Harbin Institute of Technology Shenzhen Graduate School. Cryptography ( 密碼學 ) 陳建銘 Chien-Ming Chen Ph. D. Assistant Professor

Size: px
Start display at page:

Download "Harbin Institute of Technology Shenzhen Graduate School. Cryptography ( 密碼學 ) 陳建銘 Chien-Ming Chen Ph. D. Assistant Professor"

Transcription

1 Harbin Institute of Technology Shenzhen Graduate School Cryptography ( 密碼學 ) 陳建銘 Chien-Ming Chen Ph. D. Assistant Professor

2

3 Outline Data Hiding Cryptography Key Management in Cryptography

4 Data Hiding

5 Data Hiding Data Hiding 資料隱藏 Steganography 藏匿學 Cryptography 密碼學

6 STEGANOGRAPHY( 藏匿學 ) 6

7 Steganography( 藏匿學 ) Physical wax tablet messenger's body invisible ink microdots

8

9

10

11 Steganography( 藏匿學 ) 唐伯虎 西江月我聞西方大士, 為人了卻凡心 秋來明月照蓬門, 香滿禪房出徑 屈指靈山會後, 居然紫竹成林 童男童女拜觀音, 僕僕何嫌榮頓 內嵌 :[ 我為秋香屈居童僕 ]

12 Steganography( 藏匿學 ) 別氣節, 讓名冊, 勝登雅堂, 文人骨無存, 不想鴉片殺人身, 開燃有益, 心存漢奸志 別羞恥, 讓關說, 勝攫諸地, 文行建不農, 不視兒女兩三歲, 開戶自耕, 心念祖國風 別帝家, 讓妻籍, 勝戰守中, 文齒皆未通, 不顧龍馬皆期任, 開言戮諷, 心無感恩情 12

13 Steganography( 藏匿學 ) 13

14 Steganography ( 藏匿學 ) Digital photo, video, audio, etc.

15 CRYPTOGRAPHY ( 密碼學 ) 15

16 Cryptography Convert ordinary information into unintelligible gibberish Transposition Substitution zpvbsfbhppetqfblfs

17 Cryptography Transposition for example COW, CWO, OCW, OWC, WCO, WOC Scytale first mentioned in the 7th century BC

18 Cryptography Rail Fence cipher write message letters out diagonally over a number of rows then read off cipher row by row eg. write message out as: m e m a t r h t g p r y e t e f e t e o a a t giving ciphertext MEMATRHTGPRYETEFETEOAAT ncecipher.html

19 Cryptography Substitution Example 1: A B C D E X Y Plaintext: C A D E Ciphertext: Example 2: A B C D E X Y Z r z k a t b n s Plaintext: C A D E Ciphertext: k r a t

20 Cryptography Caesar cipher 58 BC

21 Cryptography Substitution: Caesar cipher Each letter is translated to the letter a fixed number of letters after it in the alphabet. Note: Julius Caesar only used a shift of 3. (Primitive Caesar Cipher) Caesar Cipher (general) c = (m) = (m + 4) mod 26 Plaintext m Cipher (m) Cipher (in lower case) A E e B F f C G g D H h E I i F J j... U Y y V Z z W A a X B b Y C c Z D d

22 22

23 Cryptography Substitution: Caesar cipher Try to break this ciphertext zpvbsfbhppetqfblfs

24 24

25 25

26 Monoalphabetic Cipher rather than just shifting the alphabet could shuffle (jumble) the letters arbitrarily each plaintext letter maps to a different random ciphertext letter hence key is 26 letters long Plain: abcdefghijklmnopqrstuvwxyz Cipher: DKVQFIBJWPESCXHTMYAUOLRGZN Plaintext: ifwewishtoreplaceletters Ciphertext: WIRFRWAJUHYFTSDVFSFUUFYA

27 Monoalphabetic Cipher Security now have a total of 26! = 4 x keys with so many keys, might think is secure but would be!!!wrong!!! problem is language characteristics Cryptography-Security Ch02-27

28 English Letter Frequencies

29 Monoalphabetic cipher: attack uzqsovuohxmopvgpozpevsgzwszopfpesxudbmetsxaizvuephzhm it a i e e te a that e e a i a t i e t dzshzowsfpappdtsvpquzwymxuzuhsxepyepopdzszufpombzwp ta t ha e ee a e ith i i a e e e ta i e the letter probability p 13.33% z 11.67% s 8.33% u 8.33% o 7.5% By statistics and guess: p e, z t, {s,u,o} {r,i,a,n,o,s} zw th, zwsz that, s a

30 Vigenere cipher Vigenere cipher (1585)

31 Vigenere cipher Vigenere cipher: an example Plaintext: ATTACKATDAWN Key: lemon Plain A T T A C K A T D A W N KEY L E M O N L E M O N L E cipher L X F O P V E F R N H R

32 Vigenere cipher KEY:SECURE plaintext JINGLE BELLS JINGLE BELLS JINGLE ALL THE WAY ciphertext BMPACITINFJNARIFVFWPNMAMFKNYRPDXJYNEQ 明文 J I N G L E B E L L S J I N G L E B E L L S J I N G L E A L L T H E W A Y 金鑰 S E C U R E S E C U R E S E C U R E S E C U R E S E C U R E S E C U R E S 密文 B M P A C I T I N F J N A R I F V F W P N M A M F K N Y R P D X J Y N E Q 32

33 Enigma Rotor machine The computer era Enigma Rotor machine adopted by Germany military and government during World War II.

34 DES DES (Data Encryption Standard) Designed by IBM selected by the NIST (National Institute of Standards and Technology) as an official FIPS (Federal Information Processing Standards) standard in 1976 Since the early 90's, theoretical attacks on the DES have been developed.

35 AES AES (Advanced Encryption Standard) NIST issued a request for possible candidates in Sept 1997 Submissions are due by June 15, /04/05 (5 candidate algorithms) Mars IBM (USA) RC6 RSADSI (USA) Rijndael V. Rijmen and J. Daemen (Belgium) Serpent R. Anderson et al. (UK, Israel, Norway) Twofish B. Schneier et al. (USA) 2000/10/02: Rijndael was selected as AES

36

37 THE KEY PROBLEM!!!!!! 37

38 Key Problem Two ways to solve this problem Asymmetric cryptosystem Key agreement 38

39 Asymmetric Cryptosystem RSA Ron Rivest, Adi Shamir and Leonard Adleman Adi Shamir, Ron Rivest, Len Adleman 39

40 RSA 40

41 Key Management Diffie-Hellman key exchange published by Whitfield Diffie and Martin Hellman in

42 Key Management

43 Key Management Two party Three party Group Time-bound Etc.. 43

44 Q&A 44

1999 version 2001 simplified version

1999 version 2001 simplified version 香港中文大學讀書會 1999 version 2001 simplified version Author Simon Singh http://simonsingh.net/ 1. Fermat s Last Theorem the epic quest to Solve the World's Greatest Mathematical Problem(2007) 2. The Code Book(1999)

More information

Definition: For a positive integer n, if 0<a<n and gcd(a,n)=1, a is relatively prime to n. Ahmet Burak Can Hacettepe University

Definition: For a positive integer n, if 0<a<n and gcd(a,n)=1, a is relatively prime to n. Ahmet Burak Can Hacettepe University Number Theory, Public Key Cryptography, RSA Ahmet Burak Can Hacettepe University abc@hacettepe.edu.tr The Euler Phi Function For a positive integer n, if 0

More information

Cryptography. P. Danziger. Transmit...Bob...

Cryptography. P. Danziger. Transmit...Bob... 10.4 Cryptography P. Danziger 1 Cipher Schemes A cryptographic scheme is an example of a code. The special requirement is that the encoded message be difficult to retrieve without some special piece of

More information

Final Exam Math 105: Topics in Mathematics Cryptology, the Science of Secret Writing Rhodes College Tuesday, 30 April :30 11:00 a.m.

Final Exam Math 105: Topics in Mathematics Cryptology, the Science of Secret Writing Rhodes College Tuesday, 30 April :30 11:00 a.m. Final Exam Math 10: Topics in Mathematics Cryptology, the Science of Secret Writing Rhodes College Tuesday, 0 April 2002 :0 11:00 a.m. Instructions: Please be as neat as possible (use a pencil), and show

More information

CRYPTOGRAPHY AND NUMBER THEORY

CRYPTOGRAPHY AND NUMBER THEORY CRYPTOGRAPHY AND NUMBER THEORY XINYU SHI Abstract. In this paper, we will discuss a few examples of cryptographic systems, categorized into two different types: symmetric and asymmetric cryptography. We

More information

Cook-Levin Theorem. SAT is NP-complete

Cook-Levin Theorem. SAT is NP-complete Cook-Levin Theorem SAT is NP-complete In other words SAT NP A NP A P SAT 1 Consider any A NP NTM N that decides A in polytime n k For any input w Σ * valid tableau of configurations 2 Properties of an

More information

Slides by Kent Seamons and Tim van der Horst Last Updated: Oct 1, 2013

Slides by Kent Seamons and Tim van der Horst Last Updated: Oct 1, 2013 RSA Slides by Kent Seamons and Tim van der Horst Last Updated: Oct 1, 2013 Recap Recap Number theory o What is a prime number? o What is prime factorization? o What is a GCD? o What does relatively prime

More information

Great Theoretical Ideas in Computer Science

Great Theoretical Ideas in Computer Science 15-251 Great Theoretical Ideas in Computer Science Lecture 22: Cryptography November 12th, 2015 What is cryptography about? Adversary Eavesdropper I will cut your throat I will cut your throat What is

More information

Powers in Modular Arithmetic, and RSA Public Key Cryptography

Powers in Modular Arithmetic, and RSA Public Key Cryptography 1 Powers in Modular Arithmetic, and RSA Public Key Cryptography Lecture notes for Access 2006, by Nick Korevaar. It was a long time from Mary Queen of Scotts and substitution ciphers until the end of the

More information

An Introduction to Cryptography

An Introduction to Cryptography An Introduction to Cryptography Spotlight on Science J. Robert Buchanan Department of Mathematics Spring 2008 What is Cryptography? cryptography: study of methods for sending messages in a form that only

More information

My brief introduction to cryptography

My brief introduction to cryptography My brief introduction to cryptography David Thomson dthomson@math.carleton.ca Carleton University September 7, 2013 introduction to cryptography September 7, 2013 1 / 28 Outline 1 The general framework

More information

Innovation and Cryptoventures. Cryptology. Campbell R. Harvey. Duke University, NBER and Investment Strategy Advisor, Man Group, plc.

Innovation and Cryptoventures. Cryptology. Campbell R. Harvey. Duke University, NBER and Investment Strategy Advisor, Man Group, plc. Innovation and Cryptoventures Cryptology Campbell R. Harvey Duke University, NBER and Investment Strategy Advisor, Man Group, plc January 20, 2017 Overview Cryptology Cryptography Cryptanalysis Symmetric

More information

Cryptography CS 555. Topic 2: Evolution of Classical Cryptography CS555. Topic 2 1

Cryptography CS 555. Topic 2: Evolution of Classical Cryptography CS555. Topic 2 1 Cryptography CS 555 Topic 2: Evolution of Classical Cryptography Topic 2 1 Lecture Outline Basics of probability Vigenere cipher. Attacks on Vigenere: Kasisky Test and Index of Coincidence Cipher machines:

More information

CryptoCurrency and Blockchain (1) Status of Bitcoin 密碼貨幣市值 密碼貨幣市值 金融科技導論 陳君明

CryptoCurrency and Blockchain (1) Status of Bitcoin 密碼貨幣市值 密碼貨幣市值 金融科技導論 陳君明 CryptoCurrency and Blockchain (1) 金融科技導論 Status of Bitcoin 陳君明 jmchen@crypto.tw 2 密碼貨幣市值 http://coinmarketcap.com 2018.12.03 12:00 密碼貨幣市值 http://coinmarketcap.com 2017.12.11 12:00 密碼貨幣市值 http://coinmarketcap.com

More information

Public-key Cryptography and elliptic curves

Public-key Cryptography and elliptic curves Public-key Cryptography and elliptic curves Dan Nichols nichols@math.umass.edu University of Massachusetts Oct. 14, 2015 Cryptography basics Cryptography is the study of secure communications. Here are

More information

Number Theory in Cryptography

Number Theory in Cryptography Number Theory in Cryptography Introduction September 20, 2006 Universidad de los Andes 1 Guessing Numbers 2 Guessing Numbers (person x) (last 6 digits of phone number of x) 3 Guessing Numbers (person x)

More information

RSA RSA public key cryptosystem

RSA RSA public key cryptosystem RSA 1 RSA As we have seen, the security of most cipher systems rests on the users keeping secret a special key, for anyone possessing the key can encrypt and/or decrypt the messages sent between them.

More information

Chapter 8 Public-key Cryptography and Digital Signatures

Chapter 8 Public-key Cryptography and Digital Signatures Chapter 8 Public-key Cryptography and Digital Signatures v 1. Introduction to Public-key Cryptography 2. Example of Public-key Algorithm: Diffie- Hellman Key Exchange Scheme 3. RSA Encryption and Digital

More information

CSCI3381-Cryptography

CSCI3381-Cryptography CSCI3381-Cryptography Lecture 2: Classical Cryptosystems September 3, 2014 This describes some cryptographic systems in use before the advent of computers. All of these methods are quite insecure, from

More information

8.1 Principles of Public-Key Cryptosystems

8.1 Principles of Public-Key Cryptosystems Public-key cryptography is a radical departure from all that has gone before. Right up to modern times all cryptographic systems have been based on the elementary tools of substitution and permutation.

More information

Introduction to Cryptology. Lecture 2

Introduction to Cryptology. Lecture 2 Introduction to Cryptology Lecture 2 Announcements 2 nd vs. 1 st edition of textbook HW1 due Tuesday 2/9 Readings/quizzes (on Canvas) due Friday 2/12 Agenda Last time Historical ciphers and their cryptanalysis

More information

University of Regina Department of Mathematics & Statistics Final Examination (April 21, 2009)

University of Regina Department of Mathematics & Statistics Final Examination (April 21, 2009) Make sure that this examination has 10 numbered pages University of Regina Department of Mathematics & Statistics Final Examination 200910 (April 21, 2009) Mathematics 124 The Art and Science of Secret

More information

Biomedical Security. Overview 9/15/2017. Erwin M. Bakker

Biomedical Security. Overview 9/15/2017. Erwin M. Bakker Biomedical Security Erwin M. Bakker Overview Cryptography: Algorithms Cryptography: Protocols Pretty Good Privacy (PGP) / B. Schneier Workshop Biomedical Security Biomedical Application Security (guest

More information

Introduction to Cryptography. Susan Hohenberger

Introduction to Cryptography. Susan Hohenberger Introduction to Cryptography Susan Hohenberger 1 Cryptography -- from art to science -- more than just encryption -- essential today for non-military applications 2 Symmetric Crypto Shared secret K =>

More information

The RSA cryptosystem and primality tests

The RSA cryptosystem and primality tests Mathematics, KTH Bengt Ek November 2015 Supplementary material for SF2736, Discrete mathematics: The RSA cryptosystem and primality tests Secret codes (i.e. codes used to make messages unreadable to outsiders

More information

Real scripts backgrounder 3 - Polyalphabetic encipherment - XOR as a cipher - RSA algorithm. David Morgan

Real scripts backgrounder 3 - Polyalphabetic encipherment - XOR as a cipher - RSA algorithm. David Morgan Real scripts backgrounder 3 - Polyalphabetic encipherment - XOR as a cipher - RSA algorithm David Morgan XOR as a cipher Bit element encipherment elements are 0 and 1 use modulo-2 arithmetic Example: 1

More information

Cryptanalysis on An ElGamal-Like Cryptosystem for Encrypting Large Messages

Cryptanalysis on An ElGamal-Like Cryptosystem for Encrypting Large Messages Cryptanalysis on An ElGamal-Like Cryptosystem for Encrypting Large Messages MEI-NA WANG Institute for Information Industry Networks and Multimedia Institute TAIWAN, R.O.C. myrawang@iii.org.tw SUNG-MING

More information

dit-upm RSA Cybersecurity Cryptography

dit-upm RSA Cybersecurity Cryptography -upm Cybersecurity Cryptography José A. Mañas < http://www.dit.upm.es/~pepe/> Information Technology Department Universidad Politécnica de Madrid 4 october 2018 public key (asymmetric) public key secret

More information

Public-key Cryptography and elliptic curves

Public-key Cryptography and elliptic curves Public-key Cryptography and elliptic curves Dan Nichols University of Massachusetts Amherst nichols@math.umass.edu WINRS Research Symposium Brown University March 4, 2017 Cryptography basics Cryptography

More information

ECE 646 Lecture 9. RSA: Genesis, operation & security

ECE 646 Lecture 9. RSA: Genesis, operation & security ECE 646 Lecture 9 RSA: Genesis, operation & security Required Reading (1) W. Stallings, "Cryptography and Network-Security," Chapter 8.1 Prime Numbers Chapter 8.2 Fermat's and Euler's Theorems Chapter

More information

10 Modular Arithmetic and Cryptography

10 Modular Arithmetic and Cryptography 10 Modular Arithmetic and Cryptography 10.1 Encryption and Decryption Encryption is used to send messages secretly. The sender has a message or plaintext. Encryption by the sender takes the plaintext and

More information

Cryptography. The Making and Breaking of Secret Codes. 5/29/2009 John C. Polking, Rice University 1

Cryptography. The Making and Breaking of Secret Codes. 5/29/2009 John C. Polking, Rice University 1 Cryptography The Making and Breaking of Secret Codes. 5/29/2009 John C. Polking, Rice University 1 Need for Cryptography Many areas of human endeavor require secret communication. Modern methods of communication

More information

... Assignment 3 - Cryptography. Information & Communication Security (WS 2018/19) Abtin Shahkarami, M.Sc.

... Assignment 3 - Cryptography. Information & Communication Security (WS 2018/19) Abtin Shahkarami, M.Sc. Assignment 3 - Cryptography Information & Communication Security (WS 2018/19) Abtin Shahkarami, M.Sc. Deutsche Telekom Chair of Mobile Business & Multilateral Security Goethe-University Frankfurt a. M.

More information

Security Issues in Cloud Computing Modern Cryptography II Asymmetric Cryptography

Security Issues in Cloud Computing Modern Cryptography II Asymmetric Cryptography Security Issues in Cloud Computing Modern Cryptography II Asymmetric Cryptography Peter Schwabe October 21 and 28, 2011 So far we assumed that Alice and Bob both have some key, which nobody else has. How

More information

Candidates must show on each answer book the type of calculator used. Only calculators permitted under UEA Regulations may be used.

Candidates must show on each answer book the type of calculator used. Only calculators permitted under UEA Regulations may be used. UNIVERSITY OF EAST ANGLIA School of Mathematics May/June UG Examination 2010 2011 CRYPTOGRAPHY Time allowed: 2 hours Attempt THREE questions. Candidates must show on each answer book the type of calculator

More information

PHI7470 Topics in Applied Philosophy: The Philosopher and Sociology

PHI7470 Topics in Applied Philosophy: The Philosopher and Sociology PHI7470 Topics in Applied Philosophy: The Philosopher and Sociology Mr. Lui Ping Keung (frcisco@netvigator.com) Sociology grew and continues to grow from philosophy. At the same time, sociology has made

More information

Introduction to Cryptography

Introduction to Cryptography T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A Introduction to Cryptography EECE 412 1 Module Outline Historical background Classic ciphers One-time pad The Random Oracle model Random functions:

More information

COS433/Math 473: Cryptography. Mark Zhandry Princeton University Spring 2017

COS433/Math 473: Cryptography. Mark Zhandry Princeton University Spring 2017 COS433/Math 473: Cryptography Mark Zhandry Princeton University Spring 2017 Previously on COS 433 Pre- modern Cryptography 1900 B.C. mid 1900 s A.D With few exceptions, synonymous with encryption c = Enc(k,m)

More information

Circuit Complexity. Circuit complexity is based on boolean circuits instead of Turing machines.

Circuit Complexity. Circuit complexity is based on boolean circuits instead of Turing machines. Circuit Complexity Circuit complexity is based on boolean circuits instead of Turing machines. A boolean circuit with n inputs computes a boolean function of n variables. Now, identify true/1 with yes

More information

Public Key Cryptography

Public Key Cryptography Public Key Cryptography Spotlight on Science J. Robert Buchanan Department of Mathematics 2011 What is Cryptography? cryptography: study of methods for sending messages in a form that only be understood

More information

I.T.I.S. E. DIVINI SAN SEVERINO MARCHE. CRIPTOGRAPHY Monday 9th January 2006

I.T.I.S. E. DIVINI SAN SEVERINO MARCHE. CRIPTOGRAPHY Monday 9th January 2006 I.T.I.S. E. DIVINI SAN SEVERINO MARCHE CRIPTOGRAPHY Monday 9th January 2006 History of cryptography The history of cryptography dates back thousands of years. Until recent decades, it has been a history

More information

Clock Arithmetic and Euclid s Algorithm

Clock Arithmetic and Euclid s Algorithm Clock Arithmetic and Euclid s Algorithm Lecture notes for Access 2008 by Erin Chamberlain. Earlier we discussed Caesar Shifts and other substitution ciphers, and we saw how easy it was to break these ciphers

More information

1/18 2/16 3/20 4/17 5/6 6/9 7/14 % Please do not write in the spaces above.

1/18 2/16 3/20 4/17 5/6 6/9 7/14 % Please do not write in the spaces above. 1/18 2/16 3/20 4/17 5/6 6/9 7/14 % Please do not write in the spaces above. Directions: You have 50 minutes in which to complete this exam. Please make sure that you read through this entire exam before

More information

Lecture 5: Arithmetic Modulo m, Primes and Greatest Common Divisors Lecturer: Lale Özkahya

Lecture 5: Arithmetic Modulo m, Primes and Greatest Common Divisors Lecturer: Lale Özkahya BBM 205 Discrete Mathematics Hacettepe University http://web.cs.hacettepe.edu.tr/ bbm205 Lecture 5: Arithmetic Modulo m, Primes and Greatest Common Divisors Lecturer: Lale Özkahya Resources: Kenneth Rosen,

More information

monoalphabetic cryptanalysis Character Frequencies (English) Security in Computing Common English Digrams and Trigrams Chapter 2

monoalphabetic cryptanalysis Character Frequencies (English) Security in Computing Common English Digrams and Trigrams Chapter 2 Common English Digrams and Trigrams Digrams EN RE ER NT TH ON IN TF AN OR Trigrams ENT ION AND ING IVE TIO FOR OUR THI ONE monoalphabetic cryptanalysis See class example Pfleeger, Security in Computing,

More information

CS 4770: Cryptography. CS 6750: Cryptography and Communication Security. Alina Oprea Associate Professor, CCIS Northeastern University

CS 4770: Cryptography. CS 6750: Cryptography and Communication Security. Alina Oprea Associate Professor, CCIS Northeastern University CS 4770: Cryptography CS 6750: Cryptography and Communication Security Alina Oprea Associate Professor, CCIS Northeastern University February 5 2018 Review Relation between PRF and PRG Construct PRF from

More information

CPE 776:DATA SECURITY & CRYPTOGRAPHY. Some Number Theory and Classical Crypto Systems

CPE 776:DATA SECURITY & CRYPTOGRAPHY. Some Number Theory and Classical Crypto Systems CPE 776:DATA SECURITY & CRYPTOGRAPHY Some Number Theory and Classical Crypto Systems Dr. Lo ai Tawalbeh Computer Engineering Department Jordan University of Science and Technology Jordan Some Number Theory

More information

RSA Algorithm. Factoring, EulerPhi, Breaking RSA. Çetin Kaya Koç Spring / 14

RSA Algorithm. Factoring, EulerPhi, Breaking RSA.   Çetin Kaya Koç Spring / 14 RSA Algorithm http://koclab.org Çetin Kaya Koç Spring 2018 1 / 14 Well-Known One-Way Functions Discrete Logarithm: Given p, g, and x, computing y in y = g x (mod p) is EASY Given p, g, y, computing x in

More information

Polyalphabetic Ciphers

Polyalphabetic Ciphers Polyalphabetic Ciphers 1 Basic Idea: The substitution alphabet used for enciphering successive letters of plaintext changes. The selection of alphabets may depend on a keyword, a key stream, or electromechanical

More information

Cryptography and Secure Communication Protocols

Cryptography and Secure Communication Protocols Cryptography and Secure Communication Protocols Jayadev Misra The University of Texas at Austin October 1, 2003 Contents 1 Introduction 1 2 Early Encryption Schemes 2 2.1 Substitution cyphers.........................

More information

Shift Cipher. For 0 i 25, the ith plaintext character is. E.g. k = 3

Shift Cipher. For 0 i 25, the ith plaintext character is. E.g. k = 3 Shift Cipher For 0 i 25, the ith plaintext character is shifted by some value 0 k 25 (mod 26). E.g. k = 3 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 D E F G H I J K L M N O P Q R S T U V W X Y

More information

Biomedical Security. Some Security News 9/17/2018. Erwin M. Bakker. Blockchains are not safe for voting (slashdot.org) : From: paragonie.

Biomedical Security. Some Security News 9/17/2018. Erwin M. Bakker. Blockchains are not safe for voting (slashdot.org) : From: paragonie. Biomedical Security Erwin M. Bakker Some Security News From: NYTimes Blockchains are not safe for voting (slashdot.org) : From Motherboard.vice.com ECDAA: Eliptic Curve Direct Anonymous Attestation for

More information

Sol: First, calculate the number of integers which are relative prime with = (1 1 7 ) (1 1 3 ) = = 2268

Sol: First, calculate the number of integers which are relative prime with = (1 1 7 ) (1 1 3 ) = = 2268 ò{çd@àt ø 2005.0.3. Suppose the plaintext alphabets include a z, A Z, 0 9, and the space character, therefore, we work on 63 instead of 26 for an affine cipher. How many keys are possible? What if we add

More information

Ti Secured communications

Ti Secured communications Ti5318800 Secured communications Pekka Jäppinen September 20, 2007 Pekka Jäppinen, Lappeenranta University of Technology: September 20, 2007 Relies on use of two keys: Public and private Sometimes called

More information

Data and information security: 2. Classical cryptography

Data and information security: 2. Classical cryptography ICS 423: s Data and information security: 2. Classical cryptography UHM ICS 423 Fall 2014 Outline ICS 423: s s and crypto systems ciphers ciphers Breaking ciphers What did we learn? Outline ICS 423: s

More information

Week 7 An Application to Cryptography

Week 7 An Application to Cryptography SECTION 9. EULER S GENERALIZATION OF FERMAT S THEOREM 55 Week 7 An Application to Cryptography Cryptography the study of the design and analysis of mathematical techniques that ensure secure communications

More information

Cryptography. pieces from work by Gordon Royle

Cryptography. pieces from work by Gordon Royle Cryptography pieces from work by Gordon Royle The set-up Cryptography is the mathematics of devising secure communication systems, whereas cryptanalysis is the mathematics of breaking such systems. We

More information

Public Key 9/17/2018. Symmetric Cryptography Review. Symmetric Cryptography: Shortcomings (1) Symmetric Cryptography: Analogy

Public Key 9/17/2018. Symmetric Cryptography Review. Symmetric Cryptography: Shortcomings (1) Symmetric Cryptography: Analogy Symmetric Cryptography Review Alice Bob Public Key x e K (x) y d K (y) x K K Instructor: Dr. Wei (Lisa) Li Department of Computer Science, GSU Two properties of symmetric (secret-key) crypto-systems: The

More information

Number Theory & Modern Cryptography

Number Theory & Modern Cryptography Number Theory & Modern Cryptography Week 12 Stallings: Ch 4, 8, 9, 10 CNT-4403: 2.April.2015 1 Introduction Increasing importance in cryptography Public Key Crypto and Signatures Concern operations on

More information

RSA. Ramki Thurimella

RSA. Ramki Thurimella RSA Ramki Thurimella Public-Key Cryptography Symmetric cryptography: same key is used for encryption and decryption. Asymmetric cryptography: different keys used for encryption and decryption. Public-Key

More information

Asymmetric Encryption

Asymmetric Encryption -3 s s Encryption Comp Sci 3600 Outline -3 s s 1-3 2 3 4 5 s s Outline -3 s s 1-3 2 3 4 5 s s Function Using Bitwise XOR -3 s s Key Properties for -3 s s The most important property of a hash function

More information

secretsaremadetobefoundoutwithtime UGETGVUCTGOCFGVQDGHQWPFQWVYKVJVKOG Breaking the Code

secretsaremadetobefoundoutwithtime UGETGVUCTGOCFGVQDGHQWPFQWVYKVJVKOG Breaking the Code Breaking the Code To keep your secret is wisdom; but to expect others to keep it is folly. Samuel Johnson Secrets are made to be found out with time Charles Sanford Codes have been used by the military

More information

Simple Codes MTH 440

Simple Codes MTH 440 Simple Codes MTH 440 Not all codes are for the purpose of secrecy Morse Code ASCII Zip codes Area codes Library book codes Credit Cards ASCII Code Steganography: Hidden in plain sight (example from http://www.bbc.co.uk/news/10

More information

Discrete mathematics I - Number theory

Discrete mathematics I - Number theory Discrete mathematics I - Number theory Emil Vatai (based on hungarian slides by László Mérai) 1 January 31, 2018 1 Financed from the financial support ELTE won from the Higher Education

More information

Public Key Algorithms

Public Key Algorithms Public Key Algorithms Raj Jain Washington University in Saint Louis Saint Louis, MO 63130 Jain@cse.wustl.edu Audio/Video recordings of this lecture are available at: http://www.cse.wustl.edu/~jain/cse571-09/

More information

Cryptography: A Fairy Tale for Mathematicians and Starring Mathematicians!

Cryptography: A Fairy Tale for Mathematicians and Starring Mathematicians! Cryptography: A Fairy Tale for Mathematicians and Starring Mathematicians! University of California, Berkeley Mathematics Undergraduate Student Association October 27, 2014 Why Crypto? So why on earth

More information

Post-Quantum Cryptography

Post-Quantum Cryptography Post-Quantum Cryptography Sebastian Schmittner Institute for Theoretical Physics University of Cologne 2015-10-26 Talk @ U23 @ CCC Cologne This work is licensed under a Creative Commons Attribution-ShareAlike

More information

CIS 551 / TCOM 401 Computer and Network Security

CIS 551 / TCOM 401 Computer and Network Security CIS 551 / TCOM 401 Computer and Network Security Spring 2008 Lecture 15 3/20/08 CIS/TCOM 551 1 Announcements Project 3 available on the web. Get the handout in class today. Project 3 is due April 4th It

More information

AN INTRODUCTION TO THE UNDERLYING COMPUTATIONAL PROBLEM OF THE ELGAMAL CRYPTOSYSTEM

AN INTRODUCTION TO THE UNDERLYING COMPUTATIONAL PROBLEM OF THE ELGAMAL CRYPTOSYSTEM AN INTRODUCTION TO THE UNDERLYING COMPUTATIONAL PROBLEM OF THE ELGAMAL CRYPTOSYSTEM VORA,VRUSHANK APPRENTICE PROGRAM Abstract. This paper will analyze the strengths and weaknesses of the underlying computational

More information

CPSC 467: Cryptography and Computer Security

CPSC 467: Cryptography and Computer Security CPSC 467: Cryptography and Computer Security Michael J. Fischer Lecture 11 October 7, 2015 CPSC 467, Lecture 11 1/37 Digital Signature Algorithms Signatures from commutative cryptosystems Signatures from

More information

Theme : Cryptography. Instructor : Prof. C Pandu Rangan. Speaker : Arun Moorthy CS

Theme : Cryptography. Instructor : Prof. C Pandu Rangan. Speaker : Arun Moorthy CS 1 C Theme : Cryptography Instructor : Prof. C Pandu Rangan Speaker : Arun Moorthy 93115 CS 2 RSA Cryptosystem Outline of the Talk! Introduction to RSA! Working of the RSA system and associated terminology!

More information

Gurgen Khachatrian Martun Karapetyan

Gurgen Khachatrian Martun Karapetyan 34 International Journal Information Theories and Applications, Vol. 23, Number 1, (c) 2016 On a public key encryption algorithm based on Permutation Polynomials and performance analyses Gurgen Khachatrian

More information

BLOCK CIPHERS KEY-RECOVERY SECURITY

BLOCK CIPHERS KEY-RECOVERY SECURITY BLOCK CIPHERS and KEY-RECOVERY SECURITY Mihir Bellare UCSD 1 Notation Mihir Bellare UCSD 2 Notation {0, 1} n is the set of n-bit strings and {0, 1} is the set of all strings of finite length. By ε we denote

More information

Math 412: Number Theory Lecture 13 Applications of

Math 412: Number Theory Lecture 13 Applications of Math 412: Number Theory Lecture 13 Applications of Gexin Yu gyu@wm.edu College of William and Mary Partition of integers A partition λ of the positive integer n is a non increasing sequence of positive

More information

Lecture (04) Classical Encryption Techniques (III)

Lecture (04) Classical Encryption Techniques (III) Lecture (04) Classical Encryption Techniques (III) Dr. Ahmed M. ElShafee ١ Playfair Cipher one approach to improve security was to encrypt multiple letters the Playfair Cipher is an example invented by

More information

one approach to improve security was to encrypt multiple letters invented by Charles Wheatstone in 1854, but named after his

one approach to improve security was to encrypt multiple letters invented by Charles Wheatstone in 1854, but named after his Lecture (04) Classical Encryption Techniques (III) Dr. Ahmed M. ElShafee ١ The rules for filling in this 5x5 matrix are: L to R, top to bottom, first with keyword after duplicate letters have been removed,

More information

ECE297:11 Lecture 12

ECE297:11 Lecture 12 ECE297:11 Lecture 12 RSA Genesis, operation & security Public Key (Asymmetric) Cryptosystems Public key of Bob - K B Private key of Bob - k B Network Alice Encryption Decryption Bob 1 Trap-door one-way

More information

5. Classical Cryptographic Techniques from modular arithmetic perspective

5. Classical Cryptographic Techniques from modular arithmetic perspective . Classical Cryptographic Techniques from modular arithmetic perspective By classical cryptography we mean methods of encipherment that have been used from antiquity through the middle of the twentieth

More information

The Elliptic Curve in https

The Elliptic Curve in https The Elliptic Curve in https Marco Streng Universiteit Leiden 25 November 2014 Marco Streng (Universiteit Leiden) The Elliptic Curve in https 25-11-2014 1 The s in https:// HyperText Transfer Protocol

More information

Differential-Linear Cryptanalysis of Serpent

Differential-Linear Cryptanalysis of Serpent Differential-Linear Cryptanalysis of Serpent Eli Biham, 1 Orr Dunkelman, 1 Nathan Keller 2 1 Computer Science Department, Technion. Haifa 32000, Israel {biham,orrd}@cs.technion.ac.il 2 Mathematics Department,

More information

A Quick Look at some Mathematics and Cryptography A Talk for CLIR at UConn

A Quick Look at some Mathematics and Cryptography A Talk for CLIR at UConn A Quick Look at some Mathematics and Cryptography A Talk for CLIR at UConn Jeremy Teitelbaum September 5, 2014 Secret Key Ciphers A cipher is a method of communication in which the letters making up the

More information

A Five-Round Algebraic Property of the Advanced Encryption Standard

A Five-Round Algebraic Property of the Advanced Encryption Standard A Five-Round Algebraic Property of the Advanced Encryption Standard Jianyong Huang, Jennifer Seberry and Willy Susilo Centre for Computer and Information Security Research (CCI) School of Computer Science

More information

Lecture V : Public Key Cryptography

Lecture V : Public Key Cryptography Lecture V : Public Key Cryptography Internet Security: Principles & Practices John K. Zao, PhD (Harvard) SMIEEE Amir Rezapoor Computer Science Department, National Chiao Tung University 2 Outline Functional

More information

THE UNIVERSITY OF CALGARY FACULTY OF SCIENCE DEPARTMENT OF COMPUTER SCIENCE DEPARTMENT OF MATHEMATICS & STATISTICS MIDTERM EXAMINATION 1 FALL 2018

THE UNIVERSITY OF CALGARY FACULTY OF SCIENCE DEPARTMENT OF COMPUTER SCIENCE DEPARTMENT OF MATHEMATICS & STATISTICS MIDTERM EXAMINATION 1 FALL 2018 THE UNIVERSITY OF CALGARY FACULTY OF SCIENCE DEPARTMENT OF COMPUTER SCIENCE DEPARTMENT OF MATHEMATICS & STATISTICS MIDTERM EXAMINATION 1 FALL 2018 CPSC 418/MATH 318 L01 October 17, 2018 Time: 50 minutes

More information

Lecture 8 - Cryptography and Information Theory

Lecture 8 - Cryptography and Information Theory Lecture 8 - Cryptography and Information Theory Jan Bouda FI MU April 22, 2010 Jan Bouda (FI MU) Lecture 8 - Cryptography and Information Theory April 22, 2010 1 / 25 Part I Cryptosystem Jan Bouda (FI

More information

19. Coding for Secrecy

19. Coding for Secrecy 19. Coding for Secrecy 19.1 Introduction Protecting sensitive information from the prying eyes and ears of others is an important issue today as much as it has been for thousands of years. Government secrets,

More information

Chapter 2 Classical Cryptosystems

Chapter 2 Classical Cryptosystems Chapter 2 Classical Cryptosystems Note We will use the convention that plaintext will be lowercase and ciphertext will be in all capitals. 2.1 Shift Ciphers The idea of the Caesar cipher: To encrypt, shift

More information

Public Key Cryptography

Public Key Cryptography T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A Public Key Cryptography EECE 412 1 What is it? Two keys Sender uses recipient s public key to encrypt Receiver uses his private key to decrypt

More information

Computer Security. 07. Cryptography. Paul Krzyzanowski. Rutgers University. Spring 2017

Computer Security. 07. Cryptography. Paul Krzyzanowski. Rutgers University. Spring 2017 Computer Security 07. Cryptography Paul Krzyzanowski Rutgers University Spring 2017 March 26, 2017 CS 419 2017 Paul Krzyzanowski 1 cryptography κρυπός γραφία hidden writing A secret manner of writing,

More information

Question: Total Points: Score:

Question: Total Points: Score: University of California, Irvine COMPSCI 134: Elements of Cryptography and Computer and Network Security Midterm Exam (Fall 2016) Duration: 90 minutes November 2, 2016, 7pm-8:30pm Name (First, Last): Please

More information

Public Key Cryptography

Public Key Cryptography Public Key Cryptography Ali El Kaafarani 1 Mathematical Institute 2 PQShield Ltd. 1 of 44 Outline 1 Public Key Encryption: security notions 2 RSA Encryption Scheme 2 of 44 Course main reference 3 of 44

More information

EE4.07 Coding Theory

EE4.07 Coding Theory EE4.07 Coding Theory W. Dai Imperial College London (IC) 2017 W. Dai (IC) EE4.07 Coding Theory 2017 page 0-1 Syllabus Instructor: Dr. Wei Dai Lectures: Monday 16:00-17:00, 509B (Wks 2-11, 09/10/2017-11/12/2017)

More information

The CRYPTOGRAPHY. Classical cryptography. 1. History of cryptography

The CRYPTOGRAPHY. Classical cryptography. 1. History of cryptography The CRYPTOGRAPHY 1. History of cryptography The history of cryptography dates back thousands of years. Until recent decades, it has been a history of classic cryptography of methods of encryption that

More information

RSA ENCRYPTION USING THREE MERSENNE PRIMES

RSA ENCRYPTION USING THREE MERSENNE PRIMES Int. J. Chem. Sci.: 14(4), 2016, 2273-2278 ISSN 0972-768X www.sadgurupublications.com RSA ENCRYPTION USING THREE MERSENNE PRIMES Ch. J. L. PADMAJA a*, V. S. BHAGAVAN a and B. SRINIVAS b a Department of

More information

大原利明 算法点竄指南 点竄術 算 額 絵馬堂

大原利明 算法点竄指南 点竄術 算 額 絵馬堂 算額 大原利明 算法点竄指南 点竄術 算 額 絵馬 絵 馬 絵馬堂 甲 一 乙 二 丙 三 丁 四 戊 五 己 六 庚 七 辛 八 壬 九 癸 十 十五 二十 百 千 甲 乙 丙 丁 傍書法 関孝和 点竄術 松永良弼 甲 甲 甲 甲 甲 乙 甲 甲 乙 甲 乙 甲 乙 甲 乙 丙 丁 戊 a + b 2 c 甲 a a 二乙 2 b b 2 小 c c SOLVING SANGAKU 5 3.1.

More information

Introduction to Cryptography

Introduction to Cryptography slides available for download at: www.math.cm.is.nagoya-u.ac.jp/~buscemi/crypto.pdf Introduction to Cryptography from ancient ciphers to quantum cryptography ブシェーミ F( 計算機数理科学専攻 )buscemi@is.nagoya-u.ac.jp

More information

QUANTUM CRYPTOGRAPHY. BCS, Plymouth University, December 1, Professor Kurt Langfeld Centre for Mathematical Sciences, Plymouth University

QUANTUM CRYPTOGRAPHY. BCS, Plymouth University, December 1, Professor Kurt Langfeld Centre for Mathematical Sciences, Plymouth University QUANTUM CRYPTOGRAPHY BCS, Plymouth University, December 1, 2015 Professor Kurt Langfeld Centre for Mathematical Sciences, Plymouth University OUTLOOK: Quantum Physics Essentials: particles and light are

More information

L7. Diffie-Hellman (Key Exchange) Protocol. Rocky K. C. Chang, 5 March 2015

L7. Diffie-Hellman (Key Exchange) Protocol. Rocky K. C. Chang, 5 March 2015 L7. Diffie-Hellman (Key Exchange) Protocol Rocky K. C. Chang, 5 March 2015 1 Outline The basic foundation: multiplicative group modulo prime The basic Diffie-Hellman (DH) protocol The discrete logarithm

More information

ACCESS: Cryptography

ACCESS: Cryptography ACCESS: Cryptography E. Chamberlain, F. Guevara Vasquez, C. Hohenegger, and N. Korevaar June 24, 2014 1 Introduction Cryptography or the art of transmitted hidden messages has been long associated for

More information

Historical cryptography

Historical cryptography Historical cryptography Alice Bob Eve CSCI 470: Web Science Keith Vertanen Overview Historical cryptography Monoalphabetic substitution ciphers Breaking them Some improvements The cipher of Mary Queen

More information