Cryptographic Hash Functions Overview

Cryptography and Network Security - Week 9-11

• Message Integrity: Cryptography systems often provide secrecy but not integrity. Integrity is required when secrecy is not necessary, ensuring data hasn't been altered.
• Document and Fingerprint: One way to ensure document integrity is through fingerprinting. A digital "fingerprint" (message digest) is comparable to a fingerprint and is linked to the document.
• Message and Message Digest: The electronic equivalent of a document/fingerprint is a message/digest pair. A hash function generates the digest (fingerprint) from the message.
• Difference: Documents and fingerprints are physically linked. Messages and digests can be separated, and critically, the digest needs protection from tampering.
• Checking Integrity: A hash function produces a current digest for a message. Comparing this to an earlier digest (known value) ensures data integrity, and if the digests match the message hasn't changed.

Cryptographic Hash Function Criteria

• Preimage Resistance: Given a hash value, it is computationally infeasible to find an input that produces that hash value.
• Second Preimage Resistance: Given an input and a hash value, it is computationally infeasible to find another input that produces the same hash value.
• Collision Resistance: It is computationally infeasible to find two different inputs that produce the same hash.

Random Oracle Model

• The Random Oracle Model was introduced in 1993 by Bellare and Rogaway.
• An ideal model for hash functions, assuming the hash function outputs a random result, uncorrelated with the input.
• This is a mathematical model for assessing if hash functions are trustworthy.
• It simplifies the analysis of cryptographic protocols. (Simplified by ignoring the specific mathematical implementation)
• The random values are only used for evaluating, that is, evaluating only.

Attacks on Random Oracle Model

• Preimage Attack: Algorithm that tries to find an input that maps to a given hash value.
• The difficulty is proportional to 2ⁿ, where n is the number of bits in the hash.
• Second Preimage Attack: Given a message and its hash, tries to find another message with the same hash.
• The difficulty is proportional to 2ⁿ.
• Collision Attack: Seeks to find two different messages that produce the same hash.
• The difficulty is proportional to 2^n/2, where n is the number of bits in the hash.

Message Authentication

• Modification Detection Code (MDC): A message digest verifying message integrity, not the sender.
• Message Authentication Code (MAC): Used to authenticate the originator of a message. It involves a secret key only known to sender and receiver.
• MAC Properties: A MAC is a condensed checksum of a variable-length message using a secret key. It should be computationally hard to find different messages that result in the same MAC.
• MAC Requirements: Knowing a message and its MAC, it should be infeasible to find another message having the same MAC. MACs should be distributed uniformly. A MAC should depend equally on all bits of the message.

Keyed Hash Functions

• Cryptographic hash functions can also be used for keyed-MACs
• Generally faster than block ciphers
• Improved by using HMAC (Hash-based message authentication code)
• Addresses some weaknesses in earlier keyed hash designs with a more rigorous method.

HMAC

• A keyed hash function, standardized in RFC2104.
• Designed to use a hash function without modification.
• Has added overhead for key-use, often just 3 hash block calculations.
• Provides the security of the underlying hash algorithm and addresses some vulnerabilities in earlier designs.

Hash Function Requirements

• Variable Input Size: Hash functions can accept messages of any length.
• Fixed Output Size: Hash functions produce a hash of fixed length.
• Efficiency: Hash computation should be relatively quick, for practical use.
• Preimage Resistance: Finding an input that produces a given output should be computationally difficult.
• Second Preimage Resistance: Finding a second input that has the same output as a given input should be computationally difficult.
• Collision Resistance: Finding two different inputs that produce the same output should be computationally difficult.
• Pseudorandomness: The output of the hash function should satisfy standards for pseudorandomness tests.

Birthday Attacks

• A collision attack technique that exploits the properties of hash functions.
• It attempts to find two different inputs that produce the same hash.
• Its difficulty is proportional to the square root of the number of possible hash outputs.

Hash Function Cryptanalysis

• Hash functions use iterative structures, processing messages in blocks.
• Cryptanalysis attacks exploit structural weaknesses in hash functions.

Block Ciphers as Hash Functions

• Some simple methods use block ciphers as hash functions.
• These functions often result in small/insufficient hash values (e.g., 64 bits).

Secure Hash Algorithm (SHA-1 and SHA-512)

• SHA-1: A secure hash algorithm, producing a 160-bit hash value.
• SHA-512: A revised version, producing 512-bit hash values. More secure and robust.
• SHA algorithms use a compression function, iterative in nature.
• Both use a modular-style structure for calculating the hash.
• The algorithms involve various cryptographic transformations like (e.g., rotations, additions, non-linear functions).

MD5

• A 128-bit hash algorithm.
• Designed by Ronald Rivest, it was used extensively before its vulnerabilities were discovered.
• Multiple security concerns and attacks have been found.
• Now considered insecure for most purposes.
• An example of a hash function often used in the past but now considered less secure against new attacks.

Modified Secure Hash Algorithms (SHA-256, SHA-384, SHA-512)

• SHA-2 algorithms are stronger and more resistant to attacks.

Additional Security Services

• Confidentiality: Applies a layer of encryption to prevent unauthorized access to the message.
• Nonrepudiation: Ensures that the sender cannot deny sending the message.
• A digital signature can typically handle the latter three (integrity, authenticity and nonrepudiation) by itself, while confidentiality typically requires additional encryption layers.

Attack Types and Forgery Types

• Key-Only Attacks: Attacks focusing on obtaining the secret key.
• Known-Message Attacks: Attacks making use of known pairs of messages, keys, and MAC values
• Chosen-Message Attacks: Attacks where an attacker can choose messages to be signed.
• Existential Forgery: Attack where an attacker can create a valid signature for a message without knowing the private key.
• Selective Forgery: Attack where an attacker has some control over the messages used in the forgery.
• Total Break: An attacker is able to derive the private key from the algorithm.

Digital Signature Schemes

• RSA: A public-key-based digital signature scheme.
• ElGamal: Another public-key-based digital signature scheme.
• Schnorr: A digital signature scheme.
• DSS (Digital Signature Standard): A standard for digital signatures.
• ECDSA (Elliptic Curve Digital Signature Algorithm): A digital signature scheme that is based on elliptic curve cryptography.

Conclusion:

• Modern hashing and keying mechanisms are becoming more sophisticated, to provide better security, and more efficient processes.

This quiz explores fundamental concepts related to cryptographic hash functions, including their properties, limitations, and the Secure Hash Algorithm (SHA). It also examines the methodologies behind using block ciphers as hash functions and the implications of various security features. Test your knowledge and understanding of cryptographic principles.