Applied Cryptography

1
Applied Cryptography

• Main goal
• Give some practical experience on cryptographic
  technics used today.
• Show how to use existing cryptographic software.
• Examination Practical assignments and written
  exam
• Homepage containg latest course information
  http//www.nada.kth.se/marten/AppliedCryptography
  
• Check course program (from homepage) for detailed
  information
• First time course is given feedback welcome!

2
Requirements

• Attend lectures (if you want to)
• Solve the three assigments to get bonus points.
  (Not required, but highly recommended.)
• Each assignment replaces a problem at the exam
• By solving the assignments you dont have to
  solve the problem at the exam
• The assignments will be programming tasks to be
  solved in a language of your choice
• Pass the written exam!

3
Outline of course program

• N.B. Course program is subject to change. Check
  the home page for the latest information
• Lectures 1-4 Basic cryptographic functions
• Lectures 5-8 SSL and PGP
• Lectures 9-10 Key management
• Lectures 11-12 Smartcards in financial
  transactions
• Lectures 13-14 To be decided. Possible areas
  Hardware solutions, e-commerce, firewalls and
  intrusion detection. Input welcome!

4
Why cryptography

• Reason for using cryptography
• Protect from eaves-dropping (confidentiality)
• Ensure data is not modified (integrity)
• Certify identity of sender (authenticity)
• Requirements (application dependent)
• Simple key management
• Low hardware requirements (smart card
  applications, mobile phones)
• Cost of bandwidth

5
Simple example substitution cipher

• The key is a permutation of the letters of the
  alphabet, i.e. a bijection
• Encryption is performed by substituting each
  letter for its corresponding letter
• Decryption is the same as encryption with the
  difference that the inverse is used

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Substitution cipher example

• Example Encrypt MY DOG ATE YOUR CAT using the
  key

ABCDEFGHIJKLMNOPQRSTUVWXYZ
UWGRPNQSBJXMECAIZOYTDFHKLV
U
7
Breaking the substitution cipher

• Substitution ciphers are easily broken using
  frequency analysis
• We use the fact that different letters (or
  combination of letters) occur with different
  probability
• Example break TK IL KQ JKT TK IL TBST CR TBL
  OULRTCKJ
• Frequency of letters in English ETAOINSHRDLU
• Most common two letter words OF TO IN IS IT BE
  BY HE AS ON AT OR AN SO IF NO

8
Symmetric vs. asymmetric cryptography

• Symmetric ciphers sender and recipient use the
  same key
• Dkey(Ekey(m)) m
• Substitution cipher is an example of a symmetric
  cipher
• Impractical for big systems number of keys is
  quadratic in the number of users
• The solution asymmtric algorithms. Think of a
  locked mailbox! Different keys for encryption and
  decryption
• Dprivate key(Epublic key(m)) m

9
Asymmetric cryptography

• Each user has a public and a private key
• The public key is published in a phone book
• The private key is kept secret
• Messages encrypted with the public key can be
  decrypted with the private key
• To send a message to Mårten, look up Mårtens
  public key in the phone book.
• Mårten can then decrypt the message with his
  private key
• Number of keys is linear in the number of users

10
RSA

• Asymmetric cryptographic algorithm published in
  1978
• The most popular asymmetric algorithm used today
• Now free to use patent expired in 2000
• Relies on the hardness of factoring a number
  consisting of two primes

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The RSA algorithm key generation

• Generate two primes p, q and set n pq
• Choose e such that gcd(e, (p 1)(q 1)) 1
• Compute d such that ed 1 mod ((p 1)(q 1))
• The public key is the pair (e, n)
• The private key is the pair (d, n)

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RSA encryption and decryption

• Message m number 0 lt m lt n
• Encryption E(m) me mod n
• Decryption D(m) md mod n
• Number theoretical exercise check that D(E(m))
  m.

13
Breaking RSA

• If we can factor n we can break RSA
• Suppose we know p, q such that pq n
• We can compute (p 1)(q 1)
• It is now trivial to compute d e-1 mod ((p
  1)(q 1))
• The largest number that is (publicly) known to
  have been factored today is 512 bits
• Other attacks exist for certain uses of RSA