Solutions of Exam I

Solutions of Exam I - 1. (4 pt) Increasing the key length...

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

View Full Document Right Arrow Icon
1. (4 pt) Increasing the key length is one way to increase security of an encryption algorithm against the brute-force type of attack. DES uses 56-bit key, which is not secure, given the modern computing power. Assume that 56-bit key was just sufficient in 1979 when DES was standardized, and assume that the hardware performance improves about 40% per year, then how many bits of a DES key would just suffice this year? Until what year would a 112-bit DES key be sufficient? Answer: 40% improvement per year doubles the performance every two years (1.4×1.4 2). So keys must grow by about 1 bit every two years. (2008-1979)/2+56=70.5, so we need 71 bit keys which would just suffice this year. (x-1979)/2+56=112, x=2091; 112-bit key would suffice till year 2091. 2. (6 pt) Suppose you encrypt message m by computing . How do you decrypt? 13 mod77 cm Answer: (77) (7 11) (7 1)(11 1) 60 ϕ = = 13 is relatively prime to 60, 1 13 mod60 d = Show steps of extended Euclidean algorithm to find d= -23 mod 60 or 37 mod 60 = 37 13 13 0 60 86 041 3 51 318 3815 2513 1312 =−× =− × × ՜ 31( 513 ) 2315 2( 815 )15 2835 283( 1 ) 5831 3 5 (60 4 13) 3 13 5 60 23 13 =−× −× =×−× = × −× −× = × −× =×−× −× =×−× =× −× −× =× − × So, 37 mc = 3. (6 pt) the following figure shows Electronic Code Book (ECB) encryption. A major
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

Solutions of Exam I - 1. (4 pt) Increasing the key length...

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