Understanding Cryptocurrency: Exploring Cryptographic Hash Functions and Digital Signatures

TL;DR: This article dives deep into cryptographic hash functions and their role in cryptocurrencies, primarily focusing on collision-free, hiding, and puzzle-friendly properties. It also explains SHA-256, the hash function used by Bitcoin, along with hash pointers, blockchain, and Merkle trees. Lastly, it elucidates digital signatures and their implementation in cryptocurrencies, considering the public keys as identities and privacy concerns that arise from it.


Cryptocurrencies, the most famous of which is Bitcoin, rely on advanced cryptographic techniques to secure transactions and control the creation of new units. Two essential components of these techniques are cryptographic hash functions and digital signatures. In this article, we will examine these concepts in depth, explaining their role and importance in cryptocurrency systems.

Cryptographic Hash Functions

A cryptographic hash function is a mathematical function with three main attributes:

  1. It can take any string as input.
  2. It produces a fixed-size output.
  3. It is efficiently computable.

For cryptocurrencies, we need cryptographically secure hash functions that feature three additional properties:


In a collision-free hash function, no two different inputs will result in the same output. However, it’s essential to understand that no hash function is proven to be entirely collision-free. Still, the likelihood of collision is so low that it’s practically negligible, making the function practically collision-free.


Hiding means that, given the output of the hash function, it’s virtually impossible to figure out the input. To ensure the “hiding” property, the hash function usually combines the input with a random number (r) selected from a highly distributed range. This mechanism, known as a commitment scheme, is integral to maintaining the integrity of cryptocurrency transactions.


A puzzle-friendly hash function means it’s infeasible to select an input that will result in a predetermined output, even if a part of the input is fixed and known.

The SHA-256 hash function, used by Bitcoin, adheres to all these principles. It operates on input messages broken into 512-bit blocks, padded as necessary, and applies a compression function to produce a final 256-bit output, or hash.

Hash Pointers and Data Structures

A hash pointer serves as a reference to where information is stored and a cryptographic hash of the information itself. This design allows us to retrieve the information and verify that it hasn’t been tampered with. By using hash pointers instead of regular pointers, we can create structures such as blockchains and Merkle trees, providing a tamper-evident log functionality. Any changes in the data would result in a change in its hash, alerting us to the tampering.

Digital Signatures

Digital signatures, similar to paper signatures, provide a mechanism for verifying the authenticity of a message. They enable only the legitimate owner to sign a document, allow anyone to verify the signature, and tie the signature to a specific document to prevent forgery.

Digital signatures involve three primary operations:

  1. Generating keys.
  2. Signing messages with the private key.
  3. Verifying the signature with the corresponding public key.

The requirements for digital signatures are strict. They should always verify when signed with the correct private key, and it should be computationally unfeasible to forge signatures.

Public Keys as Identities

In cryptocurrency systems, public keys can serve as identities. Whoever possesses the corresponding private key can “speak for” and issue statements as that identity. Since generating new key pairs is straightforward, this allows for decentralized identity management.

While this allows users to have multiple identities and can offer a degree of anonymity, it also raises privacy concerns. Although the identities are not tied to real-world identities, patterns in activity can potentially reveal information about the users behind the identities.


Understanding cryptographic hash functions and digital signatures is fundamental to comprehending how cryptocurrencies function. These two concepts form the backbone of cryptocurrencies, enabling secure, verifiable transactions while maintaining user anonymity. As cryptocurrencies continue to evolve, it’s essential to continue deepening our understanding of these underlying cryptographic principles.