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Cryptographic hash function 29 Cryptographic hash function A cryptographic hash function is a hash function that it can be defined as a deterministic procedure that takes an arbitrary block of data and returns a fixed-size bit string, the (cryptographic) hash value, such that an accidental or intentional change to the data will change the hash value. The data to be encoded is often called the "message," and the hash value is sometimes called the message digest or simply digest. The ideal cryptographic hash function has four main or significant properties: • it is easy (but not necessarily quick) to compute the hash value for any given message • it is infeasible to generate a message that has a given hash • it is infeasible to modify a message without changing the hash • it is infeasible to find two different messages with the same hash A cryptographic hash function (specifically, SHA-1) at work. Note that even small changes in the source input (here in the word "over") drastically change the resulting output, by the so-called avalanche effect. Cryptographic hash functions have many information security applications, notably in digital signatures, message authentication codes (MACs), and other forms of authentication. They can also be used as ordinary hash functions, to index data in hash tables, for fingerprinting, to detect duplicate data or uniquely identify files, and as checksums to detect accidental data corruption. Indeed, in information security contexts, cryptographic hash values are sometimes called (digital) fingerprints, checksums, or just hash values, even though all these terms stand for functions with rather different properties and purposes. Properties Most cryptographic hash functions are designed to take a string of any length as input and produce a fixed-length hash value. A cryptographic hash function must be able to withstand all known types of cryptanalytic attack. As a minimum, it must have the following properties: • Preimage resistance Given a hash it should be difficult to find any message such that . This concept is related to that of one-way function. Functions that lack this property are vulnerable to preimage attacks. • Second-preimage resistance Given an input it should be difficult to find another input — where — such that . This property is sometimes referred to as weak collision resistance, and functions that lack this property are vulnerable to second-preimage attacks. • Collision resistance It should be difficult to find two different messages and such that . Such a pair is called a cryptographic hash collision. This property is sometimes referred to as strong collision
Cryptographic hash function 30 resistance. It requires a hash value at least twice as long as that required for preimage-resistance, otherwise collisions may be found by a birthday attack. These properties imply that a malicious adversary cannot replace or modify the input data without changing its digest. Thus, if two strings have the same digest, one can be very confident that they are identical. A function meeting these criteria may still have undesirable properties. Currently popular cryptographic hash functions are vulnerable to length-extension attacks: given and but not , by choosing a suitable an attacker can calculate where denotes concatenation. This property can be used to break naive authentication schemes based on hash functions. The HMAC construction works around these problems. Ideally, one may wish for even stronger conditions. It should be impossible for an adversary to find two messages with substantially similar digests; or to infer any useful information about the data, given only its digest. Therefore, a cryptographic hash function should behave as much as possible like a random function while still being deterministic and efficiently computable. Checksum algorithms, such as CRC32 and other cyclic redundancy checks, are designed to meet much weaker requirements, and are generally unsuitable as cryptographic hash functions. For example, a CRC was used for message integrity in the WEP encryption standard, but an attack was readily discovered which exploited the linearity of the checksum. Degree of difficulty In cryptographic practice, “difficult” generally means “almost certainly beyond the reach of any adversary who must be prevented <strong>from</strong> breaking the system for as long as the security of the system is deemed important.” The meaning of the term is therefore somewhat dependent on the application, since the effort that a malicious agent may put into the task is usually proportional to his expected gain. However, since the needed effort usually grows very quickly with the digest length, even a thousand-fold advantage in processing power can be neutralized by adding a few dozen bits to the latter. In some theoretical analyses “difficult” has a specific mathematical meaning, such as not solvable in asymptotic polynomial time. Such interpretations of difficulty are important in the study of provably secure cryptographic hash functions but do not usually have a strong connection to practical security. For example, an exponential time algorithm can sometimes still be fast enough to make a feasible attack. Conversely, a polynomial time algorithm (e.g. one that requires n 20 steps for n-digit keys) may be too slow for any practical use. Illustration An illustration of the potential use of a cryptographic hash is as follows: Alice poses a tough math problem to Bob, and claims she has solved it. Bob would like to try it himself, but would yet like to be sure that Alice is not bluffing. Therefore, Alice writes down her solution, appends a random nonce, computes its hash and tells Bob the hash value (whilst keeping the solution and nonce secret). This way, when Bob comes up with the solution himself a few days later, Alice can prove that she had the solution earlier by revealing the nonce to Bob. (This is an example of a simple commitment scheme; in actual practice, Alice and Bob will often be computer programs, and the secret would be something less easily spoofed than a claimed puzzle solution).
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Page 5 and 6: Advanced Encryption Standard 2 is a
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Page 9 and 10: Advanced Encryption Standard 6 Know
Page 11 and 12: Advanced Encryption Standard 8 Test
Page 13 and 14: Block cipher 10 Block cipher In cry
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Page 27 and 28: Certificate authority 24 Certificat
Page 29 and 30: Certificate authority 26 Security T
Page 31: CMAC 28 The CMAC tag generation pro
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Page 37 and 38: Cryptographic hash function 34 Algo
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Page 47 and 48: Digital signature 44 every paramete
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Page 51 and 52: Digital signature 48 authority). Fo
Page 53 and 54: Digital Signature Algorithm 50 Digi
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Page 57 and 58: HMAC 54 Implementation The followin
Page 59 and 60: HMAC 56 External links • FIPS PUB
Page 61 and 62: HTTP Secure 58 Browser integration
Page 63 and 64: HTTP Secure 60 From an architectura
Page 65 and 66: IPsec 62 IPsec Internet Protocol Se
Page 67 and 68: IPsec 64 operates directly on top o
Page 69 and 70: IPsec 66 Cryptographic algorithms C
Page 71 and 72: IPsec 68 External links • All IET
Page 73 and 74: Kerberos (protocol) 70 Kerberos (pr
Page 75 and 76: Kerberos (protocol) 72 Client Authe
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NeedhamSchroeder protocol 80 S resp
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Pretty Good Privacy 82 Pretty Good
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Pretty Good Privacy 84 Security qua
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Pretty Good Privacy 86 PGP 3 and fo
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Pretty Good Privacy 88 based on sec
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Public key certificate 90 Public ke
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Public key certificate 92 (b) ensur
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Public key certificate 94 Usefulnes
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Public key infrastructure 96 As tim
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Public key infrastructure 98 Extern
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Public-key cryptography 100 In cont
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Public-key cryptography 102 To achi
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Public-key cryptography 104 using t
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Public-key cryptography 106 Spreadi
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Public-key cryptography 108 Externa
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RSA (algorithm) 110 The RSA algorit
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RSA (algorithm) 112 A working examp
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RSA (algorithm) 114 Signing message
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RSA (algorithm) 116 Side-channel an
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RSA (algorithm) 118 • The PKCS #1
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S/MIME 120 administrative overhead
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Secure Electronic Transaction 122 T
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Secure Shell 124 Usage SSH is typic
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Secure Shell 126 • RFC 4462, Gene
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Secure Shell 128 ability to multipl
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Security service (telecommunication
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Security service (telecommunication
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SHA-1 134 SHA-1 SHA-1 General Desig
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SHA-1 136 Applications SHA-1 forms
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SHA-1 138 At the Rump Session of CR
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SHA-1 140 a = temp Add this chunk's
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SHA-1 142 • Xiaoyun Wang, Yiqun L
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Stream cipher 144 Types of stream c
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Stream cipher 146 Filter generator
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Stream cipher 148 SNOW Pre-2003 Ver
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Symmetric-key algorithm 150 Key gen
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Transport Layer Security 152 TLS 1.
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Transport Layer Security 154 • SS
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Transport Layer Security 156 • Fi
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Transport Layer Security 158 Length
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Transport Layer Security 160 layer
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Transport Layer Security 162 Suppor
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Transport Layer Security 164 • RF
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Transport Layer Security 166 Extern
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X.509 168 Extensions informing a sp
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X.509 170 00:d3:a4:50:6e:c8:ff:56:6
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X.509 172 Exploits • MD2-based ce
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X.509 174 External links • ITU-T
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Article Sources and Contributors 17
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Article Sources and Contributors 17
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License 180 License Creative Common
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