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RSA Algorithm

RSA (Rivest–Shamir–Adleman) is an algorithm used by modern computers to encrypt and decrypt messages. It is an asymmetric cryptographic algorithm.

Cryptography and Network Security William Stallings Lawrie Brown

Cryptography and Network Security William Stallings Lawrie BrownInformation Security Awareness Group

Block ciphers like DES encrypt data in blocks and are based on the Feistel cipher structure. DES encrypts 64-bit blocks using a 56-bit key and 16 rounds of encryption. Modern cryptanalysis techniques like differential and linear cryptanalysis use statistical analysis to reveal weaknesses in block ciphers, though DES remains relatively secure against these attacks. Careful design of block ciphers, including aspects like non-linear substitution boxes and complex key scheduling, aims to provide security against cryptanalysis.Design and Simulation Triple-DES

The document discusses the simulation of a Triple Data Encryption Standard (Triple DES) circuit using VHDL. It provides background on Triple DES, describes the design and structure of the Triple DES circuit in VHDL, and presents the results of testing the encryption and decryption functions of the circuit through simulation. Testing showed the circuit correctly performed encryption and decryption on input data using the Triple DES algorithm. The design utilized some FPGA resources but would require a clock generator and RAM for implementation on an actual FPGA board.

2. public key cryptography and RSA

Public Key Cryptography,Public-Key Cryptosystem,Rivest-Shamir-Adleman (RSA) Scheme,The Security of RSA,Optimal Asymmetric Encryption Padding (OAEP)

Principles of public key cryptography and its Uses

This document discusses the principles of public key cryptography. It begins by defining asymmetric encryption and how it uses a public key and private key instead of a single shared key. It then discusses key concepts like digital certificates and public key infrastructure. The document also provides examples of how public key cryptography can be used, including the RSA algorithm and key distribution methods like public key directories and certificates. It explains how public key cryptography solves the key distribution problem present in symmetric encryption.

Cryptography.ppt

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.

Diffie-hellman algorithm

The Diffie-Hellman algorithm was developed by Whitfield Diffie and Martin Hellman in 1976.
This algorithm was devices not to encrypt the data but to generate same private cryptographic key at both ends so that there is no need to transfer this key from one communication end to another.
Diffie – Hellman algorithm is an algorithm that allows two parties to get the shared secret key using the communication channel, which is not protected from the interception but is protected from modification.

Hash Function

This document discusses message authentication techniques including message encryption, message authentication codes (MACs), and hash functions. It describes how each technique can be used to authenticate messages and protect against various security threats. It also covers how symmetric and asymmetric encryption can provide authentication when used with MACs or digital signatures. Specific MAC and hash functions are examined like HMAC, SHA-1, and SHA-2. X.509 is introduced as a standard for digital certificates.

RSA Algorithm

RSA (Rivest–Shamir–Adleman) is an algorithm used by modern computers to encrypt and decrypt messages. It is an asymmetric cryptographic algorithm.

Cryptography and Network Security William Stallings Lawrie Brown

Cryptography and Network Security William Stallings Lawrie BrownInformation Security Awareness Group

Block ciphers like DES encrypt data in blocks and are based on the Feistel cipher structure. DES encrypts 64-bit blocks using a 56-bit key and 16 rounds of encryption. Modern cryptanalysis techniques like differential and linear cryptanalysis use statistical analysis to reveal weaknesses in block ciphers, though DES remains relatively secure against these attacks. Careful design of block ciphers, including aspects like non-linear substitution boxes and complex key scheduling, aims to provide security against cryptanalysis.Design and Simulation Triple-DES

The document discusses the simulation of a Triple Data Encryption Standard (Triple DES) circuit using VHDL. It provides background on Triple DES, describes the design and structure of the Triple DES circuit in VHDL, and presents the results of testing the encryption and decryption functions of the circuit through simulation. Testing showed the circuit correctly performed encryption and decryption on input data using the Triple DES algorithm. The design utilized some FPGA resources but would require a clock generator and RAM for implementation on an actual FPGA board.

2. public key cryptography and RSA

Public Key Cryptography,Public-Key Cryptosystem,Rivest-Shamir-Adleman (RSA) Scheme,The Security of RSA,Optimal Asymmetric Encryption Padding (OAEP)

Principles of public key cryptography and its Uses

This document discusses the principles of public key cryptography. It begins by defining asymmetric encryption and how it uses a public key and private key instead of a single shared key. It then discusses key concepts like digital certificates and public key infrastructure. The document also provides examples of how public key cryptography can be used, including the RSA algorithm and key distribution methods like public key directories and certificates. It explains how public key cryptography solves the key distribution problem present in symmetric encryption.

Cryptography.ppt

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.

Diffie-hellman algorithm

The Diffie-Hellman algorithm was developed by Whitfield Diffie and Martin Hellman in 1976.
This algorithm was devices not to encrypt the data but to generate same private cryptographic key at both ends so that there is no need to transfer this key from one communication end to another.
Diffie – Hellman algorithm is an algorithm that allows two parties to get the shared secret key using the communication channel, which is not protected from the interception but is protected from modification.

Hash Function

This document discusses message authentication techniques including message encryption, message authentication codes (MACs), and hash functions. It describes how each technique can be used to authenticate messages and protect against various security threats. It also covers how symmetric and asymmetric encryption can provide authentication when used with MACs or digital signatures. Specific MAC and hash functions are examined like HMAC, SHA-1, and SHA-2. X.509 is introduced as a standard for digital certificates.

RSA ALGORITHM

RSA is an asymmetric cryptographic algorithm used for encrypting and decrypting messages. It uses a public key for encryption and a private key for decryption such that a message encrypted with the public key can only be decrypted with the corresponding private key. The RSA algorithm involves three steps: key generation, encryption, and decryption. It addresses issues of key distribution and digital signatures.

RSA algorithm

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

Cryptography

Cryptography is the practice and study of securing communication through techniques like encryption. It has evolved through manual, mechanical, and modern eras using computers. Cryptography aims to achieve goals like authentication, confidentiality, integrity, and non-repudiation. Common attacks include brute force, chosen plaintext, and differential power analysis. Symmetric cryptography uses a shared key while asymmetric uses public/private key pairs. Digital signatures and watermarks can authenticate documents. DRM and watermarks control digital content distribution.

Hash Function

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.

Authentication Protocols

The document discusses authentication protocols and digital signatures. It describes mutual authentication protocols that allow two parties to verify each other's identities and exchange session keys. It also discusses one-way authentication protocols. The document focuses on explaining the Digital Signature Standard (DSS) and the Digital Signature Algorithm (DSA). It provides details on how DSA uses public/private key pairs to generate and verify digital signatures for authenticating messages and senders.

Pgp

This document discusses email security and the Pretty Good Privacy (PGP) encryption software. It describes why email security is important given threats like loss of confidentiality and integrity. It then provides details on PGP, including how it uses public/private key encryption and digital signatures to encrypt messages and authenticate senders. PGP uses symmetric encryption of messages and asymmetric encryption of session keys, storing keys in a local ring. The document discusses PGP key management and its use of a web of trust model without a central authority.

Public Key Cryptography

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

CS6701 CRYPTOGRAPHY AND NETWORK SECURITY

E-MAIL, IP & WEB SECURITY
E-mail Security: Security Services for E-mail-attacks possible through E-mail – establishing keys privacy-authentication of the source-Message Integrity-Non-repudiation-Pretty Good Privacy-S/MIME. IPSecurity: Overview of IPSec – IP and IPv6-Authentication Header-Encapsulation Security Payload (ESP)-Internet Key Exchange (Phases of IKE, ISAKMP/IKE Encoding). Web Security:

MAC-Message Authentication Codes

Brief Presentation about message authentication codes and HMAC with requirements, functions and security issues in cryptography

Data Encryption Standard (DES)

- DES (Data Encryption Standard) is a symmetric block cipher algorithm that encrypts data in 64-bit blocks using a 56-bit key. It was the first encryption standard adopted by the U.S. government for protecting sensitive unclassified federal government information.
- DES works by performing 16 rounds of complex substitutions and permutations on each data block, encrypting it using the key. It has various modes of operation like ECB, CBC, CFB, OFB, and CTR that specify how it operates on data.
- In 1998, DES was broken using a brute force attack by the Electronic Frontier Foundation in just 3 days, showing the need for stronger algorithms like AES which replaced DES as the encryption standard

Cryptography.ppt

This document provides an overview of cryptography. It defines cryptography as the science of securing messages from attacks. It discusses basic cryptography terms like plain text, cipher text, encryption, decryption, and keys. It describes symmetric key cryptography, where the same key is used for encryption and decryption, and asymmetric key cryptography, which uses different public and private keys. It also covers traditional cipher techniques like substitution and transposition ciphers. The document concludes by listing some applications of cryptography like e-commerce, secure data, and access control.

Symmetric & Asymmetric Cryptography

This document summarizes symmetric and asymmetric cryptography. Symmetric cryptography involves both parties agreeing on an encryption algorithm and key beforehand to encrypt and decrypt messages. Asymmetric cryptography uses public and private key pairs, where the public key encrypts messages and the private key decrypts them, allowing encryption without pre-sharing keys. It also discusses digital signatures, where messages are signed with a private key and verified with the corresponding public key. Common attacks on public-key cryptography like man-in-the-middle attacks are addressed. The document is intended for a computer science course on cryptography fundamentals and security mechanisms.

Network Security and Cryptography

A brief discussion of network security and an introduction to cryptography. We end the presentation with a discussion of the RSA algorithm, and show how it works with a basic example.

Message digest 5

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.

CRYPTOGRAPHY & NETWORK SECURITY- Cryptographic Hash Functions

CRYPTOGRAPHY & NETWORK SECURITY- Cryptographic Hash FunctionsJyothishmathi Institute of Technology and Science Karimnagar

Cryptographic Hash Functions: Message Authentication, Secure Hash Algorithm (SHA-512), Message authentication codes: Authentication requirements, HMAC, CMAC, Digital signatures, Elgamal Digital Signature Scheme. Key Management and Distribution: Symmetric Key Distribution Using Symmetric & Asymmetric Encryption, Distribution of Public Keys, Kerberos, X.509 Authentication Service, Public – Key Infrastructure symmetric key encryption algorithms

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.

Message authentication and hash function

The document discusses message authentication and hash functions. It covers security requirements including integrity, authentication and non-repudiation. It describes different authentication functions such as message encryption, message authentication codes (MACs), and hash functions. It provides examples of how hash functions work and evaluates the security of hash functions and MACs against brute force and cryptanalytic attacks.

Rsa

traditional private/secret/single key cryptography uses one key
Key is shared by both sender and receiver
if the key is disclosed communications are compromised
also known as symmetric, both parties are equal
hence does not protect sender from receiver forging a message & claiming is sent by sender

RSA ALGORITHM

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.

One Time Pad Encryption Technique

The document describes the one-time pad cipher, which is considered theoretically unbreakable. It works by combining a plaintext message with a randomly generated key that is at least as long as the message. Each character of the key is combined with the corresponding character of the message using modular arithmetic. The key is then destroyed after use, and both the sender and receiver must have identical copies of the key to encrypt and decrypt messages. It provides perfect secrecy because an attacker with infinite computing power could not determine the original plaintext without the key.

Public Key Cryptography and RSA algorithm

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.

Digital Signature Recognition using RSA Algorithm

The document provides an overview of the RSA public key encryption algorithm. It discusses how RSA uses a public key and private key pair, with the public key used to encrypt messages and the private key used to decrypt them. The security of RSA relies on the difficulty of factoring the product of two large prime numbers. The document outlines the RSA algorithm steps of key generation, encryption, and decryption. It also discusses RSA applications, standardization, speed, weaknesses, and history.

RSA ALGORITHM

RSA is an asymmetric cryptographic algorithm used for encrypting and decrypting messages. It uses a public key for encryption and a private key for decryption such that a message encrypted with the public key can only be decrypted with the corresponding private key. The RSA algorithm involves three steps: key generation, encryption, and decryption. It addresses issues of key distribution and digital signatures.

RSA algorithm

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

Cryptography

Cryptography is the practice and study of securing communication through techniques like encryption. It has evolved through manual, mechanical, and modern eras using computers. Cryptography aims to achieve goals like authentication, confidentiality, integrity, and non-repudiation. Common attacks include brute force, chosen plaintext, and differential power analysis. Symmetric cryptography uses a shared key while asymmetric uses public/private key pairs. Digital signatures and watermarks can authenticate documents. DRM and watermarks control digital content distribution.

Hash Function

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.

Authentication Protocols

The document discusses authentication protocols and digital signatures. It describes mutual authentication protocols that allow two parties to verify each other's identities and exchange session keys. It also discusses one-way authentication protocols. The document focuses on explaining the Digital Signature Standard (DSS) and the Digital Signature Algorithm (DSA). It provides details on how DSA uses public/private key pairs to generate and verify digital signatures for authenticating messages and senders.

Pgp

This document discusses email security and the Pretty Good Privacy (PGP) encryption software. It describes why email security is important given threats like loss of confidentiality and integrity. It then provides details on PGP, including how it uses public/private key encryption and digital signatures to encrypt messages and authenticate senders. PGP uses symmetric encryption of messages and asymmetric encryption of session keys, storing keys in a local ring. The document discusses PGP key management and its use of a web of trust model without a central authority.

Public Key Cryptography

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

CS6701 CRYPTOGRAPHY AND NETWORK SECURITY

E-MAIL, IP & WEB SECURITY
E-mail Security: Security Services for E-mail-attacks possible through E-mail – establishing keys privacy-authentication of the source-Message Integrity-Non-repudiation-Pretty Good Privacy-S/MIME. IPSecurity: Overview of IPSec – IP and IPv6-Authentication Header-Encapsulation Security Payload (ESP)-Internet Key Exchange (Phases of IKE, ISAKMP/IKE Encoding). Web Security:

MAC-Message Authentication Codes

Brief Presentation about message authentication codes and HMAC with requirements, functions and security issues in cryptography

Data Encryption Standard (DES)

- DES (Data Encryption Standard) is a symmetric block cipher algorithm that encrypts data in 64-bit blocks using a 56-bit key. It was the first encryption standard adopted by the U.S. government for protecting sensitive unclassified federal government information.
- DES works by performing 16 rounds of complex substitutions and permutations on each data block, encrypting it using the key. It has various modes of operation like ECB, CBC, CFB, OFB, and CTR that specify how it operates on data.
- In 1998, DES was broken using a brute force attack by the Electronic Frontier Foundation in just 3 days, showing the need for stronger algorithms like AES which replaced DES as the encryption standard

Cryptography.ppt

This document provides an overview of cryptography. It defines cryptography as the science of securing messages from attacks. It discusses basic cryptography terms like plain text, cipher text, encryption, decryption, and keys. It describes symmetric key cryptography, where the same key is used for encryption and decryption, and asymmetric key cryptography, which uses different public and private keys. It also covers traditional cipher techniques like substitution and transposition ciphers. The document concludes by listing some applications of cryptography like e-commerce, secure data, and access control.

Symmetric & Asymmetric Cryptography

This document summarizes symmetric and asymmetric cryptography. Symmetric cryptography involves both parties agreeing on an encryption algorithm and key beforehand to encrypt and decrypt messages. Asymmetric cryptography uses public and private key pairs, where the public key encrypts messages and the private key decrypts them, allowing encryption without pre-sharing keys. It also discusses digital signatures, where messages are signed with a private key and verified with the corresponding public key. Common attacks on public-key cryptography like man-in-the-middle attacks are addressed. The document is intended for a computer science course on cryptography fundamentals and security mechanisms.

Network Security and Cryptography

A brief discussion of network security and an introduction to cryptography. We end the presentation with a discussion of the RSA algorithm, and show how it works with a basic example.

Message digest 5

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.

CRYPTOGRAPHY & NETWORK SECURITY- Cryptographic Hash Functions

CRYPTOGRAPHY & NETWORK SECURITY- Cryptographic Hash FunctionsJyothishmathi Institute of Technology and Science Karimnagar

Cryptographic Hash Functions: Message Authentication, Secure Hash Algorithm (SHA-512), Message authentication codes: Authentication requirements, HMAC, CMAC, Digital signatures, Elgamal Digital Signature Scheme. Key Management and Distribution: Symmetric Key Distribution Using Symmetric & Asymmetric Encryption, Distribution of Public Keys, Kerberos, X.509 Authentication Service, Public – Key Infrastructure symmetric key encryption algorithms

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.

Message authentication and hash function

The document discusses message authentication and hash functions. It covers security requirements including integrity, authentication and non-repudiation. It describes different authentication functions such as message encryption, message authentication codes (MACs), and hash functions. It provides examples of how hash functions work and evaluates the security of hash functions and MACs against brute force and cryptanalytic attacks.

Rsa

traditional private/secret/single key cryptography uses one key
Key is shared by both sender and receiver
if the key is disclosed communications are compromised
also known as symmetric, both parties are equal
hence does not protect sender from receiver forging a message & claiming is sent by sender

RSA ALGORITHM

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.

One Time Pad Encryption Technique

The document describes the one-time pad cipher, which is considered theoretically unbreakable. It works by combining a plaintext message with a randomly generated key that is at least as long as the message. Each character of the key is combined with the corresponding character of the message using modular arithmetic. The key is then destroyed after use, and both the sender and receiver must have identical copies of the key to encrypt and decrypt messages. It provides perfect secrecy because an attacker with infinite computing power could not determine the original plaintext without the key.

RSA ALGORITHM

RSA ALGORITHM

RSA algorithm

RSA algorithm

Cryptography

Cryptography

Hash Function

Hash Function

Authentication Protocols

Authentication Protocols

Pgp

Pgp

Public Key Cryptography

Public Key Cryptography

CS6701 CRYPTOGRAPHY AND NETWORK SECURITY

CS6701 CRYPTOGRAPHY AND NETWORK SECURITY

MAC-Message Authentication Codes

MAC-Message Authentication Codes

Data Encryption Standard (DES)

Data Encryption Standard (DES)

Cryptography.ppt

Cryptography.ppt

Symmetric & Asymmetric Cryptography

Symmetric & Asymmetric Cryptography

Network Security and Cryptography

Network Security and Cryptography

Message digest 5

Message digest 5

CRYPTOGRAPHY & NETWORK SECURITY- Cryptographic Hash Functions

CRYPTOGRAPHY & NETWORK SECURITY- Cryptographic Hash Functions

symmetric key encryption algorithms

symmetric key encryption algorithms

Message authentication and hash function

Message authentication and hash function

Rsa

Rsa

RSA ALGORITHM

RSA ALGORITHM

One Time Pad Encryption Technique

One Time Pad Encryption Technique

Public Key Cryptography and RSA algorithm

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.

Digital Signature Recognition using RSA Algorithm

The document provides an overview of the RSA public key encryption algorithm. It discusses how RSA uses a public key and private key pair, with the public key used to encrypt messages and the private key used to decrypt them. The security of RSA relies on the difficulty of factoring the product of two large prime numbers. The document outlines the RSA algorithm steps of key generation, encryption, and decryption. It also discusses RSA applications, standardization, speed, weaknesses, and history.

Rsa Algorithm

The RSA algorithm document describes the steps to generate a public/private key pair for encryption and decryption. It involves selecting two large prime numbers p and q, computing n as their product, and using n along with the prime factors to calculate the private key exponent d that corresponds to the public key exponent e, such that ed = 1 mod φ(n). The example demonstrates computing the values for a specific case where p=3 and q=11.
The Diffie-Hellman key exchange document describes a protocol where Alice and Bob can establish a shared secret key over an insecure channel. It involves Alice generating a public value gx mod p and Bob generating a public value gy mod p, then each uses the other

Public key cryptography and RSA

1. The document discusses public-key cryptography and some of its key concepts like asymmetric encryption where each user has a public and private key.
2. It also covers applications like encryption, digital signatures, and key exchange. It notes that while public-key crypto has advantages, symmetric crypto is still important due to public-key crypto's lower speed.
3. The RSA algorithm is presented as one of the first implementations of public-key cryptography based on the difficulty of factoring large integers.

The rsa algorithm

This document provides an overview of the RSA algorithm for public-key cryptography. It explains that RSA uses a public key and private key pair, with the public key used for encryption and the private key used for decryption. The security of RSA relies on the difficulty of factoring large prime numbers. It then provides details on how the RSA algorithm works, including choosing two large prime numbers to generate keys, encrypting and decrypting messages, and an example calculation. Potential attacks on RSA like brute force key searching and timing analysis are also summarized.

Idea(international data encryption algorithm)

The document discusses the International Data Encryption Algorithm (IDEA). It was developed in 1990 as a replacement for the Data Encryption Standard. IDEA is a symmetric block cipher that uses a 128-bit key to encrypt 64-bit blocks of plaintext into ciphertext. The key is divided into 52 subkeys that are used in 8 rounds of encryption/decryption operations involving XOR, addition, and multiplication. IDEA was used in PGP v2.0 and can encrypt sensitive data for applications like financial services, broadcasting, and government use.

RSA Algorithm

The document describes the RSA algorithm for public-key cryptography. It begins with an introduction and overview of the algorithm, which involves choosing two prime numbers to generate a public key and private key. It then discusses how the algorithm is used to encrypt and decrypt messages. Examples are provided to illustrate the key generation and encryption/decryption processes. Usage areas like communication, banking, signatures, and certificates are also covered at a high level.

Digital Signature

The document discusses different types of digital signatures, including direct digital signatures and arbitrated digital signatures. A direct digital signature only involves a sender and receiver, while an arbitrated digital signature includes a third party arbiter to verify the signature before the recipient receives the message. The advantages of digital signatures are authentication and verification between sender and recipient, while disadvantages include relying on the sender owning their public key and potential delays in signature generation and verification.

Rsa Crptosystem

This ppt contains description about data and information,cryptography and how information can be protected using RSA cryptosystem.

RSA - ENCRYPTION ALGORITHM CRYPTOGRAPHY

This document discusses public key cryptography and the RSA encryption algorithm. It provides an overview of public key cryptography, how the RSA algorithm works using a public and private key pair, and some of its applications. The RSA algorithm is based on the difficulty of factoring large prime numbers and allows for secure communication without needing to share secret keys. Some advantages are convenience and enabling message authentication and non-repudiation using digital signatures, while disadvantages include slower performance and the need to authenticate public keys.

RSA криптосистем

The RSA cryptosystem is the most widely used public key cryptosystem. It uses a "trapdoor" one-way function to encrypt and decrypt messages. While textbook RSA is insecure, common implementations prepend random padding like OAEP to the message before encryption, which provides chosen ciphertext security. Despite its widespread use, RSA remains computationally intensive due to the need for large key sizes for security equivalents to modern block ciphers. Timing and fault attacks remain a concern if proper countermeasures are not implemented.

Cryptography using rsa cryptosystem

The presentation explains basis of cryptography using RSA cryptosystem.
The whole mathematics behind the algorithm has been explained.

One-Time Pad Encryption

One-Time Pad (OTP) encryption uses truly random keys that are only used once to encrypt plaintext. If the keys are random, only used once, and securely transferred and destroyed, then OTP provides perfect secrecy since the ciphertext reveals no information about the plaintext. However, achieving these strict conditions is difficult in practice, requiring solutions for secure key generation, transfer, storage and destruction. While OTP provides unbreakable encryption theoretically, more practical algorithms are needed to address its limitations.

Public key cryptography

The document discusses public key cryptography, digital certificates, and Transport Layer Security (TLS). It provides an overview of symmetric and asymmetric key cryptography, algorithms like RSA and ElGamal, the use of digital signatures and certificates, and how TLS uses public key encryption to securely transmit data over the internet, such as for email.

Cryptography

The document provides an overview of cryptography concepts including secrecy ciphers, secret key cryptography, public key cryptography, digital signatures, and their applications to internet security. It discusses how early ciphers like Caesar cipher could be broken through frequency analysis but were made more secure through techniques like modular exponentiation. It introduces key concepts like Diffie-Hellman key exchange that allow parties to establish a shared secret key over insecure channels and digital signatures to authenticate messages and identities. It also discusses how certification authorities help validate public keys on the internet.

Rsa encryption

The document discusses the RSA encryption algorithm and provides a mathematical background on topics related to RSA. It begins with an abstract and index, then covers notation, definitions, big-O notation, binary operations and their time complexities, linear congruences, relatively prime numbers, Euler's totient function, and the Miller-Rabin primality test. It analyzes the RSA algorithm, provides an example, and presents Python code to implement RSA encryption.

IDRBT Project: Application Development in Java for public key cryptography

The document describes two projects completed as an intern at IDRBT. Project 1 involves building a desktop application using Java and OpenSSL libraries that allows users to perform public key cryptography tasks through a graphical user interface. It discusses functionality like key generation, encryption, signatures and certificates. Project 2 involves deploying the OX AppSuite over IDRBT's intranet and exploring its potential deployment over cloud systems. It provides installation instructions and highlights challenges of moving applications to the cloud.

Kerberos using public key cryptography

This document discusses adding public key cryptography to Kerberos to address limitations. It introduces three extensions: PKINIT for initial authentication using public keys; PKCROSS for cross-realm authentication using public keys between KDCs; and PKTAPP for authenticating to application servers using public keys. It analyzes performance and security issues when using these extensions and concludes they can improve Kerberos scalability in large networks.

ContikiMAC : Radio Duty Cycling Protocol

ContikiMAC is a radio duty cycling protocol that uses periodic wake-ups to listen for packet transmissions from neighbors. It keeps the radio on only when needed to receive packets, sending acknowledgments and retransmitting packets as necessary. The timing of transmissions and wake-ups is precise to enable efficient communication while minimizing energy usage. Phase awareness allows senders to transmit packets just before expected receiver wake-ups. ContikiMAC is implemented using real-time timers in Contiki to ensure stable and accurate timing.

Cryptography - key sharing - RSA

This document discusses public key cryptography and the RSA algorithm. It explains that prime numbers are divisible only by 1 and themselves, and any other number can be factored into prime numbers. The discrete logarithm problem involves finding the exponent given the result. RSA uses public and private keys based on prime numbers to encrypt and decrypt messages securely, even when the keys are shared publicly. The private key is based on the totient function and modular inverse to decrypt the ciphertext into plaintext.

Public Key Cryptography and RSA algorithm

Public Key Cryptography and RSA algorithm

Digital Signature Recognition using RSA Algorithm

Digital Signature Recognition using RSA Algorithm

Rsa Algorithm

Rsa Algorithm

Public key cryptography and RSA

Public key cryptography and RSA

The rsa algorithm

The rsa algorithm

Idea(international data encryption algorithm)

Idea(international data encryption algorithm)

RSA Algorithm

RSA Algorithm

Digital Signature

Digital Signature

Rsa Crptosystem

Rsa Crptosystem

RSA - ENCRYPTION ALGORITHM CRYPTOGRAPHY

RSA - ENCRYPTION ALGORITHM CRYPTOGRAPHY

RSA криптосистем

RSA криптосистем

Cryptography using rsa cryptosystem

Cryptography using rsa cryptosystem

One-Time Pad Encryption

One-Time Pad Encryption

Public key cryptography

Public key cryptography

Cryptography

Cryptography

Rsa encryption

Rsa encryption

IDRBT Project: Application Development in Java for public key cryptography

IDRBT Project: Application Development in Java for public key cryptography

Kerberos using public key cryptography

Kerberos using public key cryptography

ContikiMAC : Radio Duty Cycling Protocol

ContikiMAC : Radio Duty Cycling Protocol

Cryptography - key sharing - RSA

Cryptography - key sharing - RSA

3 public key cryptography

Public key cryptography uses asymmetric encryption with two related keys - a public key and a private key. The public key can be shared openly but the private key is kept secret. When Alice wants to send a confidential message to Bob, she encrypts it with Bob's public key. Only Bob can decrypt it using his private key. Public key infrastructure involves policies and technologies for issuing, managing, and revoking digital certificates that bind public keys to identities. Popular public key algorithms like RSA are based on the difficulty of factoring large prime numbers.

Pooguzhali

This document discusses public key cryptography and the RSA algorithm. It provides explanations of public key encryption including its key components like plaintext, encryption algorithm, public and private keys, and decryption algorithm. It then describes the conventional encryption method versus public key encryption. Finally, it explains the RSA algorithm in detail, including how it generates key pairs, how encryption and decryption works using the keys, and some of the mathematical concepts that make RSA secure like the difficulty of factoring large numbers.

Unit --3.ppt

Public-key cryptography uses two keys: a public key to encrypt messages and verify signatures, and a private key for decryption and signing. RSA is the most widely used public-key cryptosystem, using large prime factorization and exponentiation modulo n for encryption and decryption. While faster than brute-force, breaking RSA remains computationally infeasible with sufficiently large key sizes over 1024 bits.

RSA 32-bit Implementation Technique

Encryption is a technique that transforms a code from an understandable into an incomprehensible code. Many methods can be applied to an encryption process. One such method is RSA. RSA works by appointing on byte values. The value is obtained from character conversion to ASCII code. This algorithm is based on the multiplication of two relatively large primes. Applications of the RSA algorithm can be used in data security. This research provides RSA algorithm application on data security system that can guarantee data confidentiality. RSA algorithm is known as a very secure algorithm. This algorithm works with the number of bits in the search for prime numbers. The larger the bits, the less chance of ciphertext can be solved. The weakness of this method is the amount of ciphertext capacity will be floating in line with the number of prime numbers used. Also, to perform the process of encryption and decryption, RSA requires a relatively long time than other algorithms. The advantage of RSA is that complicated ciphertext is solved into plaintext.

ch09_rsa_nemo.ppt

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.

Public key algorithm

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.

RSA Algorithem and information about rsa

RSA was developed in 1977 by Ron Rivest, Adi Shamir and Leonard Adleman. It uses public and private key pairs to encrypt and decrypt messages. The security of RSA relies on the difficulty of factoring large prime numbers. It is commonly used for encryption and digital signatures in applications like SSL/TLS and SSH.

PUBLIC KEY & RSA.ppt

Public key cryptography uses two keys - a public key that can be shared openly and a private key that is kept secret. The RSA algorithm, invented in 1977, is the most widely used public key cryptosystem. It uses a public and private key pair generated from two large prime numbers. The public key is used to encrypt messages, while the private key is used to decrypt messages. The security of RSA relies on the difficulty of factoring the product of the two primes.

Rsa

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.

Unit 3(1)

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.

Ch9

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.

18CS2005 Cryptography and Network Security

Module 2: Public Key Cryptography Principles of public key cryptosystems-RSA algorithm-Diffie- Hellman Key Exchange-ElGamal Cryptosystem- Elliptic Curve Cryptography

Introduction to cryptography

Bob and Alice want to securely communicate messages between each other over an insecure channel. Cryptography allows them to encrypt messages using public key encryption so that only the intended recipient can decrypt it. The document discusses the basics of public key cryptography including how it works, the RSA algorithm, key generation process, and approaches to attacking public key cryptography like brute force attacks or mathematical attacks like integer factorization to derive the private key.

Cryptography based chat system

crypography based chat system is a secured chat system based on RSA algorithm. secure our information from various attacks.

Network security

Network security involves securing computer networks and systems. It is handled by network administrators who implement security policies, software, and hardware to protect networks from unauthorized access, misuse, or denial of resources. Network security aims to authenticate users, control access to resources, and ensure confidentiality, integrity, non-repudiation and availability of networks and resources. Common methods include authentication, access control, encryption, digital signatures, and monitoring systems for security audits.

RSA Algm.pptx

Public key cryptography uses two keys - a public key for encryption and a private key for decryption. The RSA algorithm is a widely used public key cryptosystem that is based on the difficulty of factoring large prime numbers. It uses a public key for encryption and a related private key for decryption. The security of RSA relies on the fact that it is computationally infeasible to determine the private key from the public key for sufficiently large key sizes.

Cryptography & Security

The document discusses the RSA algorithm and its implementation in SSL-VPN architectures. It begins by introducing SSL-VPN and how it uses the RSA algorithm. It then provides a high-level overview of the mathematical concepts behind the RSA algorithm, including generating public and private key pairs using large prime numbers. It also describes how the RSA algorithm is used for encryption and decryption in SSL-VPN systems to securely transmit encrypted data between private networks over the internet.

Email Encryption using Tri-Cryptosystem Based on Android

The document proposes a tri-cryptosystem for securing email on Android devices using a combination of symmetric, asymmetric, and hash cryptography. Specifically, it uses the PingPong-128 symmetric stream cipher to encrypt messages, RSA for key exchange, and MD5 hashing to verify message integrity. This approach aims to address the weaknesses of single cryptosystem approaches by leveraging the speed of symmetric encryption and security of asymmetric techniques. The tri-cryptosystem encrypts a randomly generated symmetric key with the recipient's public RSA key. This encrypted key and the symmetric encrypted message are then sent to the recipient who can decrypt the key and message to obtain the plaintext.

Vtu network security(10 ec832) unit 3 notes.

UNIT - 3
Principles of Public-Key Cryptosystems, The RSA algorithm, Key Management, Diffie - Hellman Key Exchange, Elliptic Curve Arithmetic, and Authentication functions, Hash Functions.

Unit-III_3R-CRYPTO_2021-22_VSM.pptx

This document discusses public-key cryptography and digital signatures. It begins with an introduction to symmetric and asymmetric key cryptography, including the basic concepts and differences between the two approaches. It then provides more details on public-key cryptography principles, including how public/private key pairs are generated and used. The document explains the RSA algorithm for public-key encryption and decryption in detail with examples. It also covers digital signature models and how they provide message authentication, integrity, and non-repudiation using public-key techniques. Diffie-Hellman key exchange is introduced as a method for securely transmitting a symmetric secret key between two parties.

3 public key cryptography

3 public key cryptography

Pooguzhali

Pooguzhali

Unit --3.ppt

Unit --3.ppt

RSA 32-bit Implementation Technique

RSA 32-bit Implementation Technique

ch09_rsa_nemo.ppt

ch09_rsa_nemo.ppt

Public key algorithm

Public key algorithm

RSA Algorithem and information about rsa

RSA Algorithem and information about rsa

PUBLIC KEY & RSA.ppt

PUBLIC KEY & RSA.ppt

Rsa

Rsa

Unit 3(1)

Unit 3(1)

Ch9

Ch9

18CS2005 Cryptography and Network Security

18CS2005 Cryptography and Network Security

Introduction to cryptography

Introduction to cryptography

Cryptography based chat system

Cryptography based chat system

Network security

Network security

RSA Algm.pptx

RSA Algm.pptx

Cryptography & Security

Cryptography & Security

Email Encryption using Tri-Cryptosystem Based on Android

Email Encryption using Tri-Cryptosystem Based on Android

Vtu network security(10 ec832) unit 3 notes.

Vtu network security(10 ec832) unit 3 notes.

Unit-III_3R-CRYPTO_2021-22_VSM.pptx

Unit-III_3R-CRYPTO_2021-22_VSM.pptx

Robotic surgery

Robotic surgery uses robotic systems to assist surgeons in performing minimally invasive surgery. The robotic systems allow for enhanced visualization, improved dexterity and precision, and smaller incisions compared to traditional open surgery. Some key benefits of robotic surgery for patients include less pain, shorter hospital stays, smaller scars, and faster recovery times. Common applications of robotic surgery include procedures in areas like cardiology, urology, gynecology, and orthopedics. While robotic surgery provides advantages, it also faces challenges like high costs and potential mechanical and software issues.

Augmented Reality - 8th Mass Media

Augmented reality (AR) enhances real-world environments by adding digital elements like information, images, and sounds. AR systems combine real and virtual objects, aligning them in real-time and allowing interaction. AR is enabled by head-mounted displays, tracking systems, and mobile computing power. Current applications of AR include translation, tourism, education, and navigation. While AR offers benefits like enhancing daily life, limitations include privacy concerns and challenges in accurate tracking, orientation, and sufficient computing power in wearable devices.

Environmenal degradation

The document discusses environmental degradation and its causes and effects. It states that environmental degradation is one of the greatest threats facing the world today as it endangers ecosystems and human existence. Factors that contribute to environmental degradation include urbanization, population growth, intensive agriculture, increased energy and transportation, which damage air, water, and soil quality. As a result of degradation, the planet is facing problems like global warming, water scarcity, and climate change, which threaten global sustainability.

Environmental Degradation PPT

Presentation on Environmental Degradation
Its causes and effects on the environment
Awareness of environmental Degradation
Preventive Measures for environmental degradation

Augmented Reality pdf

This document discusses augmented reality (AR) and its applications. It begins with an abstract that defines AR as a technology that augments the real world with computer-generated sensory input. It then covers how AR works, the differences between AR and virtual reality, components of an AR system like head-mounted displays and tracking systems, and recent advances in AR technologies like Google Glass. Finally, it discusses several applications of AR in fields like medicine, archaeology, tourism, translation, navigation, industrial design, the military, and education.

Robotic Surgery by muthugomathy and meenakshi shetti.

Here is the very animatedly designed Presentation that explains briefly about Robotic Surgery , Uses of Robobic Surgery, Robotic Surgery Advantages and Disadvantages and about its future scope.

Robotic surgery

Robotic surgery

Augmented Reality - 8th Mass Media

Augmented Reality - 8th Mass Media

Environmenal degradation

Environmenal degradation

Environmental Degradation PPT

Environmental Degradation PPT

Augmented Reality pdf

Augmented Reality pdf

Robotic Surgery by muthugomathy and meenakshi shetti.

Robotic Surgery by muthugomathy and meenakshi shetti.

Contiguity Of Various Message Forms - Rupam Chandra.pptx

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(A Free eBook comprising 3 Sets of Presentation of a selection of Puzzles, Brain Teasers and Thinking Problems to exercise both the mind and the Right and Left Brain. To help keep the mind and brain fit and healthy. Good for both the young and old alike.
Answers are given for all the puzzles and problems.)
With Metta,
Bro. Oh Teik Bin 🙏🤓🤔🥰

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In this webinar, member learned how to stay in compliance with generally accepted accounting principles (GAAP) for restricted grants.

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إضغ بين إيديكم من أقوى الملازم التي صممتها
ملزمة تشريح الجهاز الهيكلي (نظري 3)
💀💀💀💀💀💀💀💀💀💀
تتميز هذهِ الملزمة بعِدة مُميزات :
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2- تحتوي على 78 رسم توضيحي لكل كلمة موجودة بالملزمة (لكل كلمة !!!!)
#فهم_ماكو_درخ
3- دقة الكتابة والصور عالية جداً جداً جداً
4- هُنالك بعض المعلومات تم توضيحها بشكل تفصيلي جداً (تُعتبر لدى الطالب أو الطالبة بإنها معلومات مُبهمة ومع ذلك تم توضيح هذهِ المعلومات المُبهمة بشكل تفصيلي جداً
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6- تحتوي الملزمة في اول سلايد على خارطة تتضمن جميع تفرُعات معلومات الجهاز الهيكلي المذكورة في هذهِ الملزمة
واخيراً هذهِ الملزمة حلالٌ عليكم وإتمنى منكم إن تدعولي بالخير والصحة والعافية فقط
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INDIA`S OWN LITERARY GENIUS MR.KHUSHWANT SINGH WAS TRULY A VERY BRAVE SOUL AND WAS AWARDED WITH THE MAGIC OF WORDS BY GOD.

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- 1. PUBLIC KEY CRYPTOGRAPHY RSA ENCRYPTION ALGORITHM Meenakshi Shetti Muthu Gomahty V
- 2. CONTENTS • CRYPTOGRAPHY • WHAT IS A KEY ? • PRIVATE KEY CRYPTOGRAPHY • PUBLIC KEY CRYPTOGRAPHY • RSA ALGORITHM • ADVANTAGES • DISADVANTAGES • REFERENCES
- 3. CRYPTOGRAPHY •It’s a greek word which means hidden secret in writing •Cryptography is the practice and study of techniques for secure communication in the presence of third parties(called adversaries).
- 4. What is a “key”? A key is a piece of information (a parameter) that determines the functional output of a cryptographic algorithm or cipher.
- 5. PRIVATE KEY CRYPTOGRAPHY • Also called as Symmetric-key algorithms • They are a class of algorithms for cryptography that use the same cryptographic keys for both encryption of plaintext and decryption of ciphertext.
- 6. Public key cryptography • Also known as asymmetric cryptography • Refers to a cryptographic algorithm which requires two separate keys, one of which is secret (or private) and one of which is public.
- 7. Non secret ENCRYTION USING LOCK ALICE BOB
- 10. TRAP DOOR –ONE WAY FUNCTION EASY HARD
- 11. EXPONENET REMAINDER 12345 mod 17 ≡ 135903 346 mod 12 ≡10 BASE MODULUS
- 12. memod N ≡ c
- 13. EASY memod N ≡ c HARD ?emod N ≡ c
- 14. memod N ≡ c emod N- public key C -remainder m- message
- 15. me mod N ≡ c cd mod N ≡ m medmod N ≡ m e- encryption d - decryption
- 16. For computation of e and d STEP 1 -> PRIME FACTORIZATION STEP 2 -> PHI FUNCTION STEP 3-> EULER’S THEOREM
- 17. Multiplication of two extra large numbers are easy to compute. But prime factorization of a number is the hardness of the problem . Prime factorization is what used to build the trap door
- 18. STEP 1 -> PRIME FACTORIZATION P1 – 150 digits long P2 – 150 digits long P1 * P2 = N N- 300 digits long
- 19. STEP 2 -> PHI FUNCTION - breakability of a number Given a number N – it output’s how many integers are less than or equal to N that do not share a common factor with N ɸ[8] = 1 2 3 4 5 6 7 8 ɸ[8] = 1 2 3 4 5 6 7 8 We want to find ɸ[8] , we look at all integers from 1 to 8 , then we count how many integers does not share a factor greater than 1 ɸ[8] = 4
- 20. • In the case of ɸ of a prime number – As prime numbers does not share common factor of any number greater than ɸ[P]=P-1 i.e, ɸ[7] = 1 2 3 4 5 6 7 As none of them share a common factor with 7 ɸ[7] = 7-1 ɸ[7] = 6
- 21. ɸ[N] is also multiplicative ɸ[A*B] = ɸ[A] * ɸ[B] = (A-1) * (B-1) ɸ[N] = ɸ[P1] * ɸ[P2] ɸ[N] = (P1-1) * (P2-1) 77=7*11 ɸ[7] = ɸ[7] * ɸ[11] ɸ[7] = (7-1) * (11-1) = 6 * 10 =60
- 22. STEP 3-> EULER’S THEOREM - Relation between the phi function and modular exponentiation mɸ[N]= 1 mod N Pick 2 numbers that do not share a common factor m=5, n=8 5ɸ[8]= 1 mod 8 54= 1 mod 8 625=1 mod 8
- 23. Modify this equation using 2 simple rules 1) 1k=1 mk*ɸ[N]= 1 mod N We multiply eponent ɸ[N] by any number k, the solution is still 1 2) 1*m=m m*mk*ɸ[N]= m mod N mk*ɸ[N]+1= m mod N
- 24. We now have an equation to find e and d which depends on ɸ[N] mk*ɸ[N]+1= m mod N me*d= m mod N Where d= k*ɸ[N]+1 e Meaning d is ALICE’s private key . It is the trap door which will perform undo operation
- 25. EVE N=3127 ALICE BOB P1=53 d=2011 P1=59 N= 53* 59 N=3127 ɸ[N]=52*58 e=3 d=2*(3016)+1 3 d=2011 e=3 hi m=hi m=89 893 mod 3127=1394 c=1394 ɸ[N]=3016 cd mod N = m 13942011 mod 3127 = 89 m=89 m=hi c=1394
- 26. • Any one wth N, e and c can find d if and only if they know the prime factorization of N • If N is large enough it requirs 100 to 1000 years to find factorize • It is the most widely used public key cryptography algorithm and most copied software in the history • Every internet user is using RSA whether they realise on the hardness of prime factorization which results in deep question of distribution of prime numbers.
- 27. APPLICATIONS • When it comes to assymetric cryptography the most popular and widely used application that comes to anyone's mind is PGP. PGP stands for “Pretty Good Privacy” and is the standard public key cryptography application used today. In the examples of this project we chose to use PGP Desktop. The reason for this choice is that PGP Desktop is easier to use than other text-based versions of PGP such as gnuPGP. PGP Desktop provides us with a very intuitive GUI accessible from the Windows Start Menu ,the PGP taskbar icon and from Windows explorer (shell integration). So from now on, every time we mention PGP, we will be referring to the PGP Desktop version.
- 28. ADVANTAGES 1. Convenience: It solves the problem of distributing the key for encryption. 2. Provides for message authentication: Public key encryption allows the use of digital signatures which enables the recipient of a message to verify that the message is truly from a particular sender. 3. Detection of tampering: The use of digital signatures in public key encryption allows the receiver to detect if the message was altered in transit. A digitally signed message cannot be modified without invalidating the signature. 4. Provide for non-repudiation: Digitally signing a message is akin to physically signing a document. It is an acknowledgement of the message and thus, the sender cannot deny it.
- 29. DISADVANTAGES 1. Public keys should/must be authenticated: No one can be absolutely sure that a public key belongs to the person it specifies and so everyone must verify that their public keys belong to them. 2. Slow: Public key encryption is slow compared to symmetric encryption. Not feasible for use in decrypting bulk messages. 3. Uses up more computer resources: It requires a lot more computer supplies compared to single-key encryption. 4. Widespread security compromise is possible: If an attacker determines a person's private key, his or her entire messages can be read. 5. Loss of private key may be irreparable: The loss of a private key means that all received messages cannot be decrypted
- 30. REFERENCES 1. Frederick J. Hirsch. "SSL/TLS Strong Encryption: An Introduction". Apache HTTP Server. Retrieved 2013-04-17.. The first two sections contain a very good introduction to public-key cryptography. 2. N. Ferguson; B. Schneier (2003). Practical Cryptography. Wiley. ISBN 0-471-22357-3. 3. J. Katz; Y. Lindell (2007). Introduction to Modern Cryptography. CRC Press. ISBN 1-58488-551-3. 4. A. J. Menezes; P. C. van Oorschot; S. A. Vanstone (1997). Handbook of Applied Cryptography. ISBN 0-8493-8523-7.
- 31. THANK YOU