Walter Unger WS 2012/2013
Sascha Geulen October 17, 2012
Exercise
Algorithmic Cryptography
Sheet 1
Exercise 1.1: (4 points)
Decrypt the following ciphertext and explain your approach.
HCDDW CQHEE UPVFA XUEFD REFDE VAQUP VFAWA KUQEE AHVND LVGDP AWACL AAEHP WVFUL VAAPS UPTVA EPDLV FAHEV HPWXG PDLVF SHUPX LHPJF EAKAP VFQUS XAHEV EUWAE FDDVN LDSVF AQANV AGADN VFAWA HVFEF AHWHX AAQUP ANLDS VFAVL AAVFL DTCFV FAEFD VNUNV GNAAV DTVAW CHLHQ QHPRD AVFAC DQWXT C
Hint: The text is in English and the letters appear with the following frequency:
A B C D E F G H I J K L M
36 0 7 18 16 20 4 15 0 1 2 11 0
N O P Q R S T U V W X Y Z
8 0 14 9 2 5 4 11 27 10 6 0 0
Exercise 1.2: (4 points)
Prove: If in DES each bit in the plaintext and in the key is replaced by its com- plement, then each bit in the ciphertext is also replaced by its complement.
Exercise 1.3: (4 points)
Consider the keys K1, K2, . . . , K16 used in DES in the function f(Ri−1, Ki). Let K10, K20, . . . , K160 be these keys in reverse order, i.e.,K10 =K16, K20 =K15, . . . , K160 = K1.
What happens if DES uses the keys Ki0 instead of the standard keys Ki and what is the relation between the plain- and ciphertext of the standard and this modified DES?
Exercise 1.4: (4 points)
Consider the AES-256 key expansion algorithm:
Leta=0x11111111,b=0x01010101, and 0=0x00000000 be 32 bit strings. Fur- thermore, let k1 be a AES-256 key and k2 = k1 ⊕bbbba0a0. Expand the keys to 1024 bits and compare these expanded keys with each other. What do you notice?
Deadline: Wednesday, October 24, 2012, 15:00,
in the lecture or in the letterbox in front of i1.
