BEGINNER · 10 MIN · FREE LESSON

Cryptographic hash functions

Explore cryptographic hash functions through a visual, step-by-step model.

Size 8

Use {"text":"hello","byte":0}. Flip one low bit of one UTF-8 input byte and compare actual SHA-256 outputs. This demonstrates avalanche, not a proof of security.

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? comparing
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✓ visited
Q queued
✓ done

One input bit changes before two real SHA-256 computations.

Code language

Speed

1 / 34

Live variables

inputBytes: 5
changedByte: 0

Operation counters

comparisons: 0
swaps: 0
reads: 0
writes: 0
hashes: 2
hashInputBytes: 10

Complexity · O(n)

best: O(n) input hashing
average: O(n)
worst: O(n)
space: O(1) digest/state, excluding input buffers

SHA-256 processes fixed-size blocks and emits 256 bits. A fixed-length digest cannot uniquely encode every input; collision resistance is a computational property, not an absence of possible collisions.

n=8

n=16

n=32

n=64

128

Input bytes hashed by two digests, seed 42. Plotted sample sizes respect each lesson’s explicit input limits.

Keyboard: Space play/pause · ←/→ step · R restart · 1–5 speed. Reduced motion disables transitions.

Cryptographic Hash Functions

Hook

A cryptographic fingerprint is deliberately sensitive to changes anywhere in its input.

Watch

Change one bit. Compare the whole digest. The inputs are examples, never application secrets. Public fixed fixtures make repeated traces deterministic.

How it works

Encode the example as UTF-8 bytes.
Flip one selected input bit.
Compute actual SHA-256 digests.
Count the differing output bits.

Try it

Predict the verification outcome or modular-arithmetic decision. Toggle tampering or change the input, then explain why the observed result changes.

Complexity

O(n) input hashing and fixed-size digest state. Library calls perform real cryptographic operations; the trace illustrates protocol-level stages rather than claiming to animate every internal cipher round. Big-integer and curve costs depend on security parameters.

Code

Node.js uses its standard crypto/TLS libraries. Python AES/Ed25519 references require the maintained cryptography package; other Python references use the standard library. Java uses JDK cryptography/TLS APIs. C++ references require OpenSSL headers and linking libcrypto/libssl where used. Textbook RSA and tiny-group DH snippets are explicitly insecure mathematical demonstrations.

When to use

Use standard cryptographic hashes for integrity constructions and established protocols, with authentication where required.

Interview pitfalls

A digest is not encryption. Avalanche examples do not prove preimage or collision resistance.

Quiz

Distinguish confidentiality, integrity, identity and the limits of a demonstration.

MAKE IT STICK

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