1. Cryptographic Hash Functions and Protocol Analysis

2. Hash Functions
Hash function h maps an input x of arbitrary length to a fixed length output h(x) (compression)
Accidental or intentional change to the data will change the hash value
Given h and x, h(x) is easy to compute (ease of computation)
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3. Good Hash Function
It is easy to compute the hash value for any given message
It is infeasible to find a message that has a given hash
It is infeasible to modify a message without changing its hash
It is infeasible to find two different messages with the same hash
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4. Hash functions
Preimage resistant (one-way): if for all specified outputs, it is computationally infeasible to find any input that hashes to that output
Second-preimage resistent (weak collision resistant): if it is computationally infeasible to find any second input which has the same output as any specified input
Collision resistant (strong collision resistant): if it is computationally infeasible to find any two distinct inputs that has the same output
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5. Attacks
First preimage attack: given a hash h, find a message m such that hash(m) = h
Second preimage attack: given a fixed message m1, find a different message m2 such that hash(m2) = hash(m1)
Attack complexity: 2n (considered too high for a typical output size of n=160 bits)
Practical attacks: Collision attack
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6. Collision Attack Birthday attack:
Cryptographic attack
Exploits the mathematics behind the birthday problem in probability theory
Given a function ƒ, the goal of the attack is to find two different inputs x1, x2 such that ƒ(x1) = ƒ(x2)
Method: evaluate the function ƒ for different input values that may be chosen randomly or pseudorandomly until the same result is found more than once (complexity is 2n/2)
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7. Hash Functions Message digest
Used for authenticity (sign hash value of a message) and integrity purposes
Algorithms:
SHA-1,MD2,MD4,
MD5
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8. MD5 Message Digest Algorithm
Input of arbitrary length
Output: 128 bits
Block size: 512 bits
1991: designed by Ron Rivest to replace MD4
1996, …, 2008: Weaknesses in MD5
Cryptographically broken
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9. MD6 MD6 was submitted to the NIST SHA-3 competition
July 1, 2009: Rivest posted a comment at NIST that MD6 is not yet ready to be candidated for SHA-3
speed issues and
inability to supply a proof of security for a faster reduced-round version
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10. MD5 Processing
Append padding bits so length  448 mod 512 (padded message 64 bits less than an integer multiplied by 512)
Append length: a 64-bit representation of the length of the original message (before the padding)  total length of message k*512 bits
Initialize MD buffer: 128-bit buffer holds intermediate and final results (4 32-bit registers, ABCD)
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11. MD5 Processing Process message in 512-bit blocks:
4 rounds of processing
Similar structure but different logical function
Each round takes the 512-bit input and values of ABCD and modifies ABCD
Output: from the last stage is a 128-bit digest
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12. Strength of MD5
Every bit of plain text influences every bit of the the hash code
Complex repetition of the basic functions  unlikely that two random messages would have similar regularities
MD5 is as strong as possible for 128-bit digest (Rivest’s conjecture)
Hasn’t been disproved yet
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13. Secure Hash Algorithm
SHA was developed by National Institute of Standards and Technology
1993: Published as Federal Information Processing Standard (FIPS PUB 180)
SHA-0, SHA-1, and SHA-2
SHA-1: best known and widely used
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14. SHA Security SHA-1: in 2005 security flaws were identified
A possible mathematical weakness might exist
SHA-2: no attacks have yet been reported
SHA-2 variants are algorithmically similar to SHA-1 and so efforts are underway to develop improved alternatives
SHA-3: new hash standard is currently under development
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15. SHA-1 Input length: max. (264 − 1) bits Output length: 160-bit
Based on principles similar to those used in the design of the MD4 and MD5
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16. SHA-2 Family 2001: first published in the draft FIPS PUB 180-2
2002, 2004: FIPS PUB modified
SHA-224, SHA-256, SHA-384, and SHA-512
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17. MD5 vs. SHA
Very similar
Security: SHA’s digest is 32 bits longer  without algorithm flaws SHA is more secure
Speed:SHA has more steps and produces 160-bit buffer  SHA slower
Simplicity and compactness: MD5 has more internal steps with varying buffer modification  SHA is simpler
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18. Protocol Analysis Exercise 1.
Assume that Jane and Paul want to efficiently send very large files to each other. They also want to provide integrity verification, third- party message authentication (i.e., a third party can verify who the originator of the message is), and limit the scope of a compromise (i.e., providing forward secrecy). You can assume that Jane and Paul have public and secret key encryption capabilities, can generate a hash function, and they have a shared secret key K0 established before the communication. They do not have access to a mutually trusted server, and no other keys but K0 are known at the beginning of the communication. Propose a security protocol to establish necessary keys and show how Jane can send a file to Paul.
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19. Exercise 2.
Message authentication and key agreement Alice wants to establish a secure communication with Bob. They agree to user the Yahalom protocol for mutual authentication and key agreement. The protocol uses symmetric key encryption only. Alice has a secret key shared with a trusted third party Server, KA and, similarly, Bob has a secret-key shared with Server, KB. NA and NB are nonces generated by Alice and Bob, respectively. E(M, K) indicates encryption of message M with key K, “||” means concatenation of messages. Explain after each protocol step what the recipient of the message knows based on the message and the properties of the encryption and what he/she is capable of doing. For example,
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20. Exercise 2.
Message1: Alice  Server: IDA || E(“request for session key to Bob”, KA)
Server:
The server sees that that claimed sender of the message is Alice.
The server can decrypt the message using KA that is shared between Alice and the Server. The message must have been sent by Alice because KA is only known by Alice and the server.
The server knows that Alice is requesting a session key to be used by Alice and Bob.
The server can generate a session key KS to be used by Alice and Bob and send the key to …
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21. Exercise 2.
Message1: Alice  Bob: IDA || NA Bob knows/can do Message2: Bob  Server: IDB || E[(IDB || NA || NB), KB] Server knows/can do Message3: Server  Alice: E[(IDB || KS || NA || NB), KA] || E[(IDA || KS), KB] Alice knows/can do Message4: Alice  Bob: E[(IDA || KS), KB] || E(NB, KS)]
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22. Exercise 3.
Secure communication Consider the following protocol. Ann wants to send a message M securely to Bob but there is no shared secret key between Ann and Bob, Ann does not even know Bob’s public key. However, using the properties of RSA (in particular the commutative property), Ann proposes the following protocol, where E(M, K) indicates encryption/decryption of message M with key K, “||” means concatenation of messages, KpubA means the public key of A, KprivA means private key of A.
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23. Exercise 3.
Message1: Ann  Bob: IDA || E(M, KpubA) Message 2: Bob  Ann: IDB || E[(E(M, KpubA)), KpubB) Message3: Ann  Bob: IDA || E(M, KpubB) Show a man-in-the-middle attack against the above protocol.
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24. Next class Review of cryptography and security protocols Lecture 8-9
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