# Error oracle attacks and CBC encryption. Chris Mitchell ISG, RHUL

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1 Error oracle attacks and CBC encryption Chris Mitchell ISG, RHUL

2 Agenda 1. Introduction 2. CBC mode 3. Error oracles 4. Example 1 5. Example 2 6. Example 3 7. Stream ciphers 8. Conclusions 2

3 Block ciphers One of the fundamental cryptographic primitives is the block cipher. When used for encryption, a block cipher takes as input a block of n bits of plaintext P and outputs a block of n bits of ciphertext C. [We call this an n-bit block cipher]. Operation is controlled by a secret key K; we write C=e K (P) and P=d K (C) where d is the decryption function. For each key, the encryption function implements a permutation on the set of all n-bit blocks. 3

4 Examples of block ciphers Some well-known examples of block ciphers: DES: the Data Encryption Standard was first published in the US in the late 1970s, and rapidly became a de facto international standard; DES suffers from a relatively short secret key (56 bits), and advances in technology have meant it is unacceptably weak. Triple DES (three iterations of DES using two or three DES keys) is a widely deployed fix to this problem. AES: the Advanced Encryption Standard, is a much more recent design with a 128-bit key, designed as a replacement for DES. 4

5 Modes of operation Using a block cipher in the naïve way, i.e. dividing the data to be encrypted into blocks, and encrypting each block separately, is not a good idea. This is because if two blocks in the plaintext are the same (often likely) then the two ciphertext blocks will be the same. That is, the ciphertext will leak information about the plaintext. Hence more complex ways of using a block cipher have been devised called modes of operation. 5

6 What is CBC mode? CBC (Cipher Block Chaining) mode is a widely used technique for encrypting data using a block cipher (i.e. it is a mode of operation). It is purely a confidentiality technique it does not provide any integrity protection for data. This is inevitable in that it does not add any redundancy i.e. n bits of plaintext encrypt to n bits of ciphertext, so all ciphertexts are valid. 6

7 Confidentiality and integrity In many cases it is necessary to provide both confidentiality and integrity. With symmetric crypto, this is typically achieved by encrypting (e.g. using CBC mode) and computing a MAC (Message Authentication Code). Recent cryptanalytic results suggest that these need to be combined with care! 7

8 Need for padding To use CBC mode, it is necessary for the data that is to be encrypted to be a multiple of n bits long (where n is the block cipher block length). This means that data often needs to be padded prior to encryption. Means must be provided for receiver of ciphertext to know which bits of final recovered plaintext are padding. 8

9 Padding oracles Recipient of ciphertext must process final block to recover and remove padding. Depending on padding method, some recovered plaintexts may be invalid. In such a case the decrypter will typically generate an error message, e.g. to request a retransmission. This is an example of a padding oracle, i.e. an entity which will indicate whether or not a ciphertext yields valid padding when decrypted. 9

10 Padding oracle attacks Suppose a cryptanalyst can modify/insert messages into a communications channel. Then a padding oracle can be used to learn information about the plaintext by repeatedly sending modified versions of the ciphertext to the oracle and seeing what the result is. This has been shown to work against real implementations of well-known protocols. 10

11 Solutions One solution is to try to limit the use of error messages this is difficult to implement. Another widely advocated solution is to use only padding methods for which all possible deciphered messages are valid. Most satisfactory solution is to always use an integrity check, and to only decrypt a message if the integrity check passes. 11

12 Need for encryption only Unfortunately, the final solution is not always practical. There are applications where encryption-only is required (these should be minimised). Examples include: encrypted voice (telephony) typically retransmission is not an option because of latency; bulk data transfer (e.g. data trunks) again retransmission not an option. 12

13 Agenda 1. Introduction 2. CBC mode 3. Error oracles 4. Example 1 5. Example 2 6. Example 3 7. Stream ciphers 8. Conclusions 13

14 Cipher Block Chaining (CBC) Mode Plaintext must be a series of n-bit blocks: P 1, P 2,..., P q. Then: C 1 = e K (P 1 IV) C i = e K (P i C i-1 ) (i>1) (where denotes bit-wise exclusive-or), and: P 1 = d K (C 1 ) IV P i = d K (C i ) C i-1 (i>1). 14

15 CBC encryption P 1 P 2 P q IV C q-1 e K e K e K C 1 C 2 C q 15

16 CBC decryption C 1 C 2 C q d K d K d K IV C q-1 P 1 P 2 P q 16

17 CBC mode properties If same message encrypted twice using same IV, then the same ciphertext results. Two identical plaintext blocks produce different ciphertext blocks. Need for padding. Error propagation one bit error in ciphertext means that one block of plaintext is lost, as well as one bit in the next block of plaintext. 17

18 An observation Suppose P 1, P 2,, P q is a (padded) plaintext message which has been encrypted to C 1, C 2,, C q using key K and IV S. Suppose X 1, X 2,, X s-1, C j, X s+1,, X t is submitted for decryption, where s>1, j>1, and decrypted result is P 1, P 2,, P t. Then we have: P s P j = X s-1 C j-1 18

19 This observation is key This simple observation is the basis of all padding oracle attacks. The observation can be use as the basis of two main types of attack designed to learn information about a plaintext message. We review these two attack approaches. 19

20 Attack type 1 This attack is designed to learn information about a single target plaintext block P j. Using the previous notation the attacker sets: X s-1 = C j-1 Q where Q is a chosen bit pattern. By our observation: P s P j = Q, i.e. the attacker can select the difference between P s and the target plaintext P j. If the attacker has some means of learning whether or not P s generates a formatting error, then he may learn something about P j. 20

21 Attack type 2 This attack involves learning information about an entire message. Suppose C 1, C 2,, C q and C* 1, C* 2,, C* t are two ciphertext messages (which may be the same) encrypted using the same key. The cryptanalyst now submits the message: C* 1, C* 2,,C* s-1, C j, C* s+1,, C* t We also suppose that, in this case, the cryptanalyst can force the oracle to decrypt this message using the same IV as was used to encrypt C* 1, C* 2,, C* t. 21

22 Attack type 2 (continued) Suppose decrypted result is P 1, P 2,, P t. Then: P i = P* i for every i s or s+1; P s P* s = P* s P j C* s-1 C j-1 ; P s+1 P* s+1 = C* s C j. If the attacker has some means of learning whether or not the plaintext generates an error, then this may reveal information about P* s P j (since everything else is known). 22

23 Agenda 1. Introduction 2. CBC mode 3. Error oracles 4. Example 1 5. Example 2 6. Example 3 7. Stream ciphers 8. Conclusions 23

24 Padding oracles reviewed In a padding oracle attack, an attacker has one or more valid ciphertexts, and can inject modified ciphertexts into the channel. The receiver will decrypt each ciphertext and generate an error message if the padding is incorrect. 24

25 Error oracles In an error oracle attack we suppose that, after decryption, the message is passed to a protocol implementation (e.g. an application) which will generate a detectable action (e.g. an error message) if the message format is incorrect. In this sense a padding oracle attack is just a special case of an error oracle attack. 25

26 Discussion Unlike padding oracles, it may not be possible to prevent error oracles. Applications are run across encrypted networks, where the application is not encryption-aware and the encryption layer is not application-aware. It is inevitable that some applications will react in unexpected ways to ill-formatted messages. Hence likelihood of error oracles should be minimised, e.g. by using authenticated encryption whenever possible. 26

27 Agenda 1. Introduction 2. CBC mode 3. Error oracles 4. Example 1 5. Example 2 6. Example 3 7. Stream ciphers 8. Conclusions 27

28 Assumptions Suppose a protocol, running at a higher layer in the protocol hierarchy than the encrypting protocol, provides error protection using a 16- bit CRC. I.e. suppose plaintext P 1, P 2,, P q corresponding to ciphertext C 1, C 2,, C q, incorporates a 16-bit CRC. Suppose attacker can also find out if error detection fails. 28

29 The error oracle query (attack type 2) The attacker replaces C s with C j for some s j. If the recovered plaintext is P 1, P 2,, P t, then: P i = P i for every i s or s+1; P s P s = P s P j C s-1 C j-1 ; P s+1 P s+1 = C s C j. Given the original message contained a valid CRC, then the corrupted message will contain a valid CRC if and only if the exor of the original and corrupted messages contains a valid CRC (by linearity). 29

30 Results The exor of the original and corrupted plaintexts will be zero in all but two blocks, and the only unknown for these two blocks is the value of P s P j. The probability the CRC will be correct is 2-16, but in that case the attacker will instantly know 16 bits of information about the message. If an 8-bit CRC is used, then information can be obtained more rapidly. 30

31 Agenda 1. Introduction 2. CBC mode 3. Error oracles 4. Example 1 5. Example 2 6. Example 3 7. Stream ciphers 8. Conclusions 31

32 A message structure attack (type 1) Suppose the target plaintext message contains a fixed byte in a known position. Suppose the fixed byte is the kth byte of block P s, for some s > 1. Many protocols contain fixed bytes (e.g. set to zero) for future-proofing perhaps containing the version number of the protocol. 32

33 The error oracle query The attacker constructs 256 queries, one for each value of t (0 t 255). The attacker replaces C s with C j for some j s, and replaces C s-1 with C j-1 Q t, where Q t has zeros everywhere except in the kth byte, which contains the binary representation of t. Precisely one of these (Q u say) will yield a plaintext with the correct value for the kth byte of the sth plaintext block. 33

34 Results By the key observation, the recovered plaintext block P s will equal: P j Q u That is, for the value of t (i.e. u) that does not yield an error, the attacker knows that the kth byte of P j Q u will equal the correct fixed byte. This immediately gives a byte of p/text block P j. Repeat for every plaintext block (except P 1 ). 34

35 Agenda 1. Introduction 2. CBC mode 3. Error oracles 4. Example 1 5. Example 2 6. Example 3 7. Stream ciphers 8. Conclusions 35

36 A content-based padding oracle attack We now describe a padding oracle attack which works against padding methods which are resistant to normal padding oracle attacks. We need to suppose that the message sent is of fixed length, and that an error message will be generated if a message is received of the wrong length. 36

37 Assumptions We suppose that the padding method in use involves adding a single one to the end of the data followed by the smallest number of zeros (at most n-1) necessary to create a whole number of n-bit blocks. This padding method is uniquely unpaddable, and resists known padding oracle attacks (almost every possible string of bits corresponds to a padded message). 37

38 The error oracle query Suppose C 1, C 2,, C q is a valid ciphertext message for which the last d bits of P q are (the fixed message length is qn-d). The attacker makes 2 d messages variants (0 t 2 d -1) by modifying the last two blocks to: C j-1 Q t, C j where Q t contains n-d zeros followed by the binary representation of t. One will not return a message length error say Q u. 38

39 Results By the key observation, the recovered plaintext block P q will equal: P j Q u That is, for the value of t (i.e. t=u) that does not yield an error, the attacker knows that the final d bits of P j Q u will equal This immediately gives d bits of p/text block P j. Repeat for every plaintext block (except P 1 ). 39

40 Agenda 1. Introduction 2. CBC mode 3. Error oracles 4. Example 1 5. Example 2 6. Example 3 7. Stream ciphers 8. Conclusions 40

41 CBC mode and stream ciphers It would thus appear that CBC mode is dangerously prone to error oracle attacks, regardless of the padding method used. One other widely used method of encryption is the stream cipher. In a stream cipher, the data is encrypted by bitwise exoring it with a pseudorandom keystream sequence (generated as a function of a secret key). 41

42 Stream ciphers and error oracles Stream ciphers do not suffer in the same way (they also do not require padding). There are examples of error oracle attacks on stream ciphers, but they seem harder to construct. Suppose two consecutive bits of a plaintext message are always equal to one of 00, 01, and 10 (and that 11 will cause a detectable behaviour by the recipient). If the second of the two corresponding ciphertext bits is changed then error/no error means that the previous bit is 1/0. 42

43 Agenda 1. Introduction 2. CBC mode 3. Error oracles 4. Example 1 5. Example 2 6. Example 3 7. Stream ciphers 8. Conclusions 43

44 Use authenticated encryption The simplest and best solution to all these attacks is to use authenticated encryption (AE). This either means use the encrypt-then-mac paradigm, or use one of the AE block cipher modes recently developed (OCB versions 1 and 2, EAX, CCM, ). Indeed, an international standard for AE schemes, ISO/IEC 19772, is being developed. 44

45 Use a stream cipher If unauthenticated encryption is really necessary, then don t use CBC mode! Probably the best choice is a stream cipher. This either means using a bespoke keystream generator (e.g. SNOW 2.0 or MUGI) or a block cipher in an appropriate mode, e.g. OFB or CTR mode. 45

46 Acknowledgements Must thank Kenny Paterson for many helpful comments. A shorter version of this talk will be presented at ISC 2005 (Singapore, September 2005). 46

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