Presentation is loading. Please wait.

Presentation is loading. Please wait.

Cryptography Made Easy Stuart Reges Principal Lecturer University of Washington.

Published byZachariah Paul Modified over 9 years ago

Similar presentations

Presentation on theme: "Cryptography Made Easy Stuart Reges Principal Lecturer University of Washington."— Presentation transcript:

1 Cryptography Made Easy Stuart Reges Principal Lecturer University of Washington

2 Why Study Cryptography? Secrets are intrinsically interesting So much real-life drama: Mary Queen of Scots executed for treason primary evidence was an encoded letter they tricked the conspirators with a forgery Students enjoy puzzles Real world application of mathematics

3 Some basic terminology Alice wants to send a secret message to Bob Eve is eavesdropping Cryptographers tell Alice and Bob how to encode their messages Cryptanalysts help Eve to break the code Historic battle between the cryptographers and the cryptanalysts that continues today

4 Start with an Algorithm The Spartans used a scytale in the fifth century BC (transposition cipher) Card trick Caesar cipher (substitution cipher): ABCDEFGHIJKLMNOPQRSTUVWXYZ GHIJKLMNOPQRSTUVWXYZABCDEF

5 Then add a secret key Both parties know that the secret word is "victory": ABCDEFGHIJKLMNOPQRSTUVWXYZ VICTORYABDEFGHJKLMNPQSUWXZ "state of the art" for hundreds of years Gave birth to cryptanalysis first in the Muslim world, later in Europe

6 Cryptographers vs Cryptanalysts A battle that continues today Cryptographers try to devise more clever algorithms and keys Cryptanalysts search for vulnerabilities Early cryptanalysts were linguists: frequency analysis properties of letters

7 Vigenère Square (polyalphabetic)

8 Vigenère Cipher More secure than simple substitution Confederate cipher disk shown (replica) Based on a secret keyword or phrase Broken by Charles Babbage

9 Cipher Machines: Enigma Germans thought it was unbreakable Highly complex plugboard to swap arbitrary letters multiple scrambler disks reflector for symmetry Broken by the British in WW II (Alan Turing)

10 Public Key Encryption Proposed by Diffie, Hellman, Merkle First big idea: use a function that cannot be reversed (a humpty dumpty function): Alice tells Bob a function to apply using a public key, and Eve can’t compute the inverse Second big idea: use asymmetric keys (sender and receiver use different keys): Alice has a private key to compute the inverse Key benefit: doesn't require the sharing of a secret key

11 RSA Encryption Named for Ron Rivest, Adi Shamir, and Leonard Adleman Invented in 1977, still the premier approach Based on Fermat's Little Theorem: a p-1  1 (mod p) for prime p, gcd(a, p) = 1 Slight variation: a (p-1)(q-1)  1 (mod pq) for distinct primes p and q, gcd(a,pq) = 1 Requires large primes (100+ digit primes)

12 Example of RSA Pick two primes p and q, compute n = p  q Pick two numbers e and d, such that: e  d = k(p-1)(q-1) + 1 (for some k) Publish n and e (public key), encode with: (original message) e mod n Keep d, p and q secret (private key), decode with: (encoded message) d mod n

13 Why does it work? Original message is carried to the e power, then to the d power: (msg e ) d = msg ed Remember how we picked e and d: msg ed = msg k(p-1)(q-1) + 1 Apply some simple algebra: msg ed = (msg (p-1)(q-1) ) k  msg 1 Applying Fermat's Little Theorem: msg ed = (1) k  msg 1 = msg

14 Politics of Cryptography British actually discovered RSA first but kept it secret Phil Zimmerman tried to bring cryptography to the masses with PGP and ended up being investigated as an arms dealer by the FBI and a grand jury The NSA hires more mathematicians than any other organization

15 Exploring further Simon Singh, The Code Book RSA Factoring Challenge (unfortunately the prizes have been withdrawn) Shor's algorithm would break RSA if only we had a quantum computer Java's BigInteger: isProbablePrime, nextProbablePrime, modPow Collection of useful links: http://www.cs.washington.edu/homes/reges/cryptography

16 Card Trick Solution Given 5 cards, at least 2 will be of the same suit (pigeon hole principle) Pick 2 such cards: one will be hidden, the other will be the first card First card tells you the suit Hide the card that has a rank that is no more than 6 higher than the other (using modular wrap-around of king to ace) Arrange other cards to encode 1 through 6

17 Encoding 1 through 6 Figure out the low, middle, and high cards rank (ace < 2 < 3... < 10 < jack < queen < king) if ranks are the same, use the name of the suit (clubs < diamonds < hearts < spades) Some rule for the 6 arrangements, as in: 1: low/mid/hi3: mid/low/hi5: hi/low/mid 2: low/hi/mid4: mid/hi/low6: hi/mid/low

Download ppt "Cryptography Made Easy Stuart Reges Principal Lecturer University of Washington."

Similar presentations

the basics cryptography deals with techniques for secure communication in the presence of third parties (adversaries). modern cryptography uses mathematics,

the basics cryptography deals with techniques for secure communication in the presence of third parties (adversaries). modern cryptography uses mathematics,
Cryptology Making & Breaking Codes & Ciphers. AJ 1152 Cryptology Cryptography –Science of creating codes or ciphers Cryptanalysis –Science of breaking.

Cryptology Making & Breaking Codes & Ciphers. AJ 1152 Cryptology Cryptography –Science of creating codes or ciphers Cryptanalysis –Science of breaking.
CSE331: Introduction to Networks and Security Lecture 19 Fall 2002.

CSE331: Introduction to Networks and Security Lecture 19 Fall 2002.
BY : Darshana Chaturvedi.  INTRODUCTION  RSA ALGORITHM  EXAMPLES  RSA IS EFFECTIVE  FERMAT’S LITTLE THEOREM  EUCLID’S ALGORITHM  REFERENCES.

BY : Darshana Chaturvedi.  INTRODUCTION  RSA ALGORITHM  EXAMPLES  RSA IS EFFECTIVE  FERMAT’S LITTLE THEOREM  EUCLID’S ALGORITHM  REFERENCES.
A Presentation by: ~Ksenia Potapov ~Amariah Condon ~Janette Fong ~Janice Lau CRYPTOGRAPHY.

A Presentation by: ~Ksenia Potapov ~Amariah Condon ~Janette Fong ~Janice Lau CRYPTOGRAPHY.
Modern Cryptography.

Modern Cryptography.
95-712 OOP/Java1 Public Key Crytography From: Introduction to Algorithms Cormen, Leiserson and Rivest.

OOP/Java1 Public Key Crytography From: Introduction to Algorithms Cormen, Leiserson and Rivest.
Creating Secret Messages. 2 Why do we need to keep things secret? Historically, secret messages were used in wars and battles For example, the Enigma.

Creating Secret Messages. 2 Why do we need to keep things secret? Historically, secret messages were used in wars and battles For example, the Enigma.
Public-key Cryptography Montclair State University CMPT 109 J.W. Benham Spring, 1998.

Public-key Cryptography Montclair State University CMPT 109 J.W. Benham Spring, 1998.
CRYPTOGRAPHY Modern techniques. Computers and Cryptography Computers allow more sophisticated enciphering than mechanical devices Computers are faster.

CRYPTOGRAPHY Modern techniques. Computers and Cryptography Computers allow more sophisticated enciphering than mechanical devices Computers are faster.
Public Key Crytography1 From: Introduction to Algorithms Cormen, Leiserson and Rivest.

Public Key Crytography1 From: Introduction to Algorithms Cormen, Leiserson and Rivest.
Cryptography Lecture 11: Oct 12. Cryptography AliceBob Cryptography is the study of methods for sending and receiving secret messages. adversary Goal:

Cryptography Lecture 11: Oct 12. Cryptography AliceBob Cryptography is the study of methods for sending and receiving secret messages. adversary Goal:
Cryptography and Internet Security How mathematics makes it safe to shop on-line John Lindsay Orr University of Nebraska - Lincoln.

Cryptography and Internet Security How mathematics makes it safe to shop on-line John Lindsay Orr University of Nebraska - Lincoln.
1 Lecture #10 Public Key Algorithms HAIT Summer 2005 Shimrit Tzur-David.

1 Lecture #10 Public Key Algorithms HAIT Summer 2005 Shimrit Tzur-David.
Cryptography CS-103 Chapter 8. History Humans have been devising systems to encode information for at least 4000 years.Humans have been devising systems.

Cryptography CS-103 Chapter 8. History Humans have been devising systems to encode information for at least 4000 years.Humans have been devising systems.
Public Encryption: RSA

Public Encryption: RSA
RSA Encryption William Lu. RSA Background  Basic technique first discovered in 1973 by Clifford Cocks of CESG (part of British GCHQ)  Invented in 1977.

RSA Encryption William Lu. RSA Background  Basic technique first discovered in 1973 by Clifford Cocks of CESG (part of British GCHQ)  Invented in 1977.
Fall 2010/Lecture 311 CS 426 (Fall 2010) Public Key Encryption and Digital Signatures.

Fall 2010/Lecture 311 CS 426 (Fall 2010) Public Key Encryption and Digital Signatures.
8: Network Security8-1 Symmetric key cryptography symmetric key crypto: Bob and Alice share know same (symmetric) key: K r e.g., key is knowing substitution.

8: Network Security8-1 Symmetric key cryptography symmetric key crypto: Bob and Alice share know same (symmetric) key: K r e.g., key is knowing substitution.
Encryption. Introduction Computer security is the prevention of or protection against –access to information by unauthorized recipients –intentional but.

Encryption. Introduction Computer security is the prevention of or protection against –access to information by unauthorized recipients –intentional but.

Similar presentations

Ads by Google