Software Tool for Implementing RSA Algorithm

Save this PDF as:

Size: px
Start display at page:

Transcription

1 Software Tool for Implementing RSA Algorithm Adriana Borodzhieva, Plamen Manoilov Rousse University Angel Kanchev, Rousse, Bulgaria Abstract: RSA is one of the most-common used algorithms for public-key cryptography applied for encrypting information in computer-communication systems. Design and operation of a software tool for implementing RSA algorithm are described in the paper. The architecture of the system and modules for generating keys and encrypting / decrypting are presented. The software tool with a friendly graphical user interface is developed in Borland Delphi and it will be applicable to the educational process in the course of Cryptography and Information Security. Keywords: communications, cryptography, RSA algorithm, software tool. 1. INTRODUCTION RSA is an algorithm for public-key cryptography, suitable for signing and encryption. The algorithm RSA was publicly described in 1977 by Rivest, Shamir, and Adleman at Massachusetts Institute of Technology (MIT) [4]. RSA is widely used in electronic commerce protocols, and is believed to be secure given sufficiently long keys and the use of up-to-date implementations. 2. ASYMMETRICAL ALGORITHM RSA Asymmetrical algorithm RSA involves a public key and a private key. The public key can be known to everyone and is used for encrypting messages. Messages encrypted with the public key can only be decrypted using the private key. The keys are generated in the following way [1, 3, 4]: 1. Choose two distinct large random prime numbers p and q. 2. Compute n = pq. The number n is used as the modulus for both the public and private keys. 3. Compute the Euler s function: ϕ( n ) = ( p 1) ( q 1). < e < ϕ n ϕ n share no factors other 4. Choose an integer e such that 1 ( ); e and ( ) than 1 (i.e. e and ϕ ( n) are co-primes); e is released as the public key exponent. 5. Compute d to satisfy the congruence relation de 1 ( mod ϕ( n) ); i.e. ( n) de = 1 + k ϕ for some integer k ; d is kept as the private key exponent. A popular choice for the public exponents is e = = Some applications choose smaller values such as e = 3, 5, 17 or 257 instead. This is done to make encryption and signature verification faster on small devices like smart cards but small public exponents can lead to greater security risks. The public key consists of the modulus n and the public (or encryption) exponent e. The private key consists of the modulus n and the private (or decryption) exponent d which must be kept secret. For efficiency a different form of the private key can be stored: p and q : the primes from the key generation; d mod ( p 1) and mod ( q 1) d ; 804

2 . All parts of the private key must be kept secret in this form. p and q are sensitive since they are the factors of n, and allow computation of d given e. If p and q are not stored in this form of the private key then they are securely deleted along with other intermediate values from key generation. Although this form allows faster decryption and signing by using the Chinese Remainder Theorem, it is considerably less secure since it enables side channel attacks. This is a particular problem if implemented on smart cards, which benefit most from the improved efficiency [4]. The RSA system can be used for encryption / decryption and digital signatures: 1. Encryption and decryption: Suppose Alice wants to send a message m to Bob. 1 q mod ( p) Alice creates the ciphertext c by exponentiating: c = m e mod n, where e and n are Bob's public key. She sends c to Bob. To decrypt, Bob also exponentiates: m = c d mod n ; the relationship between e and d ensures that Bob correctly recovers m. Since only Bob knows d, only Bob can decrypt this message. 2. Digital Signature: Suppose Alice wants to send a message m to Bob in such a way that Bob is assured the message is both authentic, has not been tampered with, and from Alice. Alice creates a digital signature s by exponentiating: s = m d mod n, where d and n are Alice's private key. She sends m and s to Bob. To verify the signature, Bob exponentiates and checks that the message m is recovered: m = s e mod n, where e and n are Alice's public key. Thus encryption and authentication take place without any sharing of private keys: each person uses only another's public key or their own private key. Anyone can send an encrypted message or verify a signed message, but only someone in possession of the correct private key can decrypt or sign a message [2]. 3. DESIGN AND SOFTWARE IMPLEMENTATION OF RSA CRYPTOSYSTEMS Design and operation of a software tool for implementing RSA algorithm are described in the paper. The architecture of the system and modules for generating keys and encrypting/decrypting are presented. The tool with a friendly graphical user interface is developed in Borland Delphi and it will be applicable to the educational process in the course of Cryptography and Information Security. To software products of this type, especially simulators of cryptographic algorithms, the following requirements are claimed: Flexibility of the system in dealing with different types of data; Visualizing the encryption and decryption processes; Storing the processed results. Some specific requirements that extend the functional capabilities and guarantee the facilities for working with the system are specified: Presence of a module for taking out the series of prime numbers this facilitates the user in choosing the numbers Р and Q necessary for determining the keys; Ensuring possibilities for choosing the type the data to be processed binary or hexadecimal; Possibility for selecting the languages of the graphical user interface; Detecting incorrectly filled-in fields; Keeping track of the current results from the system s working. 805

3 Moreover, the software products must guarantee: Convenience for working with the system; A friendly graphical user interface (GUI); Control over the user s operations by means of well-chosen dialog. The system consists of three main modules (Fig. 1) for generating the couple of keys; for encrypting and decrypting the data A module for generating the keys The major part of RSA algorithm is realized on the basis of this module, namely creating the public and the secret keys. This is done after entering two numbers P and Q that must satisfy the following conditions: The numbers must be primes, i.e. their divisors are only 1 and the number itself; The numbers P and Q must be positive and fulfil the requirement 1 < P, Q 300; The numbers P and Q must be different, P Q. Fig. 1: Architecture of the designed system The system verifies automatically whether the input numbers satisfy all conditions above to guarantee the correctness of the created couple of keys. The restriction the numbers P and Q not to exceed 300 is imposed with the purpose of preventing possible errors that can arise in the subsequent working of the program since the obtained numbers are extremely large. With violating one of these requirements, the system produces the corresponding message for an error and the user is asked to enter correct number. In aid of the users, the software product shows all primes in the range [0, 300] when pushing the button Show primes, Fig. 2. The fields for the generated couple of keys (public and private) are located in the section Crypto keys. Below the fields where the values of P and Q are entered the value of Euler s function PHI (φ(n)) is taken out. This field and the fields for the keys are forbidden for user s access. Only the system has access to these fields and manipulates their values. In this way the certainty is increased and the possibilities for entering incorrect values are reduced to 0, Fig

4 3.2. A module for encrypting This module uses the generated public key to encrypt the information located in the field Plain Text. If a couple of keys is not generated, the program produces an error message and the process of encrypting is interrupted. After pushing the button Encrypt the verification for availability of keys is done and the contents of the field Plain Text are analyzed. If any irregularity is found, the user is informed. A possible reason for generating an error is an empty field. The symbols Space and Enter are distinguished by the system and are encrypted / decrypted correctly. Another possible reason for interrupting the encryption is if the number of input symbols exceeds This requirement is imposed since the processes of encryption and decryption are delayed considerably when the number of symbols is great. It reduces the system to getting to sleep, especially when P and Q are greater and the subsequent calculations become complicated. The number of the symbols is shown below the text areas. The time necessary for encryption of the corresponding information is displayed. Fig. 2: GUI of RSA simulator Besides entering the information for encrypting by hand, the product allows working with text files (.txt) by selecting the option Import Plain Text from menu File. After specifying the file for processing its contents are written out in the field Plain Text and its name against Input file. A verification of text validity is done. A possibility for saving the encrypted text is added in menu File ( Save Cipher Text ). The results are kept only in text files (.txt). 807

5 The simulator has the possibility for encrypting data in binary or hexadecimal form. The choice of the data type is done in the field Visualisation, by the options HEX mode and BIN mode. The hexadecimal representation is chosen by default, Fig A module for decrypting This module uses the generated private key for decrypting the data in the field Cipher Text. After pushing the button Decrypt the system analyzes the field where the encrypted information is located. For lack of input data an error message is produced and the process of decrypting is stopped. If input data is available it is verified whether it conforms to the corresponding chosen option for binary or hexadecimal representation. If any inconformity is found an error message is generated. Except using encrypted information generated by the system during its work, a possibility for importing encrypted information from a text file (.txt) is implemented by selecting the option Import Cipher Text from menu File. Since incorrect encrypted data can be entered such verification is imposed before starting the veritable decrypting. The option Save Decrypt Text can be chosen from menu File also. It allows the user to save the results from decryption in a text file (.txt). The number of symbols of the encrypted information is restricted to If the number of the symbols is close to and the generated keys on the basis of the greatest values for P and Q ( 300) the time necessary for decrypting is more than 6 minutes depending on the information type. The software tool has a well-working algorithm for tracking the current state of the process. At any time of working, the user has the chance to follow the state of the system. It can be done from the field Status. Thence it can be followed whether the encrypting and decrypting are done successfully or any errors are found during this process and errors type. One of the possible errors is Error encrypting string data. It is generated in the cases when n = P.Q is less than the number that will be encrypted. A screenshot from running the RSA simulator is given in Fig. 2. The choice of numbers P and Q, and the results from generating the public and private keys are shown. The processes of encrypting and decrypting of an example text are illustrated also Additional capabilities of the implemented system The program has a graphical user interface in English and Bulgarian. The language can be selected from menu Settings Language. English is used by default. The option Crypto Model can be chosen from menu View. It illustrates the diagram where RSA encrypting is applied thoroughly, Fig. 3. Since this asymmetrical algorithm can not claim for a great response time it is not preferable to encrypt а large quantity of data. One of its functions is to assure the secure propagation of the secret key in a symmetrical cryptosystem. RSA Model can be chosen from the other option in the menu. A block-diagram of RSA is appeared at the display. It shows the conditions and the stages necessary to pass through the public and private keys generating. It can be of help for better visualization idea when this system is studied. The block-diagram is a preferable tool for representing algorithms of a similar type since its comprehension and analyzing is much easier than the mathematical formulae and relationships. The diagram is translated into Bulgarian and English, and is visualized depending on the selected language. 808

6 Fig. 3: Crypto model applications of RSA 4. RESULTS, DISCUSSIONS, CONCLUSIONS A software tool with a friendly graphical user interface for implementing the asymmetrical algorithm RSA is created. It receives the input data in binary and hexadecimal form. The values of the parameters P and Q can be in the range from 0 to 300. The architecture of the system and modules for generating keys and encrypting / decrypting are presented. The tool will be applicable to the educational process in the course of Cryptography and Information Security. 5. REFERENCES [1] Menezes, A., Oorschot, P. van, Vanstone, S. (1996) Handbook of Applied Cryptography. CRC Press. [2] RSA Laboratories, RSA Laboratories Frequently Asked Questions about Today s Cryptography, Version , [3] [4] 809

Number Theory and Cryptography using PARI/GP

Number Theory and Cryptography using Minh Van Nguyen nguyenminh2@gmail.com 25 November 2008 This article uses to study elementary number theory and the RSA public key cryptosystem. Various commands will

CRYPTOGRAPHY IN NETWORK SECURITY

ELE548 Research Essays CRYPTOGRAPHY IN NETWORK SECURITY AUTHOR: SHENGLI LI INSTRUCTOR: DR. JIEN-CHUNG LO Date: March 5, 1999 Computer network brings lots of great benefits and convenience to us. We can

Network Security. Computer Networking Lecture 08. March 19, 2012. HKU SPACE Community College. HKU SPACE CC CN Lecture 08 1/23

Network Security Computer Networking Lecture 08 HKU SPACE Community College March 19, 2012 HKU SPACE CC CN Lecture 08 1/23 Outline Introduction Cryptography Algorithms Secret Key Algorithm Message Digest

The Mathematics of the RSA Public-Key Cryptosystem

The Mathematics of the RSA Public-Key Cryptosystem Burt Kaliski RSA Laboratories ABOUT THE AUTHOR: Dr Burt Kaliski is a computer scientist whose involvement with the security industry has been through

CSCE 465 Computer & Network Security

CSCE 465 Computer & Network Security Instructor: Dr. Guofei Gu http://courses.cse.tamu.edu/guofei/csce465/ Public Key Cryptogrophy 1 Roadmap Introduction RSA Diffie-Hellman Key Exchange Public key and

CIS 6930 Emerging Topics in Network Security. Topic 2. Network Security Primitives

CIS 6930 Emerging Topics in Network Security Topic 2. Network Security Primitives 1 Outline Absolute basics Encryption/Decryption; Digital signatures; D-H key exchange; Hash functions; Application of hash

Number Theory and the RSA Public Key Cryptosystem

Number Theory and the RSA Public Key Cryptosystem Minh Van Nguyen nguyenminh2@gmail.com 05 November 2008 This tutorial uses to study elementary number theory and the RSA public key cryptosystem. A number

Today ENCRYPTION. Cryptography example. Basic principles of cryptography

Today ENCRYPTION The last class described a number of problems in ensuring your security and privacy when using a computer on-line. This lecture discusses one of the main technological solutions. The use

Public-Key Cryptography. Oregon State University

Public-Key Cryptography Çetin Kaya Koç Oregon State University 1 Sender M Receiver Adversary Objective: Secure communication over an insecure channel 2 Solution: Secret-key cryptography Exchange the key

A SOFTWARE COMPARISON OF RSA AND ECC

International Journal Of Computer Science And Applications Vol. 2, No. 1, April / May 29 ISSN: 974-13 A SOFTWARE COMPARISON OF RSA AND ECC Vivek B. Kute Lecturer. CSE Department, SVPCET, Nagpur 9975549138

SECURITY IMPROVMENTS TO THE DIFFIE-HELLMAN SCHEMES

www.arpapress.com/volumes/vol8issue1/ijrras_8_1_10.pdf SECURITY IMPROVMENTS TO THE DIFFIE-HELLMAN SCHEMES Malek Jakob Kakish Amman Arab University, Department of Computer Information Systems, P.O.Box 2234,

Cryptography and Network Security Department of Computer Science and Engineering Indian Institute of Technology Kharagpur

Cryptography and Network Security Department of Computer Science and Engineering Indian Institute of Technology Kharagpur Module No. # 01 Lecture No. # 05 Classic Cryptosystems (Refer Slide Time: 00:42)

Cryptography and Network Security Chapter 9

Cryptography and Network Security Chapter 9 Fifth Edition by William Stallings Lecture slides by Lawrie Brown (with edits by RHB) Chapter 9 Public Key Cryptography and RSA Every Egyptian received two names,

Overview of Public-Key Cryptography

CS 361S Overview of Public-Key Cryptography Vitaly Shmatikov slide 1 Reading Assignment Kaufman 6.1-6 slide 2 Public-Key Cryptography public key public key? private key Alice Bob Given: Everybody knows

Chapter 10 Asymmetric-Key Cryptography

Chapter 10 Asymmetric-Key Cryptography Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 10.1 Chapter 10 Objectives Present asymmetric-key cryptography. Distinguish

Mathematics of Internet Security. Keeping Eve The Eavesdropper Away From Your Credit Card Information

The : Keeping Eve The Eavesdropper Away From Your Credit Card Information Department of Mathematics North Dakota State University 16 September 2010 Science Cafe Introduction Disclaimer: is not an internet

9 Modular Exponentiation and Cryptography

9 Modular Exponentiation and Cryptography 9.1 Modular Exponentiation Modular arithmetic is used in cryptography. In particular, modular exponentiation is the cornerstone of what is called the RSA system.

Secure File Transfer Using USB

International Journal of Scientific and Research Publications, Volume 2, Issue 4, April 2012 1 Secure File Transfer Using USB Prof. R. M. Goudar, Tushar Jagdale, Ketan Kakade, Amol Kargal, Darshan Marode

Secure Network Communication Part II II Public Key Cryptography. Public Key Cryptography

Kommunikationssysteme (KSy) - Block 8 Secure Network Communication Part II II Public Key Cryptography Dr. Andreas Steffen 2000-2001 A. Steffen, 28.03.2001, KSy_RSA.ppt 1 Secure Key Distribution Problem

UNIVERSITY OF MASSACHUSETTS Dept. of Electrical & Computer Engineering. Introduction to Cryptography ECE 597XX/697XX

UNIVERSITY OF MASSACHUSETTS Dept. of Electrical & Computer Engineering Introduction to Cryptography ECE 597XX/697XX Part 6 Introduction to Public-Key Cryptography Israel Koren ECE597/697 Koren Part.6.1

MA2C03 Mathematics School of Mathematics, Trinity College Hilary Term 2016 Lecture 59 (April 1, 2016) David R. Wilkins

MA2C03 Mathematics School of Mathematics, Trinity College Hilary Term 2016 Lecture 59 (April 1, 2016) David R. Wilkins The RSA encryption scheme works as follows. In order to establish the necessary public

The application of prime numbers to RSA encryption

The application of prime numbers to RSA encryption Prime number definition: Let us begin with the definition of a prime number p The number p, which is a member of the set of natural numbers N, is considered

PUBLIC KEY ENCRYPTION

PUBLIC KEY ENCRYPTION http://www.tutorialspoint.com/cryptography/public_key_encryption.htm Copyright tutorialspoint.com Public Key Cryptography Unlike symmetric key cryptography, we do not find historical

MATH 168: FINAL PROJECT Troels Eriksen. 1 Introduction

MATH 168: FINAL PROJECT Troels Eriksen 1 Introduction In the later years cryptosystems using elliptic curves have shown up and are claimed to be just as secure as a system like RSA with much smaller key

Elements of Applied Cryptography Public key encryption

Network Security Elements of Applied Cryptography Public key encryption Public key cryptosystem RSA and the factorization problem RSA in practice Other asymmetric ciphers Asymmetric Encryption Scheme Let

Chapter 9 Public Key Cryptography and RSA

Chapter 9 Public Key Cryptography and RSA Cryptography and Network Security: Principles and Practices (3rd Ed.) 2004/1/15 1 9.1 Principles of Public Key Private-Key Cryptography traditional private/secret/single

NEW DIGITAL SIGNATURE PROTOCOL BASED ON ELLIPTIC CURVES

NEW DIGITAL SIGNATURE PROTOCOL BASED ON ELLIPTIC CURVES Ounasser Abid 1, Jaouad Ettanfouhi 2 and Omar Khadir 3 1,2,3 Laboratory of Mathematics, Cryptography and Mechanics, Department of Mathematics, Fstm,

Lecture 6 - Cryptography

Lecture 6 - Cryptography CSE497b - Spring 2007 Introduction Computer and Network Security Professor Jaeger www.cse.psu.edu/~tjaeger/cse497b-s07 Question 2 Setup: Assume you and I don t know anything about

Family Name:... First Name:... Section:... Advanced Cryptography Final Exam July 18 th, 2006 Start at 9:15, End at 12:00 This document consists of 12 pages. Instructions Electronic devices are not allowed.

Notes on Network Security Prof. Hemant K. Soni

Chapter 9 Public Key Cryptography and RSA Private-Key Cryptography traditional private/secret/single key cryptography uses one key shared by both sender and receiver if this key is disclosed communications

A FAST IMPLEMENTATION OF THE RSA ALGORITHM USING THE GNU MP LIBRARY

ABSTRACT A FAST IMPLEMENTATION OF THE RSA ALGORITHM USING THE GNU MP LIBRARY Rajorshi Biswas Shibdas Bandyopadhyay Anirban Banerjee IIIT-Calcutta Organizations in both public and private sectors have become

CRYPTOGRAPHIC ALGORITHMS (AES, RSA)

CALIFORNIA STATE POLYTECHNIC UNIVERSITY, POMONA CRYPTOGRAPHIC ALGORITHMS (AES, RSA) A PAPER SUBMITTED TO PROFESSOR GILBERT S. YOUNG IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE COURSE CS530 : ADVANCED

Mathematical Model Based Total Security System with Qualitative and Quantitative Data of Human

Int Jr of Mathematics Sciences & Applications Vol3, No1, January-June 2013 Copyright Mind Reader Publications ISSN No: 2230-9888 wwwjournalshubcom Mathematical Model Based Total Security System with Qualitative

RSA Attacks. By Abdulaziz Alrasheed and Fatima

RSA Attacks By Abdulaziz Alrasheed and Fatima 1 Introduction Invented by Ron Rivest, Adi Shamir, and Len Adleman [1], the RSA cryptosystem was first revealed in the August 1977 issue of Scientific American.

1 Digital Signatures. 1.1 The RSA Function: The eth Power Map on Z n. Crypto: Primitives and Protocols Lecture 6.

1 Digital Signatures A digital signature is a fundamental cryptographic primitive, technologically equivalent to a handwritten signature. In many applications, digital signatures are used as building blocks

UOSEC Week 2: Asymmetric Cryptography. Frank IRC kee Adam IRC xe0 IRC: irc.freenode.net #0x4f

UOSEC Week 2: Asymmetric Cryptography Frank farana@uoregon.edu IRC kee Adam pond2@uoregon.edu IRC xe0 IRC: irc.freenode.net #0x4f Agenda HackIM CTF Results GITSC CTF this Saturday 10:00am Basics of Asymmetric

ACTA UNIVERSITATIS APULENSIS No 13/2007 MATHEMATICAL FOUNDATION OF DIGITAL SIGNATURES. Daniela Bojan and Sidonia Vultur

ACTA UNIVERSITATIS APULENSIS No 13/2007 MATHEMATICAL FOUNDATION OF DIGITAL SIGNATURES Daniela Bojan and Sidonia Vultur Abstract.The new services available on the Internet have born the necessity of a permanent

CIS 5371 Cryptography. 8. Encryption --

CIS 5371 Cryptography p y 8. Encryption -- Asymmetric Techniques Textbook encryption algorithms In this chapter, security (confidentiality) is considered in the following sense: All-or-nothing secrecy.

Lukasz Pater CMMS Administrator and Developer

Lukasz Pater CMMS Administrator and Developer EDMS 1373428 Agenda Introduction Why do we need asymmetric ciphers? One-way functions RSA Cipher Message Integrity Examples Secure Socket Layer Single Sign

SECURITY IN NETWORKS

SECURITY IN NETWORKS GOALS Understand principles of network security: Cryptography and its many uses beyond confidentiality Authentication Message integrity Security in practice: Security in application,

Asymmetric Cryptography. Mahalingam Ramkumar Department of CSE Mississippi State University

Asymmetric Cryptography Mahalingam Ramkumar Department of CSE Mississippi State University Mathematical Preliminaries CRT Chinese Remainder Theorem Euler Phi Function Fermat's Theorem Euler Fermat's Theorem

An Introduction to the RSA Encryption Method

April 17, 2012 Outline 1 History 2 3 4 5 History RSA stands for Rivest, Shamir, and Adelman, the last names of the designers It was first published in 1978 as one of the first public-key crytographic systems

3. Applications of Number Theory

3. APPLICATIONS OF NUMBER THEORY 163 3. Applications of Number Theory 3.1. Representation of Integers. Theorem 3.1.1. Given an integer b > 1, every positive integer n can be expresses uniquely as n = a

CS Computer and Network Security: Applied Cryptography

CS 5410 - Computer and Network Security: Applied Cryptography Professor Patrick Traynor Spring 2016 Reminders Project Ideas are due on Tuesday. Where are we with these? Assignment #2 is posted. Let s get

Cryptography and Network Security

Cryptography and Network Security Fifth Edition by William Stallings Chapter 9 Public Key Cryptography and RSA Private-Key Cryptography traditional private/secret/single key cryptography uses one key shared

ANALYSIS OF RSA ALGORITHM USING GPU PROGRAMMING

ANALYSIS OF RSA ALGORITHM USING GPU PROGRAMMING Sonam Mahajan 1 and Maninder Singh 2 1 Department of Computer Science Engineering, Thapar University, Patiala, India 2 Department of Computer Science Engineering,

RSA Cryptosystem. Yufei Tao. Department of Computer Science and Engineering Chinese University of Hong Kong. RSA Cryptosystem

Yufei Tao Department of Computer Science and Engineering Chinese University of Hong Kong In this lecture, we will discuss the RSA cryptosystem, which is widely adopted as a way to encrypt a message, or

Network Security. Gaurav Naik Gus Anderson. College of Engineering. Drexel University, Philadelphia, PA. Drexel University. College of Engineering

Network Security Gaurav Naik Gus Anderson, Philadelphia, PA Lectures on Network Security Feb 12 (Today!): Public Key Crypto, Hash Functions, Digital Signatures, and the Public Key Infrastructure Feb 14:

159.334 Computer Networks. Network Security 1. Professor Richard Harris School of Engineering and Advanced Technology

Network Security 1 Professor Richard Harris School of Engineering and Advanced Technology Presentation Outline Overview of Identification and Authentication The importance of identification and Authentication

Network Security [2] Plain text Encryption algorithm Public and private key pair Cipher text Decryption algorithm. See next slide

Network Security [2] Public Key Encryption Also used in message authentication & key distribution Based on mathematical algorithms, not only on operations over bit patterns (as conventional) => much overhead

Outline. Cryptography. Bret Benesh. Math 331

Outline 1 College of St. Benedict/St. John s University Department of Mathematics Math 331 2 3 The internet is a lawless place, and people have access to all sorts of information. What is keeping people

Chapter 10 Asymmetric-Key Cryptography

Chapter 10 Asymmetric-Key Cryptography Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 10.1 Chapter 10 Objectives To distinguish between two cryptosystems: symmetric-key

1720 - Forward Secrecy: How to Secure SSL from Attacks by Government Agencies

1720 - Forward Secrecy: How to Secure SSL from Attacks by Government Agencies Dave Corbett Technical Product Manager Implementing Forward Secrecy 1 Agenda Part 1: Introduction Why is Forward Secrecy important?

Shor s algorithm and secret sharing

Shor s algorithm and secret sharing Libor Nentvich: QC 23 April 2007: Shor s algorithm and secret sharing 1/41 Goals: 1 To explain why the factoring is important. 2 To describe the oldest and most successful

Network Security. Abusayeed Saifullah. CS 5600 Computer Networks. These slides are adapted from Kurose and Ross 8-1

Network Security Abusayeed Saifullah CS 5600 Computer Networks These slides are adapted from Kurose and Ross 8-1 Public Key Cryptography symmetric key crypto v requires sender, receiver know shared secret

Outline. Computer Science 418. Digital Signatures: Observations. Digital Signatures: Definition. Definition 1 (Digital signature) Digital Signatures

Outline Computer Science 418 Digital Signatures Mike Jacobson Department of Computer Science University of Calgary Week 12 1 Digital Signatures 2 Signatures via Public Key Cryptosystems 3 Provable 4 Mike

An Efficient Data Security in Cloud Computing Using the RSA Encryption Process Algorithm

An Efficient Data Security in Cloud Computing Using the RSA Encryption Process Algorithm V.Masthanamma 1,G.Lakshmi Preya 2 UG Scholar, Department of Information Technology, Saveetha School of Engineering

The science of encryption: prime numbers and mod n arithmetic

The science of encryption: prime numbers and mod n arithmetic Go check your e-mail. You ll notice that the webpage address starts with https://. The s at the end stands for secure meaning that a process

Public Key (asymmetric) Cryptography

Public-Key Cryptography UNIVERSITA DEGLI STUDI DI PARMA Dipartimento di Ingegneria dell Informazione Public Key (asymmetric) Cryptography Luca Veltri (mail.to: luca.veltri@unipr.it) Course of Network Security,

Data Encryption A B C D E F G H I J K L M N O P Q R S T U V W X Y Z. we would encrypt the string IDESOFMARCH as follows:

Data Encryption Encryption refers to the coding of information in order to keep it secret. Encryption is accomplished by transforming the string of characters comprising the information to produce a new

Efficient on-line electronic checks

Applied Mathematics and Computation 162 (2005) 1259 1263 www.elsevier.com/locate/amc Efficient on-line electronic checks Wei-Kuei Chen Department of Computer Science and Information Engineering, Ching-Yun

Public Key Cryptography: RSA and Lots of Number Theory

Public Key Cryptography: RSA and Lots of Number Theory Public vs. Private-Key Cryptography We have just discussed traditional symmetric cryptography: Uses a single key shared between sender and receiver

CS 758: Cryptography / Network Security

CS 758: Cryptography / Network Security offered in the Fall Semester, 2003, by Doug Stinson my office: DC 3122 my email address: dstinson@uwaterloo.ca my web page: http://cacr.math.uwaterloo.ca/~dstinson/index.html

A New Efficient Digital Signature Scheme Algorithm based on Block cipher

IOSR Journal of Computer Engineering (IOSRJCE) ISSN: 2278-0661, ISBN: 2278-8727Volume 7, Issue 1 (Nov. - Dec. 2012), PP 47-52 A New Efficient Digital Signature Scheme Algorithm based on Block cipher 1

AN IMPLEMENTATION OF HYBRID ENCRYPTION-DECRYPTION (RSA WITH AES AND SHA256) FOR USE IN DATA EXCHANGE BETWEEN CLIENT APPLICATIONS AND WEB SERVICES

HYBRID RSA-AES ENCRYPTION FOR WEB SERVICES AN IMPLEMENTATION OF HYBRID ENCRYPTION-DECRYPTION (RSA WITH AES AND SHA256) FOR USE IN DATA EXCHANGE BETWEEN CLIENT APPLICATIONS AND WEB SERVICES Kalyani Ganesh

International Journal of Information Technology, Modeling and Computing (IJITMC) Vol.1, No.3,August 2013

FACTORING CRYPTOSYSTEM MODULI WHEN THE CO-FACTORS DIFFERENCE IS BOUNDED Omar Akchiche 1 and Omar Khadir 2 1,2 Laboratory of Mathematics, Cryptography and Mechanics, Fstm, University of Hassan II Mohammedia-Casablanca,

Announcements. CS243: Discrete Structures. More on Cryptography and Mathematical Induction. Agenda for Today. Cryptography

Announcements CS43: Discrete Structures More on Cryptography and Mathematical Induction Işıl Dillig Class canceled next Thursday I am out of town Homework 4 due Oct instead of next Thursday (Oct 18) Işıl

Cryptography: Authentication, Blind Signatures, and Digital Cash

Cryptography: Authentication, Blind Signatures, and Digital Cash Rebecca Bellovin 1 Introduction One of the most exciting ideas in cryptography in the past few decades, with the widest array of applications,

Discrete Mathematics, Chapter 4: Number Theory and Cryptography

Discrete Mathematics, Chapter 4: Number Theory and Cryptography Richard Mayr University of Edinburgh, UK Richard Mayr (University of Edinburgh, UK) Discrete Mathematics. Chapter 4 1 / 35 Outline 1 Divisibility

Public Key Cryptography and RSA. Review: Number Theory Basics

Public Key Cryptography and RSA Murat Kantarcioglu Based on Prof. Ninghui Li s Slides Review: Number Theory Basics Definition An integer n > 1 is called a prime number if its positive divisors are 1 and

Embedding more security in digital signature system by using combination of public key cryptography and secret sharing scheme

International Journal of Computer Sciences and Engineering Open Access Research Paper Volume-4, Issue-3 E-ISSN: 2347-2693 Embedding more security in digital signature system by using combination of public

The RSA Algorithm. Evgeny Milanov. 3 June 2009

The RSA Algorithm Evgeny Milanov 3 June 2009 In 1978, Ron Rivest, Adi Shamir, and Leonard Adleman introduced a cryptographic algorithm, which was essentially to replace the less secure National Bureau

Introduction to Cryptography

Introduction to Cryptography Part 2: public-key cryptography Jean-Sébastien Coron January 2007 Public-key cryptography Invented by Diffie and Hellman in 1976. Revolutionized the field. Each user now has

A Factoring and Discrete Logarithm based Cryptosystem

Int. J. Contemp. Math. Sciences, Vol. 8, 2013, no. 11, 511-517 HIKARI Ltd, www.m-hikari.com A Factoring and Discrete Logarithm based Cryptosystem Abdoul Aziz Ciss and Ahmed Youssef Ecole doctorale de Mathematiques

1) A very simple example of RSA encryption

Solved Examples 1) A very simple example of RSA encryption This is an extremely simple example using numbers you can work out on a pocket calculator (those of you over the age of 35 45 can probably even

Lecture 9: Application of Cryptography

Lecture topics Cryptography basics Using SSL to secure communication links in J2EE programs Programmatic use of cryptography in Java Cryptography basics Encryption Transformation of data into a form that

7! Cryptographic Techniques! A Brief Introduction

7! Cryptographic Techniques! A Brief Introduction 7.1! Introduction to Cryptography! 7.2! Symmetric Encryption! 7.3! Asymmetric (Public-Key) Encryption! 7.4! Digital Signatures! 7.5! Public Key Infrastructures

Outline. Digital signature. Symmetric-key Cryptography. Caesar cipher. Cryptography basics Digital signature

Outline Digital signature Cryptography basics Digital signature Dr. László Daragó, Ph.D. Associate professor Cryptography Cryptography encryption decryption Symmetric-key Cryptography Encryption with a

Applied Cryptography Public Key Algorithms

Applied Cryptography Public Key Algorithms Sape J. Mullender Huygens Systems Research Laboratory Universiteit Twente Enschede 1 Public Key Cryptography Independently invented by Whitfield Diffie & Martin

A Study on Asymmetric Key Cryptography Algorithms

A Study on Asymmetric Key Cryptography Algorithms ASAITHAMBI.N School of Computer Science and Engineering, Bharathidasan University, Trichy, asaicarrier@gmail.com Abstract Asymmetric key algorithms use

A Proposal for Authenticated Key Recovery System 1

A Proposal for Authenticated Key Recovery System 1 Tsuyoshi Nishioka a, Kanta Matsuura a, Yuliang Zheng b,c, and Hideki Imai b a Information & Communication Business Div. ADVANCE Co., Ltd. 5-7 Nihombashi

6 Introduction to Cryptography

6 Introduction to Cryptography This section gives a short introduction to cryptography. It is based on the recent tutorial by Jörg Rothe. For an in-depth treatment of cryptography, please consult the Handbook

CS 161 Computer Security

Song Spring 2015 CS 161 Computer Security Discussion 11 April 7 & April 8, 2015 Question 1 RSA (10 min) (a) Describe how to find a pair of public key and private key for RSA encryption system. Find two

Digital Signatures. Meka N.L.Sneha. Indiana State University. nmeka@sycamores.indstate.edu. October 2015

Digital Signatures Meka N.L.Sneha Indiana State University nmeka@sycamores.indstate.edu October 2015 1 Introduction Digital Signatures are the most trusted way to get documents signed online. A digital

Network Security. HIT Shimrit Tzur-David

Network Security HIT Shimrit Tzur-David 1 Goals: 2 Network Security Understand principles of network security: cryptography and its many uses beyond confidentiality authentication message integrity key

A DPA Attack against Asymmetric Encryption: RSA Attacks and Countermeasures

A DPA Attack against Asymmetric Encryption: RSA Attacks and Countermeasures Lesky D.S. Anatias April 18, 2008 Abstract This paper discusses side-channel attacks based on Power Analysis. This approach utilizes

ΕΠΛ 674: Εργαστήριο 3

ΕΠΛ 674: Εργαστήριο 3 Ο αλγόριθμος ασύμμετρης κρυπτογράφησης RSA Παύλος Αντωνίου Department of Computer Science Private-Key Cryptography traditional private/secret/single key cryptography uses one key

Comparative Analysis for Performance acceleration of Modern Asymmetric Crypto Systems

J. of Comp. and I.T. Vol. 3(1&2), 1-6 (2012). Comparative Analysis for Performance acceleration of Modern Asymmetric Crypto Systems RAJ KUMAR 1 and V.K. SARASWAT 2 1,2 Department of Computer Science, ICIS

Cryptography. Helmer Aslaksen Department of Mathematics National University of Singapore

Cryptography Helmer Aslaksen Department of Mathematics National University of Singapore aslaksen@math.nus.edu.sg www.math.nus.edu.sg/aslaksen/sfm/ 1 Basic Concepts There are many situations in life where

SFWR ENG 4C03 - Computer Networks & Computer Security

KEY MANAGEMENT SFWR ENG 4C03 - Computer Networks & Computer Security Researcher: Jayesh Patel Student No. 9909040 Revised: April 4, 2005 Introduction Key management deals with the secure generation, distribution,

Separable & Secure Data Hiding & Image Encryption Using Hybrid Cryptography

502 Separable & Secure Data Hiding & Image Encryption Using Hybrid Cryptography 1 Vinay Wadekar, 2 Ajinkya Jadhavrao, 3 Sharad Ghule, 4 Akshay Kapse 1,2,3,4 Computer Engineering, University Of Pune, Pune,

Chapter 10. Network Security

Chapter 10 Network Security 10.1. Chapter 10: Outline 10.1 INTRODUCTION 10.2 CONFIDENTIALITY 10.3 OTHER ASPECTS OF SECURITY 10.4 INTERNET SECURITY 10.5 FIREWALLS 10.2 Chapter 10: Objective We introduce

An Introduction to Digital Signature Schemes

An Introduction to Digital Signature Schemes Mehran Alidoost Nia #1, Ali Sajedi #2, Aryo Jamshidpey #3 #1 Computer Engineering Department, University of Guilan-Rasht, Iran m.alidoost@hotmail.com #2 Software

Cryptographic hash functions and MACs Solved Exercises for Cryptographic Hash Functions and MACs

Cryptographic hash functions and MACs Solved Exercises for Cryptographic Hash Functions and MACs Enes Pasalic University of Primorska Koper, 2014 Contents 1 Preface 3 2 Problems 4 2 1 Preface This is a

Efficient Framework for Deploying Information in Cloud Virtual Datacenters with Cryptography Algorithms

Efficient Framework for Deploying Information in Cloud Virtual Datacenters with Cryptography Algorithms Radhika G #1, K.V.V. Satyanarayana *2, Tejaswi A #3 1,2,3 Dept of CSE, K L University, Vaddeswaram-522502,

CRC Press has granted the following specific permissions for the electronic version of this book:

This is a Chapter from the Handbook of Applied Cryptography, by A. Menezes, P. van Oorschot, and S. Vanstone, CRC Press, 1996. For further information, see www.cacr.math.uwaterloo.ca/hac CRC Press has

QUANTUM COMPUTERS AND CRYPTOGRAPHY. Mark Zhandry Stanford University

QUANTUM COMPUTERS AND CRYPTOGRAPHY Mark Zhandry Stanford University Classical Encryption pk m c = E(pk,m) sk m = D(sk,c) m??? Quantum Computing Attack pk m aka Post-quantum Crypto c = E(pk,m) sk m = D(sk,c)

RSA Encryption. Tom Davis tomrdavis@earthlink.net http://www.geometer.org/mathcircles October 10, 2003

RSA Encryption Tom Davis tomrdavis@earthlink.net http://www.geometer.org/mathcircles October 10, 2003 1 Public Key Cryptography One of the biggest problems in cryptography is the distribution of keys.