Cryptographic Hash Functions

• Cryptographic hash functions transform arbitrary-sized data into fixed-size "fingerprints."
• These "fingerprints" are called hashes or message digests.
• A good hash function is easy to compute, hard to invert (preimage resistance), and avoids collisions (collision resistance).

Preimage Resistance

• Given a hash value, it's computationally infeasible to find any input that produces that hash; this is also known as one-wayness.
• Preimage resistance is like a one-way street, easy to go forward (hash), but hard to go backward (find the original message).

Second Preimage Resistance

• Given an input and its hash, it's hard to find a different input that produces the same hash.
• Second preimage resistance is weaker than collision resistance.

Collision Resistance

• It should be hard to find any two different inputs that hash to the same value.
• Finding collisions easily could allow substitution of a benign contract for a malicious one with the same hash, tricking someone into signing the malicious contract.

Birthday Paradox

• Demonstrates that finding collisions is easier than intuitively expected.
• In a room of 23 people, there's a 50% chance two share a birthday because comparisons are made between each person.
• In hashing, you only need to try the square root of the total number of possible hashes to have a high probability of finding a collision.

Properties of Cryptographic Hash Functions

• Deterministic: The same input always produces the same hash output.
• Quick Computation: Hashing any input should be easy and fast.
• Preimage Resistance: Given a hash, it should be infeasible to find the original input.
• Second Preimage Resistance: Given an input, it should be infeasible to find a different input with the same hash.
• Collision Resistance: Finding two different inputs that produce the same hash should be infeasible.

Common Hash Algorithms

• Message Digest 5 (MD5) is an older algorithm that produces 128-bit hashes and is now considered broken.
• Secure Hash Algorithm 1 (SHA-1) is another older algorithm, producing 160-bit hashes and is now considered broken.
• It is not safe to use MD5 or SHA-1 in new applications due to collision attacks.
• Secure Hash Algorithm 256 bit (SHA-256) is a widely used hash function that produces 256-bit hashes.
• Secure Hash Algorithm 384 bit (SHA-384) is a member of the SHA-2 family, producing 384-bit hashes.
• Secure Hash Algorithm 512 bit (SHA-512) is a member of the SHA-2 family, producing 512-bit hashes.
• SHA-256, SHA-384, SHA-512, and other SHA-2 variants are still considered secure.
• SHA-3 is a different hash function design than SHA-2, and the winner of a NIST competition to create a new standard.
• SHA-3 includes functions like Keccak.

Applications of Hash Functions

• Data Integrity Verification: Detects file modification by hashing a file and comparing the hash later.
• Password Storage: Protects against data breaches by storing hashes of passwords instead of plaintext passwords.
• Digital Signatures: Creates a short "summary" of a document before signing it with a private key.
• Blockchain Technology: Links blocks together and ensures data integrity.
• Message Authentication Codes (MACs): Provides data integrity and authentication when combined with secret keys.

Password Storage

• Never store passwords in plaintext.
• Even if a database is breached, the passwords remain protected.
• Instead, hash the password and store the hash.
• During login, hash the entered password and compare the hashes.
• Salting adds a unique string to each password before hashing, preventing rainbow table attacks.
• Rainbow tables are precomputed tables of hashes used to quickly reverse common passwords, and salting makes each password hash unique.
• Key Derivation Functions like Argon2, scrypt, and bcrypt are preferred for password storage as they are designed to be slow, making brute-force attacks more difficult.

Data Integrity

• Hash functions ensure data has not been tampered with.
• Hash the original data and store the hash value.
• Later, hash the data again and compare the new hash with the original hash.
• If the hashes match, the data is intact.
• If the hashes differ, the data has been modified.
• This is useful for verifying downloads, detecting file corruption, and ensuring the integrity of stored data.

Digital Signatures

• Hash functions are an essential part of digital signatures.
• Instead of signing the entire document, a hash of the document is signed.
• This is more efficient, as the hash is much smaller than the document.
• The recipient verifies the signature by hashing the document themselves and comparing the result to the signed hash.
• If the hashes match, the document's authenticity and integrity are proven.

Blockchain

• Blockchains use hash functions extensively.
• Each block contains a hash of the previous block, creating a chain of blocks that is resistant to tampering.
• If any block is modified, its hash changes, and all subsequent blocks' hashes will also change.
• Proof-of-Work algorithms often involve finding an input that, when hashed, meets certain criteria (e.g., having a certain number of leading zeros).
• This is computationally intensive and adds security to the blockchain.

Attacks on Hash Functions

• Rainbow Table Attacks: Precomputed tables of hashes used to reverse common passwords (addressed by salting).
• Brute-Force Attacks: Trying all possible inputs until a match is found (longer hashes are more resistant).
• Collision Attacks: Finding two different inputs that produce the same hash (a major weakness in older algorithms like MD5 and SHA-1).
• Length Extension Attacks: Exploiting the internal structure of some hash functions to compute a new hash based on the original hash and some appended data.
• Side-Channel Attacks: Exploiting information leaked during the hash computation process (e.g., timing information, power consumption).

Choosing a Hash Function

• Use well-established and widely-vetted algorithms like SHA-256, SHA-384, SHA-512, or SHA-3.
• Avoid older algorithms like MD5 and SHA-1.
• For password storage, use key derivation functions like Argon2, scrypt, or bcrypt.
• Consider the security requirements of your application.
• The chosen hash function is suitable for the task
• Keep up with the latest research on hash function security and be prepared to migrate to new algorithms if necessary.