Principles of Wireless Access and Localization by Pahlavan Kaveh & Krishnamurthy Prashant

Author:Pahlavan, Kaveh & Krishnamurthy, Prashant [Pahlavan, Kaveh]
Language: eng
Format: azw3
ISBN: 9781118629260
Publisher: Wiley
Published: 2013-09-02T16:00:00+00:00

Secret-key algorithms such as AES are based on two principles: confusion and diffusion. The former introduces a layer of scrambling that creates confusion as to what exactly might be the transmitted message. The latter creates a randomness whereby the effect of changing a small part of the plaintext message will result in changing half of the encrypted ciphertext. This eliminates matching patterns or frequencies of occurrence of messages. Most secret-key algorithms are thus unbreakable except by brute force [Sil00]. If the length of the key of a secret-key algorithm is n bits, at least 2n–1 steps are required to break the encryption on average. Today, a key length of 80 bits is considered to be sufficiently safe from brute force attacks even though a key size of 128 bits is usually recommended.

Example A7.1: Security of DES against brute force attacks

The Data Encryption Standard (DES) is a block cipher that encrypts plaintext messages in blocks of 64 bits using keys that are 56 bits long. The total number of keys is 256. On average, half of them will have to be examined to determine the right key if a known plaintext-ciphertext pair is available. If a 500 MHz chip is employed for this attack, and one decryption (or encryption) can be performed in one clock cycle, to test 255 keys, it will take 255 / (500 × 106) seconds = 834 days to break the encryption. This is not very secure if 834 chips are used in parallel, since the key can be obtained in a single day. The total cost will be about $ 16 680 if each chip costs $20!

Example A7.2: Security versus advances in chip speeds

DES was broken in less than a day in January 1999 at a cost of $500 000. Today, it is virtually impossible to break a well-designed block cipher with key sizes of more than 80 bits (which translates into examining around 280 keys by brute force). However, a common assumption (called Moore's Law) is that processor or chip speeds double every 18 months thereby weakening any encryption scheme with time. For example, using a speed of 500 MHz for today, in 100 years, an encryption scheme that employs key sizes twice that of DES (i.e., 112 bits) can be broken in a day.

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