2nd - CSci 5471: Modern Cryptography, Spring 2010 Homework...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CSci 5471: Modern Cryptography, Spring 2010 Homework #2 Yongdae Kim Due: Thursday, Feb. 16, 9:00 AM Show all steps. Please ask any questions, if the problems are not clear. Total 120 points. 1. Number Theory! (30 points) (a) (7 pts) Show that ax + by = c has integer solution ( x,y ) if gcd( a,b ) | c . (b) (8 pts) Show that for n > 1 , the number 1 + 1 / 2 + 1 / 3 + ... + 1 /n is not an integer. (c) (8 pts) Show that if a n- 1 is a prime, then a = 2 and n is a prime. ( n > 1 ) (Hint) You can use one of the last homework problems as a fact. (d) (7 points) If n > 1 is an integer and is not a prime, then show that there is a prime such that p | n and p n. 2. Affine Cipher (10 pts) : As we discussed in the class, Caeser cipher is not secure. To improve the Caesar cipher, Yongdae proposed a new encryption algorithm called affine cipher defined as below: c = E a,b ( m ) am + b (mod 26) . (a) To be decryptible, what kind of condition a must satisfy? (b) Write decryption algorithm D a,b ( c ) and show why the ciphertext c will be decrypted to m . (c) Suppose you are given two (plaintext, ciphertext) pairs (i.e. ( m 1 ,c 1 ) and ( m 2 ,c 2 ) ). With these two pairs, show that how one can find two keys a,b efficiently. 3. Modes of Operation (20 points) : When there is a lot of data to encrypt, using DES ECB mode is insecure because of the block permutation attack. In other words, blocks of encrypted data can be swapped without the receiver (decryptor) noticing. Suggest a secure way to address these issues. The rules of the game are:receiver (decryptor) noticing....
View Full Document

Page1 / 2

2nd - CSci 5471: Modern Cryptography, Spring 2010 Homework...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online