The RSA public-key cryptosystem cse712 e-commerce

Slides:

Advertisements

Similar presentations

Public Key Cryptography INFSCI 1075: Network Security – Spring 2013 Amir Masoumzadeh.

Advertisements

Public Key Cryptosystems - RSA Receiver Sender Eavesdroppe r p q p q p q p and q prime.

OOP/Java1 Public Key Crytography From: Introduction to Algorithms Cormen, Leiserson and Rivest.

8.4 Public Key Cryptography (1970) The Key made public because an unrealistic computer time is required to find a decrypting transformation D from the.

Public Key Crytography1 From: Introduction to Algorithms Cormen, Leiserson and Rivest.

Public Encryption: RSA

WS Algorithmentheorie 03 – Randomized Algorithms (Public Key Cryptosystems) Prof. Dr. Th. Ottmann.

Cryptography1 CPSC 3730 Cryptography Chapter 9 Public Key Cryptography and RSA.

Theory I Algorithm Design and Analysis (9 – Randomized algorithms) Prof. Dr. Th. Ottmann.

WS Algorithmentheorie 03 – Randomized Algorithms (Public Key Cryptosystems) Prof. Dr. Th. Ottmann.

Public Key Algorithms 4/17/2017 M. Chatterjee.

Introduction to Computer and Network Security Iliano Cervesato 2 September 2008 – Public-key Encryption.

Public-Key Cryptography and RSA CSE 651: Introduction to Network Security.

Public Key Model 8. Cryptography part 2.

Public Key Encryption and the RSA Public Key Algorithm CSCI 5857: Encoding and Encryption.

 Introduction  Requirements for RSA  Ingredients for RSA  RSA Algorithm  RSA Example  Problems on RSA.

Elgamal Public Key Encryption CSCI 5857: Encoding and Encryption.

Prime Numbers Prime numbers only have divisors of 1 and self

Problems with symmetric (private-key) encryption 1) secure distribution of keys 2) large number of keys Solution to both problems: Public-key (asymmetric)

Cryptography: RSA & DES Marcia Noel Ken Roe Jaime Buccheri.

CS 627 Elliptic Curves and Cryptography Paper by: Aleksandar Jurisic, Alfred J. Menezes Published: January 1998 Presented by: Sagar Chivate.

Prelude to Public-Key Cryptography Rocky K. C. Chang, February

1 Lecture 9 Public Key Cryptography Public Key Algorithms CIS CIS 5357 Network Security.

Modular Arithmetic with Applications to Cryptography Lecture 47 Section 10.4 Wed, Apr 13, 2005.

Darci Miyashiro Math 480 April 29, 2013

Cryptography and Network Security Chapter 9 - Public-Key Cryptography

Public Key Algorithms Lesson Introduction ●Modular arithmetic ●RSA ●Diffie-Hellman.

Public Key Cryptosystem Introduced in 1976 by Diffie and Hellman [2] In PKC different keys are used for encryption and decryption 1978: First Two Implementations.

CS 4803 Fall 04 Public Key Algorithms. Modular Arithmetic n Public key algorithms are based on modular arithmetic. n Modular addition. n Modular multiplication.

Encryption on the Internet Jeff Cohen. Keeping Information Secret What information do we want to be secret? –Credit card number –Social security number.

Introduction to Pubic Key Encryption CSCI 5857: Encoding and Encryption.

Introduction to Elliptic Curve Cryptography CSCI 5857: Encoding and Encryption.

Elgamal Public Key Encryption CSCI 5857: Encoding and Encryption.

RSA Cryptosystem Great Theoretical Ideas In Computer Science S. Rudich V. Adamchik CS Spring 2006 Lecture 8Feb. 09, 2006Carnegie Mellon University.

1 The RSA Algorithm Rocky K. C. Chang February 23, 2007.

Lecture 5 Asymmetric Cryptography. Private-Key Cryptography Traditional private/secret/single key cryptography uses one key Shared by both sender and.

@Yuan Xue CS 285 Network Security Public-Key Cryptography Yuan Xue Fall 2012.

Revision. Cryptography depends on some properties of prime numbers. One of these is that it is rather easy to generate large prime numbers, but much harder.

Overview Modern public-key cryptosystems: RSA

Public Key Cryptography

최신정보보호기술 경일대학교 사이버보안학과 김 현성.

CS480 Cryptography and Information Security

Public Key Encryption Major topics The RSA scheme was devised in 1978

Public Key Encryption.

Public Key Cryptosystem

Asymmetric-Key Cryptography

Lecture 5 RSA DR. Nermin Hamza.

Key Exchange References: Applied Cryptography, Bruce Schneier

Information Security message M one-way hash fingerprint f = H(M)

Prelude to Public-Key Cryptography

Public Key Encryption Systems

RSA Preliminaries.

Public-Key Cryptography and RSA

RSA and El Gamal Cryptosystems

Public Key Encryption and the RSA Algorithm

Information Security message M one-way hash fingerprint f = H(M)

Private-Key Cryptography

Asymmetric Cryptography

ICS 353: Design and Analysis of Algorithms

Public-key encryption

Analysis of the RSA Encryption Algorithm

Information Security message M one-way hash fingerprint f = H(M)

Cryptography: Basics (2)

Discrete Math for CS CMPSC 360 LECTURE 14 Last time:

Introduction to Elliptic Curve Cryptography

PUBLIC-KEY CRYPTOGRAPHY AND RSA – Chapter 9

Introduction to Algorithms Second Edition by

Introduction to Cryptography

刘振上海交通大学计算机科学与工程系电信群楼3-509

Public Key Encryption Systems

Presentation transcript:

The RSA public-key cryptosystem cse712 e-commerce 11/24/2018 The RSA public-key cryptosystem cse712 e-commerce Presented by Guowen Han

Outline Motivation Public-key cryptosystem RSA RSA digital signature Conclusion 11/24/2018

11/24/2018 Motivation The recent burgeoning of new communications technologies and, in particular, the Internet explosion have brought electronic commerce to the brink of widespread deployment. However, businesses are wary about treading beyond that brink, largely because of concerns about unknown risks may face - is security RSA -- the most trusted name in e-security

Public-key cryptosystem Diffie and Hellman Public-key & Private-key Protocol(two basic ways) 11/24/2018

Public key Private key Ciphertext Plaintext Plaintext Decrypt Encrypt System A Cipertext Plaintext Encrypt Cipertext System B Plaintext Encrypt System C Encryption Mode 11/24/2018

Private key Public key Cipertext Plaintext Plaintext Encrypt Decrypt Authentication Mode 11/24/2018

Encrypt & Decrypt functions 11/24/2018 Encrypt & Decrypt functions Encrypt function P() Decrypt function S() Plaintext M M = S(P(M)) M = P(S(M))

RSA RSA algorithm Some Mathematics background Correctness of RSA 11/24/2018

RSA algorithm Select two large prime numbers p and q Compute n by the equation n = pq Select a small odd integer e that is relatively prime to Ø(n), Compute d as the multiplicative inverse of e, modulo Ø(n). Publish the pair P = (e, n) as RSA public key Keep secret the pair S = (d, n) as RSA secret key 11/24/2018

Mathematics background Euler function Ø(n): the number of numbers that relatively prime to n. Ø(p) = p-1, if p is a prime number. For any n > 1, if gcd(a, n) = 1, then the equation ax = b has a unique solution modulo n. 11/24/2018

Mathematics background(cnt.) Miller and Rabin test can be used to find large primes in polynomial time base on the number of digital for some big number n. There is not any efficient algorithm for factoring a large integer n. 11/24/2018

Correctness of RSA 11/24/2018

RSA digital Signature Message Message Public key Private key Message Encrypt Decrypt Excepted message Signature If these are the same, the signature is verified 11/24/2018

Conclusion The security of the RSA cryprosystem rests in large part on the difficult of factoring large integers. In order to achieve security with the RSA cryptosystem, it is necessary to work with integers that are at least 400 digits in length,since factoring smaller integers is not impractical. For efficiency, RSA is often used in a key-management mode with fast non-public-key cryptosystem. 11/24/2018