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Unformatted text preview: um). A VLSI implementation of PES encrypts data at 55 megabits per second at 25 megahertz [208, 398]. Another VLSI chip developed at ETH Zurich, consisting of 251, 000 transistors on a chip 107.8 square millimeters, encrypts data using the IDEA algorithm at a 177 megabitpersecond data rate when clocked at 25 megahertz [926, 207, 397]. Table 13.4 IDEA Encryption and Decryption Subkeys Round 1st Encryption Subkeys Z1(1) Z2(1) Z3(1) Z4(1) Z5(1) Z6(1) Decryption Subkeys Z1(9)  1 –Z2(9) –Z3(9) Z4(9)  1 Z5(8) Z6(8) 2nd 3rd 4th 5th 6th 7th 8th Z1(2) Z2(2) Z3(2) Z4(2) Z5(2) Z6(2) Z1(3) Z2(3) Z3(3) Z4(3) Z5(3) Z6(3) Z1(4) Z2(4) Z3(4) Z4(4) Z5(4) Z6(4) Z1(5) Z2(5) Z3(5) Z4(5) Z5(5) Z6(5) Z1(6) Z2(6) Z3(6) Z4(6) Z5(6) Z6(6) Z1(7) Z2(7) Z3(7) Z4(7) Z5(7) Z6(7) Z1(8) Z2(8) Z3(8) Z4(8) Z5(8) Z6(8) Z1(8)  1 –Z3(8) –Z2(8) Z4(8)  1 Z5(7) Z6(7) Z1(7)  1 –Z3(7) –Z2(7) Z4(7)  1 Z5(6) Z6(6) Z1(6)  1 –Z3(6) –Z2(6) Z4(6)  1 Z5(5) Z6(5) Z1(5)  1 –Z3(5) –Z2(5) Z4(5)  1 Z55(4) Z6(4) Z1(4)  1 –Z3(4) –Z2(4) Z4(4)  1 Z5(3) Z6(3) Z1(3)  1 –Z3(3) –Z2(3) Z4(3)  1 Z5(2) Z6(2) Z1(2)  1 –Z3(2) –Z2(2) Z4(2)  1 Z5(1) Z6(1) Z1(1)  1 –Z2(1) –Z3(1) Z4(1)  1 output Z1(9) Z2(9) Z3(9) Z4(9) transformation Cryptanalysis of IDEA
IDEA’s key length is 128 bits—over twice as long as DES. Assuming that a bruteforce attack is the most efficient, it would require 2128(1038) encryptions to recover the key. Design a chip that can test a billion keys per second and throw a billion of them at the problem, and it will still take 1013 years—that’s longer than the age of the universe. An array of 1024 such chips can find the key in a day, but there aren’t enough silicon atoms in the universe to build such a machine. Now we’re getting somewhere—although I’d keep my eye on the dark matter debate. Perhaps brute force isn’t the best way to attack IDEA. The algorithm is still too new for any definitive cryptanalytic results. The designers have done their best to make the...
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This note was uploaded on 10/18/2010 for the course MATH CS 301 taught by Professor Aliulger during the Fall '10 term at Koç University.
 Fall '10
 ALIULGER
 Cryptography

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