# Double-DES, Triple-DES & Modes of Operation

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1 Double-DES, Triple-DES & Modes of Operation Prepared by: Dr. Mohamed Abd-Eldayem Ref.: Cryptography and Network Security by William Stallings & Lecture slides by Lawrie Brown

2 Multiple Encryption & DES clear a replacement for DES was needed theoretical attacks that can break it demonstrated exhaustive key search attacks AES is a new cipher alternative prior to this alternative was to use multiple encryption with DES implementations Triple-DES is the chosen form

3 Double-DES? could use 2 DES encrypts on each block C = E K2 (E K1 (P)) issue of reduction to single stage and have meet-in-the-middle attack works whenever use a cipher twice since X = E K1 (P) = D K2 (C) attack by encrypting P with all keys and store then decrypt C with keys and match X value can show takes O(2 56 ) steps

4

5 Triple-DES with Two-Keys hence must use 3 encryptions would seem to need 3 distinct keys but can use 2 keys with E-D-E sequence C = E K1 (D K2 (E K1 (P))) nb encrypt & decrypt equivalent in security if K1=K2 then can work with single DES standardized in ANSI X9.17 & ISO8732 no current known practical attacks The cost of a brute-force key search on 3DES is on the order of 2^112 (=5*10^33) brute-force key search on 3DES compared to single DES, exceeding 10^52.

6 Triple-DES with Three-Keys although are no practical attacks on two-key Triple-DES have some indications can use Triple-DES with Three-Keys to avoid even these C = E K3 (D K2 (E K1 (P))) Triple-DES with three keys (168-bits) is now being used in some Internet applications, including PGP and S/MIME, for greater security

7 Triple-DES with Three-Keys

8 Modes of Operation block ciphers encrypt fixed size blocks eg. DES encrypts 64-bit blocks with 56-bit key need some way to en/decrypt arbitrary amounts of data in practise ANSI X Modes of Use (now FIPS 81) defines 4 possible modes subsequently 5 defined for AES & DES have block and stream modes

9 Electronic Codebook Book (ECB) message is broken into independent blocks which are encrypted each block is a value which is substituted, like a codebook, hence name each block is encoded independently of the other blocks C i = DES K1 (P i ) uses: secure transmission of single values eg. a session key encrypted using a master key

10 Electronic Codebook Book (ECB)

11 Advantages and Limitations of ECB message repetitions (esp. with graphics ) may show in ciphertext if aligned with message block particularly with data such graphics or with messages that change very little, which become a code-book analysis problem weakness is due to the encrypted message blocks being independent main use is sending a few blocks of data

12 Cipher Block Chaining (CBC) To overcome the problems of repetitions and order independence in ECB message is broken into blocks linked together in encryption operation each previous cipher blocks is chained with current plaintext block, hence name use Initial Vector (IV) to start process C i = DES K1 (P i XOR C i-1 ) C -1 = IV uses: large amounts of data need to be sent securely (bulk data encryption), provided that all data is available in advance (eg , FTP, web etc). uses: authentication

13 Cipher Block Chaining (CBC)

14 Message Padding at end of message must handle a possible last short block which is not as large as block size of cipher pad last block along with count of pad size eg. [ b1 b2 b ] means have 3 data bytes, then 5 bytes pad + count this may require an extra entire block over those in message

15 Advantages and Limitations of CBC a ciphertext block depends on all blocks before it any change to a block affects all following ciphertext blocks need Initialization Vector (IV) which must be known to sender & receiver if sent in clear, attacker can change bits of first block, and change IV to compensate hence IV must either be a fixed value or must be sent encrypted in ECB mode before rest of message

16 Cipher FeedBack (CFB) message is treated as a stream of bits added to the output of the block cipher result is feed back for next stage (hence name) standard allows any number of bit (1,8, 64 or 128 etc) to be feed back denoted CFB-1, CFB-8, CFB-64, CFB-128 etc most efficient to use all bits in block (64 or 128) C i = P i XOR DES K1 (C i-1 ) C -1 = IV uses: stream data encryption, authentication

17 Cipher FeedBack (CFB)

18 Advantages and Limitations of CFB appropriate when data arrives in bits/bytes most common stream mode note that the block cipher is used in encryption mode at both ends errors propagate for several blocks after the error

19 Output FeedBack (OFB) message is treated as a stream of bits output of cipher is added to message output is then feed back (hence name) feedback is independent of message can be computed in advance C i = P i XOR O i O i = DES K1 (O i-1 ) = IV O -1 uses: stream encryption on noisy channels (eg satellite TV transmissions etc)

20 Output FeedBack (OFB)

21 Advantages and Limitations of OFB bit errors do not propagate more vulnerable to message stream modification a variation of a Vernam cipher hence must never reuse the same sequence (key+iv) sender & receiver must remain in sync originally specified with m-bit feedback

22 Counter (CTR) a new mode, though proposed early on similar to OFB but encrypts counter value rather than any feedback value must have a different key & counter value for every plaintext block (never reused) C i = P i XOR O i O i = DES K1 (i) uses: high-speed network encryptions It is being used with applications in ATM (asynchronous transfer mode) network security and IPSec (IP security).

23 Counter (CTR)

24 Advantages and Limitations of CTR efficiency can do parallel encryptions in h/w or s/w can preprocess in advance of need good for bursty high speed links random access to encrypted data blocks provable security (good as other modes) but must ensure never reuse key/counter values, otherwise could break (cf OFB)

25 Stream Ciphers process message bit by bit (as a stream) have a pseudo random keystream combined (XOR) with plaintext bit by bit randomness of stream key completely destroys statistically properties in message C i = M i XOR StreamKey i but must never reuse stream key otherwise can recover messages (cf book cipher)

26 Stream Cipher Structure

27 Stream Cipher Properties 1.The encryption sequence should have a large period, the longer the period of repeat the more difficult it will be to do cryptanalysis. 2. The keystream should approximate the properties of a true random number stream as close as possible, the more random-appearing the keystream is, the more randomized the ciphertext is, making cryptanalysis more difficult. 3. To guard against brute-force attacks, the key needs to be sufficiently long. The same considerations as apply for block ciphers are valid here.thus, with current technology, a key length of at least 128 bits is desirable. 4.large linear complexity 5.properly designed, can be as secure as a block cipher with same size key 6.but usually simpler & faster

28 RC4 a proprietary stream cipher owned by RSA DSI another Ron Rivest design, simple but effective variable key size, byte-oriented stream cipher widely used (web SSL/TLS, wireless WEP) key forms random permutation of all 8-bit values uses that permutation to scramble input info processed a byte at a time

29 RC4 Key Schedule starts with an array S of numbers: use key to well and truly shuffle S forms internal state of the cipher for i = 0 to 255 do S[i] = i T[i] = K[i mod keylen]) j = 0 for i = 0 to 255 do j = (j + S[i] + T[i]) (mod 256) swap (S[i], S[j])

30 RC4 Encryption encryption continues shuffling array values sum of shuffled pair selects "stream key" value from permutation XOR S[t] with next byte of message to en/decrypt i = j = 0 for each message byte M i i = (i + 1) (mod 256) j = (j + S[i]) (mod 256) swap(s[i], S[j]) t = (S[i] + S[j]) (mod 256) C i = M i XOR S[t]

31 RC4 Overview

32 RC4 Security claimed secure against known attacks have some analyses, none practical result is very non-linear since RC4 is a stream cipher, must never reuse a key have a concern with WEP, but due to key handling rather than RC4 itself

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