Winter 2011 Josh Benaloh Brian LaMacchia
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1 Winter 2011 Josh Benaloh Brian LaMacchia
2 Symmetric Cryptography January 20, 2011 Practical Aspects of Modern Cryptography 2
3 Agenda Symmetric key ciphers Stream ciphers Block ciphers Cryptographic hash functions January 20, 2011 Practical Aspects of Modern Cryptography 3
4 Agenda Symmetric key ciphers Stream ciphers Block ciphers Cryptographic hash functions January 20, 2011 Practical Aspects of Modern Cryptography 4
5 Public Key vs. Symmetric Key Recall from last time that in a public key cryptosystem, each participant has a key pair consisting of related keys January 20, 2011 Practical Aspects of Modern Cryptography 5
6 Public Key vs. Symmetric Key Recall from last time that in a public key cryptosystem, each participant has a key pair consisting of related keys Alice (or anyone) encrypts to Bob using Bob s public key January 20, 2011 Practical Aspects of Modern Cryptography 6
7 Public Key vs. Symmetric Key Recall from last time that in a public key cryptosystem, each participant has a key pair consisting of related keys Alice (or anyone) encrypts to Bob using Bob s public key Bob decrypts with Bob s private key January 20, 2011 Practical Aspects of Modern Cryptography 7
8 Public Key vs. Symmetric Key Recall from last time that in a public key cryptosystem, each participant has a key pair consisting of related keys Alice (or anyone) encrypts to Bob using Bob s public key Bob decrypts with Bob s private key Public keys are public January 20, 2011 Practical Aspects of Modern Cryptography 8
9 Public Key vs. Symmetric Key Recall from last time that in a public key cryptosystem, each participant has a key pair consisting of related keys Alice (or anyone) encrypts to Bob using Bob s public key Bob decrypts with Bob s private key Public keys are public They can be published in a directory, on a website, etc. January 20, 2011 Practical Aspects of Modern Cryptography 9
10 Public Key vs. Symmetric Key In contrast, in a symmetric key system, the same key is used for encryption and decryption January 20, 2011 Practical Aspects of Modern Cryptography 10
11 Public Key vs. Symmetric Key In contrast, in a symmetric key system, the same key is used for encryption and decryption Such keys must be kept secret January 20, 2011 Practical Aspects of Modern Cryptography 11
12 Public Key vs. Symmetric Key In contrast, in a symmetric key system, the same key is used for encryption and decryption Such keys must be kept secret Alice and Bob must both know the same secret key to use a symmetric cryptosystem with that key January 20, 2011 Practical Aspects of Modern Cryptography 12
13 Public Key vs. Symmetric Key In contrast, in a symmetric key system, the same key is used for encryption and decryption Such keys must be kept secret Alice and Bob must both know the same secret key to use a symmetric cryptosystem with that key Common pattern we will come back to later: January 20, 2011 Practical Aspects of Modern Cryptography 13
14 Public Key vs. Symmetric Key In contrast, in a symmetric key system, the same key is used for encryption and decryption Such keys must be kept secret Alice and Bob must both know the same secret key to use a symmetric cryptosystem with that key Common pattern we will come back to later: Use a public key cryptosystem to send/negotiate a randomly-generated secret key with the party to whom you wish to communicate January 20, 2011 Practical Aspects of Modern Cryptography 14
15 Public Key vs. Symmetric Key In contrast, in a symmetric key system, the same key is used for encryption and decryption Such keys must be kept secret Alice and Bob must both know the same secret key to use a symmetric cryptosystem with that key Common pattern we will come back to later: Use a public key cryptosystem to send/negotiate a randomly-generated secret key with the party to whom you wish to communicate Then use that secret key with a symmetric key cryptosystem January 20, 2011 Practical Aspects of Modern Cryptography 15
16 Symmetric Ciphers Private-key (symmetric) ciphers are usually divided into two classes. Stream ciphers Block ciphers January 20, 2011 Practical Aspects of Modern Cryptography 16
17 Symmetric Ciphers Private-key (symmetric) ciphers are usually divided into two classes. Stream ciphers Block ciphers January 20, 2011 Practical Aspects of Modern Cryptography 17
18 Stream Ciphers Examples of stream ciphers include RC4, A5/1, SEAL, etc. January 20, 2011 Practical Aspects of Modern Cryptography 18
19 Stream Ciphers Examples of stream ciphers include RC4, A5/1, SEAL, etc. Use the key as a seed to a pseudo-random numbergenerator. January 20, 2011 Practical Aspects of Modern Cryptography 19
20 Stream Ciphers Examples of stream ciphers include RC4, A5/1, SEAL, etc. Use the key as a seed to a pseudo-random numbergenerator. Take the stream of output bits from the PRNG and XOR it with the plaintext to form the ciphertext. January 20, 2011 Practical Aspects of Modern Cryptography 20
21 Stream Cipher Encryption Plaintext: PRNG(seed): Ciphertext: January 20, 2011 Practical Aspects of Modern Cryptography 21
22 Stream Cipher Decryption Ciphertext: PRNG(seed): Plaintext: January 20, 2011 Practical Aspects of Modern Cryptography 22
23 Some Good Properties Stream ciphers are typically very fast. January 20, 2011 Practical Aspects of Modern Cryptography 23
24 Some Good Properties Stream ciphers are typically very fast. Stream ciphers can be very simple. January 20, 2011 Practical Aspects of Modern Cryptography 24
25 Some Good Properties Stream ciphers are typically very fast. Stream ciphers can be very simple. The same function is used for encryption and decryption. January 20, 2011 Practical Aspects of Modern Cryptography 25
26 A Sample PRNG: Alleged RC4 Initialization S* = 0,1,,255 K[0..255] = Key,Key,Key, for i = 0 to 255 j = (j + S[i] + K[i]) mod 256 swap S[i] and S[j] January 20, 2011 Practical Aspects of Modern Cryptography 26
27 A Sample PRNG: Alleged RC4 Iteration i = (i + 1) mod 256 j = (j + S[i]) mod 256 swap S[i] and S[j] t = (S[i] + S[j]) mod 256 Output S[t] January 20, 2011 Practical Aspects of Modern Cryptography 27
28 Stream Cipher Security If two plaintexts are ever encrypted with the same stream cipher and key C 1 = K P 1 C 2 = K P 2 an attacker can easily compute C 1 C 2 = P 1 P 2 from which P 1 and P 2 can usually be teased apart easily. January 20, 2011 Practical Aspects of Modern Cryptography 28
29 Stream Cipher Encryption Plaintext: PRNG(seed): Ciphertext: January 20, 2011 Practical Aspects of Modern Cryptography 29
30 Stream Cipher Integrity It is easy for an adversary (even one who can t decrypt the ciphertext) to alter the plaintext in a known way. Bob to Bob s Bank: Please transfer $0,000, to the account of my good friend Alice. January 20, 2011 Practical Aspects of Modern Cryptography 30
31 Stream Cipher Integrity It is easy for an adversary (even one who can t decrypt the ciphertext) to alter the plaintext in a known way. Bob to Bob s Bank: Please transfer $1,000, to the account of my good friend Alice. January 20, 2011 Practical Aspects of Modern Cryptography 31
32 Stream Cipher Integrity It is easy for an adversary (even one who can t decrypt the ciphertext) to alter the plaintext in a known way. Bob to Bob s Bank: Please transfer $1,000, to the account of my good friend Alice. This can be protected against by the careful addition of appropriate redundancy. January 20, 2011 Practical Aspects of Modern Cryptography 32
33 Stream Ciphers are Fragile They are broken by key re-use. January 20, 2011 Practical Aspects of Modern Cryptography 33
34 Stream Ciphers are Fragile They are broken by key re-use. They require integrity checking. January 20, 2011 Practical Aspects of Modern Cryptography 34
35 Stream Ciphers are Fragile They are broken by key re-use. They require integrity checking. If you re going to use a stream cipher Seriously consider other options. Make sure you understand the risks if you make a mistake in use January 20, 2011 Practical Aspects of Modern Cryptography 35
36 Symmetric Ciphers Private-key (symmetric) ciphers are usually divided into two classes. Stream ciphers Block ciphers January 20, 2011 Practical Aspects of Modern Cryptography 36
37 Block Ciphers Why are they called block ciphers? January 20, 2011 Practical Aspects of Modern Cryptography 37
38 Block Ciphers Why are they called block ciphers? Because the cipher is defined as a function on a fixed-size block of data. January 20, 2011 Practical Aspects of Modern Cryptography 38
39 Block Ciphers Why are they called block ciphers? Because the cipher is defined as a function on a fixed-size block of data. This is called the block size and is a fundamental parameter of the cipher. January 20, 2011 Practical Aspects of Modern Cryptography 39
40 Block Ciphers Why are they called block ciphers? Because the cipher is defined as a function on a fixed-size block of data. This is called the block size and is a fundamental parameter of the cipher. Today 8- or 16-byte blocks are common, but other sizes are possible. January 20, 2011 Practical Aspects of Modern Cryptography 40
41 Block Ciphers Why are they called block ciphers? Because the cipher is defined as a function on a fixed-size block of data. This is called the block size and is a fundamental parameter of the cipher. Today 8- or 16-byte blocks are common, but other sizes are possible. Question: What s the block size of a stream cipher? January 20, 2011 Practical Aspects of Modern Cryptography 41
42 Block Ciphers -- Encryption Key Plaintext Data Usually 8 or 16 bytes Block Cipher Ciphertext January 20, 2011 Practical Aspects of Modern Cryptography 42
43 Block Ciphers -- Decryption Key Ciphertext Inverse Cipher Plaintext January 20, 2011 Practical Aspects of Modern Cryptography 43
44 Block Ciphers Q: What do I do if I want to encrypt more that one block of data with a block cipher? January 20, 2011 Practical Aspects of Modern Cryptography 44
45 Block Ciphers Q: What do I do if I want to encrypt more that one block of data with a block cipher? Simple A: Divide the to-be-encrypted plaintext into blocksize chunks, and then apply the cipher to each block. January 20, 2011 Practical Aspects of Modern Cryptography 45
46 Block Ciphers Q: What do I do if I want to encrypt more that one block of data with a block cipher? Simple A: Divide the to-be-encrypted plaintext into blocksize chunks, and then apply the cipher to each block. Real A: Divide the to-be-encrypted plaintext into blocksize chunks, and then apply the cipher to the sequence of blocks using a mode of operation. January 20, 2011 Practical Aspects of Modern Cryptography 46
47 Block Cipher Modes Electronic Code Book (ECB) Encryption: Plaintext Block Cipher Block Cipher Block Cipher Block Cipher Ciphertext January 20, 2011 Practical Aspects of Modern Cryptography 47
48 Block Cipher Modes Electronic Code Book (ECB) Decryption: Plaintext Inverse Cipher Inverse Cipher Inverse Cipher Inverse Cipher Ciphertext January 20, 2011 Practical Aspects of Modern Cryptography 48
49 Block Cipher Modes Electronic Code Book (ECB) Encryption: Plaintext Block Cipher Block Cipher Block Cipher Block Cipher Ciphertext January 20, 2011 Practical Aspects of Modern Cryptography 49
50 Why is ECB of Concern? January 20, 2011 Practical Aspects of Modern Cryptography 50
51 Why is ECB of Concern? ECB January 20, 2011 Practical Aspects of Modern Cryptography 51
52 Block Cipher Modes Cipher Block Chaining (CBC) Encryption: Incorporate an Initial Value (IV) which changes with each encryption. The IV can be A counter A random value Openly known January 20, 2011 Practical Aspects of Modern Cryptography 52
53 Block Cipher Modes Cipher Block Chaining (CBC) Encryption: IV Plaintext Block Cipher Block Cipher Block Cipher Block Cipher Ciphertext January 20, 2011 Practical Aspects of Modern Cryptography 53
54 Block Cipher Modes Cipher Block Chaining (CBC) Decryption: IV Plaintext Inverse Cipher Inverse Cipher Inverse Cipher Inverse Cipher Ciphertext January 20, 2011 Practical Aspects of Modern Cryptography 54
55 Block Cipher Modes Cipher Block Chaining (CBC) Encryption: IV Plaintext Block Cipher Block Cipher Block Cipher Block Cipher Ciphertext January 20, 2011 Practical Aspects of Modern Cryptography 55
56 Example Block Ciphers DES 3DES AES RC2, RC5, TwoFish, Serpent, etc. January 20, 2011 Practical Aspects of Modern Cryptography 56
57 Example Block Ciphers DES 3DES AES RC2, RC5, TwoFish, Serpent, etc. January 20, 2011 Practical Aspects of Modern Cryptography 57
58 Example Block Ciphers DES 3DES AES RC2, RC5, TwoFish, Serpent, etc. January 20, 2011 Practical Aspects of Modern Cryptography 58
59 Example Block Ciphers DES 3DES AES RC2, RC5, TwoFish, Serpent, etc. January 20, 2011 Practical Aspects of Modern Cryptography 59
60 How to Build a Block Cipher Plaintext Key Block Cipher Ciphertext January 20, 2011 Practical Aspects of Modern Cryptography 60
61 Feistel Ciphers Ugly January 20, 2011 Practical Aspects of Modern Cryptography 61
62 Feistel Ciphers Ugly January 20, 2011 Practical Aspects of Modern Cryptography 62
63 Feistel Ciphers Ugly January 20, 2011 Practical Aspects of Modern Cryptography 63
64 Feistel Ciphers Ugly January 20, 2011 Practical Aspects of Modern Cryptography 64
65 Feistel Ciphers Ugly Ugly January 20, 2011 Practical Aspects of Modern Cryptography 65
66 Feistel Ciphers Typically, most Feistel ciphers are iterated for about 16 rounds. Different sub-keys are used for each round. Even a weak round function can yield a strong Feistel cipher if iterated sufficiently. January 20, 2011 Practical Aspects of Modern Cryptography 66
67 Data Encryption Standard (DES) 64-bit Plaintext 56-bit Key Block Cipher 64-bit Ciphertext January 20, 2011 Practical Aspects of Modern Cryptography 67
68 Data Encryption Standard (DES) 64-bit Plaintext 56-bit Key 16 Feistel Rounds 64-bit Ciphertext January 20, 2011 Practical Aspects of Modern Cryptography 68
69 Data Encryption Standard (DES) 64-bit Plaintext 56-bit Key 16 Feistel Rounds 64-bit Ciphertext January 20, 2011 Practical Aspects of Modern Cryptography 69
70 DES Round Ugly January 20, 2011 Practical Aspects of Modern Cryptography 70
71 Simplified DES Round Function 32 bits Ugly Sub-key 4-bit substitutions 32-bit permutation January 20, 2011 Practical Aspects of Modern Cryptography 71
72 Actual DES Round Function 32 bits Ugly Sub-key 48 bits 6/4-bit substitutions 32-bit permutation January 20, 2011 Practical Aspects of Modern Cryptography 72
73 Advanced Encryption Standard Open competition run by NIST to replace DES 128-bit block size Key sizes of 128, 192, and 256 bits 15 ciphers were submitted 5 finalists were chosen January 20, 2011 Practical Aspects of Modern Cryptography 73
74 AES Finalists MARS (IBM submission) RC6 (RSA Labs submission) Rijndael (Joan Daemen and Vincent Rijmen) Serpent (Anderson, Biham, and Knudsen) Twofish (Schneier, et. al.) January 20, 2011 Practical Aspects of Modern Cryptography 74
75 AES Finalists MARS (IBM submission) RC6 (RSA Labs submission) Rijndael (Joan Daemen and Vincent Rijmen) Serpent (Anderson, Biham, and Knudsen) Twofish (Schneier, et. al.) January 20, 2011 Practical Aspects of Modern Cryptography 75
76 Rijndael k 0,0 k 0,1 k 0,2 k 0,3 k 0,4 k 0,5 k 0,6 k 0,7 k 1,0 k 1,1 k 1,2 k 1,3 k 1,4 k 1,5 k 1,6 k 1,7 k 2,0 k 2,1 k 2,2 k 2,3 k 2,4 k 2,5 k 2,6 k 2,7 k 3,0 k 3,1 k 3,2 k 3,3 k 3,4 k 3,5 k 3,6 k 3,7 16, 24, or 32 bytes of key 16, 24, or 32 bytes of data a 0,0 a 0,1 a 0,2 a 0,3 a 0,4 a 0,5 a 0,6 a 0,7 a 1,0 a 1,1 a 1,2 a 1,3 a 1,4 a 1,5 a 1,6 a 1,7 a 2,0 a 2,1 a 2,2 a 2,3 a 2,4 a 2,5 a 2,6 a 2,7 a 3,0 a 3,1 a 3,2 a 3,3 a 3,4 a 3,5 a 3,6 a 3,7 January 20, 2011 Practical Aspects of Modern Cryptography 76
77 Rijndael 4 transformations per round ByteSub: nonlinearity ShiftRow: inter-column diffusion MixColumn: inter-byte diffusion Round key addition January 20, 2011 Practical Aspects of Modern Cryptography 77
78 Rijndael ByteSub a 0,0 a 0,1 a 0,2 a 0,3 a 1,0 a 1,1 a 1,2 a 1,3 a 2,0 a 2,1 a 2,2 a 2,3 a 3,0 a 3,1 a 3,2 a 3,3 b 0,0 b 0,1 b 0,2 b 0,3 b 1,0 b 1,1 b 1,2 b 1,3 b 2,0 b 2,1 b 2,2 b 2,3 b 3,0 b 3,1 b 3,2 b 3,3 A single 8-bit to 8-bit (invertible) S-box is applied to each byte. Practical January Aspects 20, 2011 of Modern Cryptography Practical Aspects of Modern Cryptography 78 January 20,
79 Rijndael MixColumn a 0,0 a 0,1 a 0,2 a 0,3 a 1,0 a 1,1 a 1,2 a 1,3 a 2,0 a 2,1 a 2,2 a 2,3 a 3,0 a 3,1 a 3,2 a 3,3 b 0,0 b 0,1 b 0,2 b 0,3 b 1,0 b 1,1 b 1,2 b 1,3 b 2,0 b 2,1 b 2,2 b 2,3 b 3,0 b 3,1 b 3,2 b 3,3 An (invertible) linear transform is applied to each column. Practical January Aspects 20, 2011 of Modern Cryptography Practical Aspects of Modern Cryptography 79 January 20,
80 Rijndael ShiftRow a 0,0 a 0,1 a 0,2 a 0,3 a 1,0 a 1,1 a 1,2 a 1,3 a 2,0 a 2,1 a 2,2 a 2,3 a 3,0 a 3,1 a 3,2 a 3,3 a 0,0 a 0,1 a 0,2 a 0,3 a 1,3 a 1,0 a 1,1 a 1,2 a 2,2 a 2,3 a 2,0 a 2,1 a 3,1 a 3,2 a 3,3 a 3,0 A different cyclic shift is applied to each row. Practical January Aspects 20, 2011 of Modern Cryptography Practical Aspects of Modern Cryptography 80 January 20,
81 Rijndael Round key addition a 0,0 a 0,1 a 0,2 a 0,3 a 1,0 a 1,1 a 1,2 a 1,3 a 2,0 a 2,1 a 2,2 a 2,3 a 3,0 a 3,1 a 3,2 a 3,3 k 0,0 k 0,1 k 0,2 k 0,3 k 1,0 k 1,1 k 1,2 k 1,3 k 2,0 k 2,1 k 2,2 k 2,3 k 3,0 k 3,1 k 3,2 k 3,3 = b 0,0 b 0,1 b 0,2 b 0,3 b 1,0 b 1,1 b 1,2 b 1,3 b 2,0 b 2,1 b 2,2 b 2,3 b 3,0 b 3,1 b 3,2 b 3,3 The round key is XORed to complete the round. Practical January Aspects 20, 2011 of Modern Cryptography Practical Aspects of Modern Cryptography 81 January 20,
82 Rijndael Key Schedule k 0 k 1 k 2 k 3 k 4 k 5 k 6 k 7 k 8 k 9 k 10 k 11 Round key 0 Round key 1 Round key 2 The key schedule is defined on 4-byte words by k i = k i-4 k i-1 when i is not a multiple of 4 k i = k i-4 f(k i-1 ) when i is a multiple of 4 Practical January Aspects 20, 2011 of Modern Cryptography Practical Aspects of Modern Cryptography 82 January 20,
83 Agenda Symmetric key ciphers Stream ciphers Block ciphers Cryptographic hash functions January 20, 2011 Practical Aspects of Modern Cryptography 83
84 One-Way Hash Functions Generally, a one-way hash function is a function H : {0,1}* {0,1} k such that given an input value x, one cannot find a value x x such H(x) = H(x ). January 20, 2011 Practical Aspects of Modern Cryptography 84
85 One-Way Hash Functions Generally, a one-way hash function is a function H : {0,1}* {0,1} k such that given an input value x, one cannot find a value x x such H(x) = H(x ). Typically k is 128, 160, 256, 384, or 512 January 20, 2011 Practical Aspects of Modern Cryptography 85
86 One-Way Hash Functions There are many properties of one-way hashes. Non-invertability: given y, it s difficult to find any x such that H(x) = y. January 20, 2011 Practical Aspects of Modern Cryptography 86
87 One-Way Hash Functions There are many properties of one-way hashes. Non-invertability: given y, it s difficult to find any x such that H(x) = y. Second-preimage resistance: given x, it s difficult to find x x such that H(x) = H(x ). January 20, 2011 Practical Aspects of Modern Cryptography 87
88 One-Way Hash Functions There are many properties of one-way hashes. Non-invertability: given y, it s difficult to find any x such that H(x) = y. Second-preimage resistance: given x, it s difficult to find x x such that H(x) = H(x ). Collision-intractability: one cannot find a pair of values x x such that H(x) = H(x ). January 20, 2011 Practical Aspects of Modern Cryptography 88
89 Some Important Uses of One-Way Hash Functions When using a stream cipher, a hash of the message can be appended to ensure integrity. [Message Authentication Code] January 20, 2011 Practical Aspects of Modern Cryptography 89
90 Some Important Uses of One-Way Hash Functions When using a stream cipher, a hash of the message can be appended to ensure integrity. [Message Authentication Code] When forming a digital signature, the signature need only be applied to a hash of the message. [Message Digest] January 20, 2011 Practical Aspects of Modern Cryptography 90
91 What else are Hash Functions Good for? Hash functions are useful in lots of situations; here are some additional examples January 20, 2011 Practical Aspects of Modern Cryptography 91
92 What else are Hash Functions Good for? Hash functions are useful in lots of situations; here are some additional examples Uniquely and securely identify bit streams like programs. Hash is strong name for program. January 20, 2011 Practical Aspects of Modern Cryptography 92
93 What else are Hash Functions Good for? Hash functions are useful in lots of situations; here are some additional examples Uniquely and securely identify bit streams like programs. Hash is strong name for program. Entropy mixing: Since cryptographic hashes are random functions into fixed size blocks with the properties of random functions, they are often used to mix biased input to produce a seed for a pseudo-random number generator. January 20, 2011 Practical Aspects of Modern Cryptography 93
94 What else are Hash Functions Good for? Hash functions are useful in lots of situations; here are some additional examples Uniquely and securely identify bit streams like programs. Hash is strong name for program. Entropy mixing: Since cryptographic hashes are random functions into fixed size blocks with the properties of random functions, they are often used to mix biased input to produce a seed for a pseudo-random number generator. Password Protection: Store salted hash of password instead of password (Needham). January 20, 2011 Practical Aspects of Modern Cryptography 94
95 What else are Hash Functions Good for? Hash functions are useful in lots of situations; here are some additional examples Uniquely and securely identify bit streams like programs. Hash is strong name for program. Entropy mixing: Since cryptographic hashes are random functions into fixed size blocks with the properties of random functions, they are often used to mix biased input to produce a seed for a pseudo-random number generator. Password Protection: Store salted hash of password instead of password (Needham). Bit Commitment January 20, 2011 Practical Aspects of Modern Cryptography 95
96 Merkle-Damgård Construction (IV) Large Input (e.g. 512 bits) Compression Function Smaller Output (e.g. 256 bits) January 20, 2011 Practical Aspects of Modern Cryptography 96
97 A Cryptographic Hash: SHA-1 (IV) 512-bit Input Compression Function 160-bit Output January 20, 2011 Practical Aspects of Modern Cryptography 97
98 A Cryptographic Hash: SHA bit 512-bit One of 80 rounds January 20, 2011 Practical Aspects of Modern Cryptography 98
99 A Cryptographic Hash: SHA bit 512-bit No Change One of 80 rounds January 20, 2011 Practical Aspects of Modern Cryptography 99
100 A Cryptographic Hash: SHA bit 512-bit Rotate 30 bits One of 80 rounds January 20, 2011 Practical Aspects of Modern Cryptography 100
101 A Cryptographic Hash: SHA bit 512-bit No Change One of 80 rounds January 20, 2011 Practical Aspects of Modern Cryptography 101
102 A Cryptographic Hash: SHA bit 512-bit No Change One of 80 rounds January 20, 2011 Practical Aspects of Modern Cryptography 102
103 A Cryptographic Hash: SHA bit 512-bit? One of 80 rounds January 20, 2011 Practical Aspects of Modern Cryptography 103
104 A Cryptographic Hash: SHA-1 What s in the final 32-bit transform? Take the rightmost word. January 20, 2011 Practical Aspects of Modern Cryptography 104
105 A Cryptographic Hash: SHA-1 What s in the final 32-bit transform? Take the rightmost word. Add in the leftmost word rotated 5 bits. January 20, 2011 Practical Aspects of Modern Cryptography 105
106 A Cryptographic Hash: SHA-1 What s in the final 32-bit transform? Take the rightmost word. Add in the leftmost word rotated 5 bits. Add in a round-dependent function f of the middle three words. January 20, 2011 Practical Aspects of Modern Cryptography 106
107 A Cryptographic Hash: SHA bit 512-bit f One of 80 rounds January 20, 2011 Practical Aspects of Modern Cryptography 107
108 A Cryptographic Hash: SHA-1 Depending on the round, the non-linear function f is one of the following. f(x,y,z) = (X Y) (( X) Z) f(x,y,z) = (X Y) (X Z) (Y Z) f(x,y,z) = X Y Z January 20, 2011 Practical Aspects of Modern Cryptography 108
109 A Cryptographic Hash: SHA-1 What s in the final 32-bit transform? Take the rightmost word. Add in the leftmost word rotated 5 bits. Add in a round-dependent function f of the middle three words. January 20, 2011 Practical Aspects of Modern Cryptography 109
110 A Cryptographic Hash: SHA-1 What s in the final 32-bit transform? Take the rightmost word. Add in the leftmost word rotated 5 bits. Add in a round-dependent function f of the middle three words. Add in a round-dependent constant. January 20, 2011 Practical Aspects of Modern Cryptography 110
111 A Cryptographic Hash: SHA-1 What s in the final 32-bit transform? Take the rightmost word. Add in the leftmost word rotated 5 bits. Add in a round-dependent function f of the middle three words. Add in a round-dependent constant. Add in a portion of the 512-bit message. January 20, 2011 Practical Aspects of Modern Cryptography 111
112 A Cryptographic Hash: SHA-1 January 20, 2011 Practical Aspects of Modern Cryptography Picture from Wikipedia 112
113 A Cryptographic Hash: SHA bit 512-bit One of 80 rounds January 20, 2011 Practical Aspects of Modern Cryptography 113
114 From SHA-1 to SHA-2 Quick history: in 1993, NIST published SHA (Secure Hash Algorithm) as part of FIPS 180, Secure Hash Standard. January 20, 2011 Practical Aspects of Modern Cryptography 114
115 From SHA-1 to SHA-2 Quick history: in 1993, NIST published SHA (Secure Hash Algorithm) as part of FIPS 180, Secure Hash Standard. Designed by NSA January 20, 2011 Practical Aspects of Modern Cryptography 115
116 From SHA-1 to SHA-2 Quick history: in 1993, NIST published SHA (Secure Hash Algorithm) as part of FIPS 180, Secure Hash Standard. Designed by NSA Withdrawn in 1995 and replaced with SHA-1 January 20, 2011 Practical Aspects of Modern Cryptography 116
117 From SHA-1 to SHA-2 Quick history: in 1993, NIST published SHA (Secure Hash Algorithm) as part of FIPS 180, Secure Hash Standard. Designed by NSA Withdrawn in 1995 and replaced with SHA-1 One modification: single bitwise rotation added January 20, 2011 Practical Aspects of Modern Cryptography 117
118 From SHA-1 to SHA-2 Quick history: in 1993, NIST published SHA (Secure Hash Algorithm) as part of FIPS 180, Secure Hash Standard. Designed by NSA Withdrawn in 1995 and replaced with SHA-1 One modification: single bitwise rotation added In 2001, NIST revises FIPS 180 and adds SHA-2 January 20, 2011 Practical Aspects of Modern Cryptography 118
119 From SHA-1 to SHA-2 Quick history: in 1993, NIST published SHA (Secure Hash Algorithm) as part of FIPS 180, Secure Hash Standard. Designed by NSA Withdrawn in 1995 and replaced with SHA-1 One modification: single bitwise rotation added In 2001, NIST revises FIPS 180 and adds SHA-2 Also designed by NSA January 20, 2011 Practical Aspects of Modern Cryptography 119
120 From SHA-1 to SHA-2 Quick history: in 1993, NIST published SHA (Secure Hash Algorithm) as part of FIPS 180, Secure Hash Standard. Designed by NSA Withdrawn in 1995 and replaced with SHA-1 One modification: single bitwise rotation added In 2001, NIST revises FIPS 180 and adds SHA-2 Also designed by NSA Originally 3 variants: SHA-256, SHA-384, SHA-512 January 20, 2011 Practical Aspects of Modern Cryptography 120
121 From SHA-1 to SHA-2 Quick history: in 1993, NIST published SHA (Secure Hash Algorithm) as part of FIPS 180, Secure Hash Standard. Designed by NSA Withdrawn in 1995 and replaced with SHA-1 One modification: single bitwise rotation added In 2001, NIST revises FIPS 180 and adds SHA-2 Also designed by NSA Originally 3 variants: SHA-256, SHA-384, SHA-512 SHA-224 added later January 20, 2011 Practical Aspects of Modern Cryptography 121
122 Merkle-Damgård Construction (IV) Large Input (e.g. 512 bits) Compression Function Smaller Output (e.g. 256 bits) January 20, 2011 Practical Aspects of Modern Cryptography 122
123 A Cryptographic Hash: SHA-2 Prior State 256 or 512 bits New Message Bits 256 or 512 bits A B C D E F G H A B C D E F G H One of 64 rounds January 20, 2011 Practical Aspects of Modern Cryptography 123
124 A Cryptographic Hash: SHA-2 Prior State 256 or 512 bits New Message Bits 256 or 512 bits A B C D E F G H No Change A B C D E F G H One of 64 rounds B = A C = B D = C F = E G = F H = G January 20, 2011 Practical Aspects of Modern Cryptography 124
125 A Cryptographic Hash: SHA-2 Prior State 256 or 512 bits New Message Bits 256 or 512 bits A B C D E F G H What about the last 2? A B C D E F G H One of 64 rounds January 20, 2011 Practical Aspects of Modern Cryptography 125
126 A Cryptographic Hash: SHA-2 January 20, 2011 Practical Aspects of Modern Cryptography Picture from Wikipedia 126
127 From SHA-2 to SHA-3 In 2007, NIST announced that it would hold an open competition to pick a new SHA-3 hash function January 20, 2011 Practical Aspects of Modern Cryptography 127
128 From SHA-2 to SHA-3 In 2007, NIST announced that it would hold an open competition to pick a new SHA-3 hash function Similar to the competition held to pick AES. January 20, 2011 Practical Aspects of Modern Cryptography 128
129 From SHA-2 to SHA-3 In 2007, NIST announced that it would hold an open competition to pick a new SHA-3 hash function Similar to the competition held to pick AES. Submissions were due 31 October 2008 January 20, 2011 Practical Aspects of Modern Cryptography 129
130 From SHA-2 to SHA-3 In 2007, NIST announced that it would hold an open competition to pick a new SHA-3 hash function Similar to the competition held to pick AES. Submissions were due 31 October submissions accepted by NIST for Round One January 20, 2011 Practical Aspects of Modern Cryptography 130
131 From SHA-2 to SHA-3 In 2007, NIST announced that it would hold an open competition to pick a new SHA-3 hash function Similar to the competition held to pick AES. Submissions were due 31 October submissions accepted by NIST for Round One 14 submissions advanced to Round 2 January 20, 2011 Practical Aspects of Modern Cryptography 131
132 From SHA-2 to SHA-3 In 2007, NIST announced that it would hold an open competition to pick a new SHA-3 hash function Similar to the competition held to pick AES. Submissions were due 31 October submissions accepted by NIST for Round One 14 submissions advanced to Round 2 5 finalists (announced December 10, 2010) January 20, 2011 Practical Aspects of Modern Cryptography 132
133 From SHA-2 to SHA-3 In 2007, NIST announced that it would hold an open competition to pick a new SHA-3 hash function Similar to the competition held to pick AES. Submissions were due 31 October submissions accepted by NIST for Round One 14 submissions advanced to Round 2 5 finalists (announced December 10, 2010) SHA-3 expected to be formally selected in 2012 January 20, 2011 Practical Aspects of Modern Cryptography 133
134 The SHA-3 Finalists BLAKE Grøstl (Knudsen et al.) JH Keccak (Keccak team, Daemen et al.) Skein (Schneier et al.) January 20, 2011 Practical Aspects of Modern Cryptography 134
135 State of the Art for Hashes Collisions have been demonstrated for MD4 and MD5! The first SHA-1 collisions are likely to be found soon. January 20, 2011 Practical Aspects of Modern Cryptography 135
136 Integrity Checking Desirable for block ciphers Essential for stream ciphers January 20, 2011 Practical Aspects of Modern Cryptography 136
137 One-Way Hash Functions The idea of a checksum is great, but it is designed to prevent accidental changes in a message. For cryptographic integrity, we need an integrity check that is resilient against a smart and determined adversary. January 20, 2011 Practical Aspects of Modern Cryptography 137
138 Message Authentication Codes A Message Authentication Code (MAC) is often constructed with a keyed hash. If one hashes a secret key together with the correct message, an attacker who doesn t know the key will be unable to change the message without detection. But how? January 20, 2011 Practical Aspects of Modern Cryptography 138
139 Cipher Integrity Original plaintext P. Encryption key K 1. MAC key K 2. Ciphertext C=E K1 (P). MAC M=H K2 (P) or M=H K2 (C). Transmit (C,M). January 20, 2011 Practical Aspects of Modern Cryptography 139
140 Message Authentication Codes MAC key K, plaintext P, ciphertext C=E(P). MAC=H(K,P)? MAC=H(P,K)? MAC=H(K,C)? MAC=H(C,K)? There are weaknesses with all of the above. HMAC = H(K,H(K,P)) January 20, 2011 Practical Aspects of Modern Cryptography 140
141 Crypto Hygiene Do I really need to use different keys for encryption and integrity? It s always a good idea to use separate keys for separate functions, but the keys can be derived from the same master. K 1 =H( Key1,K) K 2 =H( Key2,K) January 20, 2011 Practical Aspects of Modern Cryptography 141
142 Message Digests A message digest is a short unforgeable fingerprint of a long message. A simple hash can serve as a message digest. January 20, 2011 Practical Aspects of Modern Cryptography 142
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