Constructor oopjShaishavShah8

Clipping computer graphicsShaishavShah8

Classification of debuggers spShaishavShah8

Parallel and perspective projection in 3 d cgShaishavShah8

Asymptotic notations adaShaishavShah8

Arrays in java oopjShaishavShah8

Classical cyphers python programmingShaishavShah8

Logics for non monotonic reasoning-aiShaishavShah8

Rdd transformations bdaShaishavShah8

Introduction to data warehouse dmbiShaishavShah8

Lan, wan, man mcwcShaishavShah8

Introduction to xml, uses of xml wtShaishavShah8

Agile process seShaishavShah8

Applications of huffman coding dcdrShaishavShah8

Cookie management using jsp a javaShaishavShah8

Rdd transformationsShaishavShah8

LAN, WAN, MANShaishavShah8

Introduction to data warehouseShaishavShah8

Recently uploaded (20)

Coordinated Disclosure for ML - What's Different and What's the Same.pdfPriyanka Aash

9-1-1 Addressing: End-to-End Automation Using FMESafe Software

This session will cover a common use case for local and state/provincial governments who create and/or maintain their 9-1-1 addressing data, particularly address points and road centerlines. In this session, you'll learn how FME has helped Shelby County 9-1-1 (TN) automate the 9-1-1 addressing process; including automatically assigning attributes from disparate sources, on-the-fly QAQC of said data, and reporting. The FME logic that this presentation will cover includes: Table joins using attributes and geometry, Looping in custom transformers, Working with lists and Change detection.

ReSTIR [DI]: Spatiotemporal reservoir resampling for real-time ray tracing ...revolcs10

"Scaling in space and time with Temporal", Andriy Lupa.pdfFwdays

Design patterns like Event Sourcing and Event Streaming have long become standards for building real-time analytics systems. However, when the system load becomes nonlinear with fast and often unpredictable spikes, it's crucial to respond quickly in order not to lose real-time operating itself. In this talk, I’ll share my experience implementing and using a tool like Temporal.io. We'll explore the evolution of our system for maintaining real-time report generation and discuss how we use Temporal both for short-lived pipelines and long-running background tasks.

CapCut Pro Crack For PC Latest Version {Fully Unlocked} 2025pcprocore

👉𝗡𝗼𝘁𝗲:𝗖𝗼𝗽𝘆 𝗹𝗶𝗻𝗸 & 𝗽𝗮𝘀𝘁𝗲 𝗶𝗻𝘁𝗼 𝗚𝗼𝗼𝗴𝗹𝗲 𝗻𝗲𝘄 𝘁𝗮𝗯> https://pcprocore.com/ 👈◀ CapCut Pro Crack is a powerful tool that has taken the digital world by storm, offering users a fully unlocked experience that unleashes their creativity. With its user-friendly interface and advanced features, it’s no wonder why aspiring videographers are turning to this software for their projects.

Connecting Data and Intelligence: The Role of FME in Machine LearningSafe Software

In this presentation, we want to explore powerful data integration and preparation for Machine Learning. FME is known for its ability to manipulate and transform geospatial data, connecting diverse data sources into efficient and automated workflows. By integrating FME with Machine Learning techniques, it is possible to transform raw data into valuable insights faster and more accurately, enabling intelligent analysis and data-driven decision making.

Raman Bhaumik - Passionate Tech EnthusiastRaman Bhaumik

OpenPOWER Foundation & Open-Source Core InnovationsIBM

penPOWER offers a fully open, royalty-free CPU architecture for custom chip design. It enables both lightweight FPGA cores (like Microwatt) and high-performance processors (like POWER10). Developers have full access to source code, specs, and tools for end-to-end chip creation. It supports AI, HPC, cloud, and embedded workloads with proven performance. Backed by a global community, it fosters innovation, education, and collaboration.

A Constitutional Quagmire - Ethical Minefields of AI, Cyber, and Privacy.pdfPriyanka Aash

Security Tips for Enterprise Azure SolutionsMichele Leroux Bustamante

Delivering solutions to Azure may involve a variety of architecture patterns involving your applications, APIs data and associated Azure resources that comprise the solution. This session will use reference architectures to illustrate the security considerations to protect your Azure resources and data, how to achieve Zero Trust, and why it matters. Topics covered will include specific security recommendations for types Azure resources and related network security practices. The goal is to give you a breadth of understanding as to typical security requirements to meet compliance and security controls in an enterprise solution.

Oh, the Possibilities - Balancing Innovation and Risk with Generative AI.pdfPriyanka Aash

AI Agents and FME: A How-to Guide on Generating Synthetic MetadataSafe Software

"Database isolation: how we deal with hundreds of direct connections to the d...Fwdays

What can go wrong if you allow each service to access the database directly? In a startup, this seems like a quick and easy solution, but as the system scales, problems appear that no one could have guessed. In my talk, I'll share Solidgate's experience in transforming its architecture: from the chaos of direct connections to a service-based data access model. I will talk about the transition stages, bottlenecks, and how isolation affected infrastructure support. I will honestly show what worked and what didn't. In short, we will analyze the controversy of this talk.

Cyber Defense Matrix Workshop - RSA ConferencePriyanka Aash

Mastering AI Workflows with FME by Mark DöringSafe Software

Harness the full potential of AI with FME: From creating high-quality training data to optimizing models and utilizing results, FME supports every step of your AI workflow. Seamlessly integrate a wide range of models, including those for data enhancement, forecasting, image and object recognition, and large language models. Customize AI models to meet your exact needs with FME’s powerful tools for training, optimization, and seamless integration

The Future of Product Management in AI ERA.pdfAlyona Owens

Hi, I’m Aly Owens, I have a special pleasure to stand here as over a decade ago I graduated from CityU as an international student with an MBA program. I enjoyed the diversity of the school, ability to work and study, the network that came with being here, and of course the price tag for students here has always been more affordable than most around. Since then I have worked for major corporations like T-Mobile and Microsoft and many more, and I have founded a startup. I've also been teaching product management to ensure my students save time and money to get to the same level as me faster avoiding popular mistakes. Today as I’ve transitioned to teaching and focusing on the startup, I hear everybody being concerned about Ai stealing their jobs… We’ll talk about it shortly. But before that, I want to take you back to 1997. One of my favorite movies is “Fifth Element”. It wowed me with futuristic predictions when I was a kid and I’m impressed by the number of these predictions that have already come true. Self-driving cars, video calls and smart TV, personalized ads and identity scanning. Sci-fi movies and books gave us many ideas and some are being implemented as we speak. But we often get ahead of ourselves: Flying cars,Colonized planets, Human-like AI: not yet, Time travel, Mind-machine neural interfaces for everyone: Only in experimental stages (e.g. Neuralink). Cyberpunk dystopias: Some vibes (neon signs + inequality + surveillance), but not total dystopia (thankfully). On the bright side, we predict that the working hours should drop as Ai becomes our helper and there shouldn’t be a need to work 8 hours/day. Nobody knows for sure but we can require that from legislation. Instead of waiting to see what the government and billionaires come up with, I say we should design our own future. So, we as humans, when we don’t know something - fear takes over. The same thing happened during the industrial revolution. In the Industrial Era, machines didn’t steal jobs—they transformed them but people were scared about their jobs. The AI era is making similar changes except it feels like robots will take the center stage instead of a human. First off, even when it comes to the hottest space in the military - drones, Ai does a fraction of work. AI algorithms enable real-time decision-making, obstacle avoidance, and mission optimization making drones far more autonomous and capable than traditional remote-controlled aircraft. Key technologies include computer vision for object detection, GPS-enhanced navigation, and neural networks for learning and adaptation. But guess what? There are only 2 companies right now that utilize Ai in drones to make autonomous decisions - Skydio and DJI.

Daily Lesson Log MATATAG ICT TEchnology 8LOIDAALMAZAN3

Cracking the Code - Unveiling Synergies Between Open Source Security and AI.pdfPriyanka Aash

UserCon Belgium: Honey, VMware increased my billstijn40

VMware’s pricing changes have forced organizations to rethink their datacenter cost management strategies. While FinOps is commonly associated with cloud environments, the FinOps Foundation has recently expanded its framework to include Scopes—and Datacenter is now officially part of the equation. In this session, we’ll map the FinOps Framework to a VMware-based datacenter, focusing on cost visibility, optimization, and automation. You’ll learn how to track costs more effectively, rightsize workloads, optimize licensing, and drive efficiency—all without migrating to the cloud. We’ll also explore how to align IT teams, finance, and leadership around cost-aware decision-making for on-prem environments. If your VMware bill keeps increasing and you need a new approach to cost management, this session is for you!

Tech-ASan: Two-stage check for Address Sanitizer - Yixuan Cao.pdfcaoyixuan2019

Coordinated Disclosure for ML - What's Different and What's the Same.pdfPriyanka Aash

9-1-1 Addressing: End-to-End Automation Using FMESafe Software

ReSTIR [DI]: Spatiotemporal reservoir resampling for real-time ray tracing ...revolcs10

"Scaling in space and time with Temporal", Andriy Lupa.pdfFwdays

CapCut Pro Crack For PC Latest Version {Fully Unlocked} 2025pcprocore

Connecting Data and Intelligence: The Role of FME in Machine LearningSafe Software

Raman Bhaumik - Passionate Tech EnthusiastRaman Bhaumik

OpenPOWER Foundation & Open-Source Core InnovationsIBM

A Constitutional Quagmire - Ethical Minefields of AI, Cyber, and Privacy.pdfPriyanka Aash

Security Tips for Enterprise Azure SolutionsMichele Leroux Bustamante

Oh, the Possibilities - Balancing Innovation and Risk with Generative AI.pdfPriyanka Aash

AI Agents and FME: A How-to Guide on Generating Synthetic MetadataSafe Software

"Database isolation: how we deal with hundreds of direct connections to the d...Fwdays

Cyber Defense Matrix Workshop - RSA ConferencePriyanka Aash

Mastering AI Workflows with FME by Mark DöringSafe Software

The Future of Product Management in AI ERA.pdfAlyona Owens

Daily Lesson Log MATATAG ICT TEchnology 8LOIDAALMAZAN3

Cracking the Code - Unveiling Synergies Between Open Source Security and AI.pdfPriyanka Aash

UserCon Belgium: Honey, VMware increased my billstijn40

Tech-ASan: Two-stage check for Address Sanitizer - Yixuan Cao.pdfcaoyixuan2019

Diffie hellman key algorithm

1. GANDHINAGAR INSTITUTE OF TECHNOLGY Department of Information Technology Diffie-Hellman Key Algorithm Group ID: IT_B1_00 Student Name(Enroll No): Shaishav Shah(170120116094) Name of Faculty: Prof. Alpa Oza INS(2170709)

2. Introduction • The Diffie-Hellman key agreement protocol was developed by Diffie and Hellman in 1976. • This protocol allows two users to exchange a secret key over an insecure medium without any prior secrets. • The protocol has two system parameters p and g. • They are both public and may be used by all users in a system. • Parameter p is a prime number and parameter g is an integer less than p, with the following property: – For every number n between 1 and p – 1 inclusive. – There is a power k of g such that n = 𝑔𝑘 𝑚𝑜𝑑 𝑝.

3. Introduction • The protocol depends on the discrete algorithm problem for its security. • It assumes that it is computationally infeasible to calculate the shared secret key 𝑘 = 𝑔𝑎𝑏 𝑚𝑜𝑑 𝑝 given the two public values 𝑔𝑎 𝑚𝑜𝑑 𝑝 and 𝑔𝑏 𝑚𝑜𝑑 𝑝 when the prime p is sufficiently large. • The Diffie – Hellman key exchange is vulnerable to a man-in-the- middle attack. • This vulnerability is present because Diffie-Hellman key exchange does not authenticate the participants. • Possible solutions include the use of digital signatures and other protocol variants.

4. Algorithm • Select two numbers: 1. Prime number 𝑞. 2. 𝛼 an integer that is a primitive root of 𝑞. • Suppose the users A and B wish to exchange a key. 1. User A select a random integer 𝑋𝐴 < 𝑞 and computes 𝑌 𝐴 = 𝛼𝑋𝐴 𝑚𝑜𝑑 𝑞. 2. User A select a random integer 𝑋𝐵 < 𝑞 and computes 𝑌𝐵 = 𝛼𝑋𝐵 𝑚𝑜𝑑 𝑞. 3. Both side keeps the X value private and makes the Y value available publicly to the other sides. 4. User A computes the key as 𝐾 = (𝑌𝐵)𝑋𝐴 𝑚𝑜𝑑 𝑞. 5. User B computes the key as 𝐾 = (𝑌𝐴)𝑋𝐵 𝑚𝑜𝑑 𝑞.

5. Algorithm • Both side gets same results: 𝐾 = (𝑌𝐵)𝑋𝐴 𝑚𝑜𝑑 𝑞 = (𝛼𝑋𝐵 𝑚𝑜𝑑 𝑞)𝑋𝐴 𝑚𝑜𝑑 𝑞 = (𝛼𝑋𝐵)𝑋𝐴 𝑚𝑜𝑑 𝑞 = 𝛼𝑋𝐵𝑋𝐴𝑚𝑜𝑑 𝑞 = (𝛼𝑋𝐴 𝑚𝑜𝑑 𝑞)𝑋𝐵 𝑚𝑜𝑑 𝑞 = (𝑌𝐴)𝑋𝐵 𝑚𝑜𝑑 𝑞

6. Example User A and User B use the Diffie-Hellman key exchange technique with a common prime 𝑞 = 17 and a primitive root 𝛼 = 7. a) If user A has private key 𝑋𝐴 = 5, what is A’s public key 𝑌 𝐴? b) If user B has private key 𝑋𝐵 = 12, what is B’s public key 𝑌𝐵? c) What is the shared secret key? Solution: a) A’s public key 𝒀𝑨 𝑌 𝐴 = 𝛼𝑋𝐴 𝑚𝑜𝑑 𝑞 = (7)5 𝑚𝑜𝑑 71 = 16807 mod 71 = 51 b) B’s public key 𝒀𝑩 𝑌𝐵 = 𝛼𝑋𝐵 𝑚𝑜𝑑 𝑞 = (7)12 𝑚𝑜𝑑 71 = 13841287201 mod 71 = 4 c) A’s public key 𝒀𝑨 𝐾 = (𝑌𝐵)𝑋𝐴 𝑚𝑜𝑑 𝑞 = (4)5 𝑚𝑜𝑑 71 = 1024 𝑚𝑜𝑑 71 = 30

7. Advantages 1. Any user can choose a random x and publish 𝑔𝑥 in a public database such as a phone book. 2. Phone book must be maintained by a TTP. 3. Other users can look up the database and get the public key for the individual and use it to encrypt the message. 4. Ideal for use with emails.

8. Disadvantages 1. Does not protect against man in middle attacks. 2. Even can intercept all traffic between Alice and Bob and generate separate keys for communication with them. 3. If Alice sends an encrypted message for Bob with his public key, Even simply forwards it. 4. For large prime 𝑝, 𝑝 − 1 is an even number and so 𝑍𝑝 ∗ will have an subgroup of order 2.

9. Thank You

Diffie hellman key algorithm

Recommended

More Related Content

What's hot (20)

Similar to Diffie hellman key algorithm (20)

More from ShaishavShah8 (19)

Recently uploaded (20)

Diffie hellman key algorithm