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:
Check course program (from homepage) for detailed information
Homepage mirror at
Feb 11, 2003
Mårten Trolin

2. Requirements Attend lectures (if you want to)
Collect at least 30 points
Two practical assignments give up to 20 points each
Written exam gives up to 20 points.
Feb 11, 2003
Mårten Trolin

3. Outline of course program
N.B. Course program is subject to change. Check the home page for the latest information
Lectures 1-5: Basic cryptographic functions and principles
Lectures 6-8: Smartcards in financial transactions
Lectures 9-11: SSL and PGP
Lectures 12: Passwords
Exam on April 29th.
Feb 11, 2003
Mårten Trolin

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
Feb 11, 2003
Mårten Trolin

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
Feb 11, 2003
Mårten Trolin

6. Substitution cipher – example
Example: Encrypt MY DOG ATE YOUR CAT using the key
ABCDEFGHIJKLMNOPQRSTUVWXYZ
UWGRPNQSBJXMECAIZOYTDFHKLV
Feb 11, 2003
Mårten Trolin 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
Feb 11, 2003
Mårten Trolin

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
Feb 11, 2003
Mårten Trolin

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 Mårten’s 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
Feb 11, 2003
Mårten Trolin

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
Feb 11, 2003
Mårten Trolin

11. 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)
Feb 11, 2003
Mårten Trolin

12. RSA – encryption and decryption
Message m – number 0 < m < n
Encryption E(m) = me mod n
Decryption D(m) = md mod n
Number theoretical exercise – check that D(E(m)) = m.
Feb 11, 2003
Mårten Trolin

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
Feb 11, 2003
Mårten Trolin