What is Hashing?

Using mathematical formulas to transform messages into fixed length, deterministic strings

Purpose Has the original message changed since it was hashed ?

$$ Message \xrightarrow{Hashing} Digest $$

Digest is also known as a Hash / Checksum / Fingerprint / CRC, etc

Hash Functions or Algorithms

Functions used to map data of an arbitrary size to return data of fixed size

A hash function takes some string and coverts it into a fixed length string. Hash functions are pseudo-random

Cryptographic Hash Function

• Deterministic
• Fast
• Irreversible
• Utilize the Avalanche effect
• Collision resistant

Takeaways

• Pre-image resistance
• Second pre-image resistance
• unbreakable without sing a brute force approach
• one-way

Practical Uses

• Verifying file and message integrity
• File and Data identification (Git)
• Password Verification

Rules

1. It must be deterministic same input always has the same output

2. Fixed Length Output for all possible inputs

3. Irreversible Output

examples:

Legacy: MD5, SHA1

Modern: SHA224, SHA256, SHA384, SHA512

Future: SHA3-224, SHA3-256, SHA3-384, SHA3-512

Hash Collisions

Collision refers to two messages resulting in identical digests Cannot be avoid as they are byproduct of "fixed width digests" Can only be made more rare

Ref: Birthday Paradox, Pigeonhole Principle

Data Integrity - How Hashing is used to ensure data isn't modified - HMAC

Message Authentication Code (MAC)

• Concept of combining a message with a secret key before hashing

Purpose

• Detect unauthorized alteration of message & digest
• Only whoever has the acceptable key can create an acceptable digest
• Integration and Authentication of bulk data

Challenges: Key-Exchange problem

Industry Standard Specification of combining message and key

• HMAC (Hash Based Message Authentication Code) RFC 2104

Other examples:

Legacy: (none in significant use)

Modern: HMAC, Poly1305

Future: GCM, CCM, (AEAD Ciphers)

Hashing Algorithms Examples

Real World Hashing Algorithms must satisfy four requirements

1. Infeasible to produce a given digest
2. Impossible to extract original message
3. Slight changes produce drastic differences
4. Resulting digest is fixed width

uses : Message Authentication, Digital Signatures

djb2 - simple hashing algorithm

https://theartincode.stanis.me/008-djb2/

Variable Length Output Function

MD5 Message-Digest Algorithm

https://www.ietf.org/rfc/rfc1321.txt

MD5 Function takes a 512 bits input and returns a pseudorandom 128 bits output It operates on 32 bit chucks (words)

Starts with a hardcoded 128 bit value called as a internal state and it updates as the algorithm runs and returns it in the end

SHA : Secure Hashing Algorithm