... Assignment 3 - Cryptography. Information & Communication Security (WS 2016/17) Ahmed S. Yeusf, M.Sc.
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1 Assignment 3 - Cryptography Information & Communication Security (WS 2016/17) Ahmed S. Yeusf, M.Sc. Deutsche Telekom Chair of Mobile Business & Multilateral Security Goethe-University Frankfurt a. M.
2 Caesar cipher Symmetric vs. asymmetric ciphers Stream ciphers (Vernam code) Vigenére Cipher Agenda 2
3 Exercise 1: Caesar Cipher Break the following ciphertext, given that the Caesar cipher was used to produce it is: NZIVSNCZB QA QV OMZUIVG (Hint: Start by a permutation of the alphabet by 1, then 2, until the result makes sense in English) 3
4 Caesar Cipher Ciphertext: NZIVSNCZB QA QV OMZUIVG 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 assign a number for every character. This enables us to calculate with letters as if they were numbers. 4
5 Caesar Cipher For k є {0..25} we have: An encryption function: e: x -> (x+k) mod 26 A decryption function: d: x -> (x-k) mod 26 In this case k e = k d 5
6 Let s try: Caesar Cipher Key N Z I V S N C Z B Q A 1 M Y H U R M B Y A P Z 2 L X G T Q L A X Z O Y 3 K W F S P K Z W Y N X 4 J V E R O J Y V X M W 5 I U D Q N I X U W L V 6 H T C P M H W T V K U 7 G S B O L G V S U J T 8 F R A N K F U R T I S 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
7 The plaintext The key is 8 The plain text is: FRANKFURT IS IN GERMANY 7
8 Very simple form of encryption. Assessment of Caesar Cipher The encryption and decryption algorithms are very easy and fast to compute. It uses a very limited key space (n=26) Therefore, the encryption is very easy and fast to compromise. 8
9 Encryption - Decryption 9
10 Exercise 2: Symmetric vs. asymmetric crypto What is the difference between symmetric and asymmetric crypto systems? 10
11 Which crypto system has this disadvantage? Key Server Key Server knows all secret keys! 11
12 Which crypto system has this feature? Public-key Server Server knows no secret information! 12
13 Guess which crypto system this is Symmetric or Asymmetric? 13
14 This crypto system is? Symmetric or Asymmetric? 14
15 Symmetric Encryption Advantage: Algorithms are very fast Algorithm Performance * RC6 78 ms SERPENT 95 ms IDEA 170 ms MARS 80 ms TWOFISH 100 ms DES-ede 250 ms RIJNDEAL (AES) 65 ms * Encryption of 1 MB on a Pentium 2.8 GHz, using the FlexiProvider Java) [J. Buchmann: Lecture Public Key Infrastrukturen, FG Theoretische Informatik, TU-Darmstadt] 15
16 Algorithm RSA (1024 bits) RSA (2048 bits) Performance * Disadvantage: Performance of Public Key Algorithms Performance compared to Symmetric encryption (AES) 6.6 s Factor 100 slower 11.8 s Factor 180 slower Complex operations with very big numbers Þ Algorithms are very slow * Encryption of 1 MB on a Pentium 2.8 GHz, using the FlexiProvider (Java) [J. Buchmann: Lecture Public Key Infrastrukturen, FG Theoretische Informatik, TU-Darmstadt] 16
17 Differences between symmetric and asymmetric cryptosystems. Symmetric Both encryption and decryption is done with the same key. One key per communication pair is necessary. Efficient in terms of performance Keys have to be kept secret Secure agreement and transfer are necessary. A center for key distribution is possible but this party then knows all secret keys! Asymmetric Encryption with public key, decryption with private key. Summary Does not require a secure communication channel. Public key can be freely distributed. Less efficient Only keep own private key secret Does not require agreement on a shared key. A center for key distribution is possible and this party does not know the secret keys. 17
18 Exercise 3: Stream ciphers a) What is a one-time pad (Vernam-code)? 18
19 One Time Pad Invented by Gilbert Vernam The length of the key is as long as the length of the plaintext. The key is randomly chosen and only used once. Every key has the same probability. 19
20 Example One Time Pad area that needs to be protected to keep the key secret 0/1 k Key generation k random number 0/1 X i S i Y i Truth Table of the XOR operation 0 1 xor 0/1 1/0 xor 0 1 plaintext encrypted text plaintext x E e:= E(x,k) D x=d(e)=d(e(x,k)) [based on Federrath and Pfitzmann 1997] 20
21 Exercise 3: Stream ciphers b) Alice wants to encrypt the letter A, where the letter is given in ASCII code. The ASCII value for A is = Using Vernam-code, which of the following keys are suitable to encrypt this plaintext: X b1) i S i Y i b2) b3) Truth Table of the XOR operation 21
22 Exercise 3: Stream ciphers c) Encrypt the message using Vernam code and using XOR as an encryption function and the key in b). Plaintext (A) Key (B) Ciphertext (A xor B) X i S i Y i Truth Table of the XOR operation 22
23 Exercise 4: Vigenére Cipher a) What is a Vigenére Cipher? b)you want to encrypt the message I am studying in Frankfurt to your friend living in Berlin. What will be your cypher text encrypted using the key Berlin? Show the necessary steps (Use the Vigenére tableau below when necessary). 23
24 Vigenére Tableau 24
25 Exercise 4(a): Vigenére Cipher The Vigenére cipher chooses a sequence of keys, represented by a string. The key letters are applied to successive plaintext characters. When the end of the key is reached, the key starts over. The length of the key is called the period of the cipher. [Bi2005] 25
26 b)you want to encrypt the message I am studying in Frankfurt Exercise 4(b): to your friend living in Berlin. What will be your cypher text encrypted using the key Berlin? Show the necessary steps (Use the Vigenére tableau below when necessary). 26
27 Plain text The plain text I am studying in Frankfurt The key Berlin I A M S T U D Y I N G I N F R A N K F U R T Key B E R L I N B E R L I N B E R L I N B E R L Cypher text j e d d b h e c z y o v o j i l v x g y i e 27
28 Assessment Vigenére Cipher Then a Prussian cavalry officer named Kasiski noticed that repetitions occur when characters of the key appear over the same characters in the plaintext. The number of characters between successive repetitions is a multiple of the period (key length). Given this information and a short period the Vigenére cipher is quite easily breakable. Example: The Caesar cipher is a Vigenére cipher with a period of 1. [Bi2005] 28
29 Thank you! Questions: 29
30 References [Federrath Pfitzmann 1997] Hannes Federrath, Andreas Pfitzmann: Bausteine zur Realisierung mehrseitiger Sicherheit. in: Günter Müller, Andreas Pfitzmann (Hrsg.): Mehrseitige Sicherheit in der Kommunikationstechnik, Addison-Wesley- Longman1997,
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