Theory & Background

AES operates on 4×4 byte state matrices. Key expansion: generate 14 round keys from 256-bit master key using Rijndael key schedule. Each of 14 rounds applies 4 transformations: SubBytes (16-entry S-box substitution), ShiftRows (rotate each row left by its index), MixColumns (GF(2^8) matrix multiplication — most complex step), AddRoundKey (XOR with round key). Implement GF(2^8) arithmetic: multiplication uses XTIMES function and Russian peasant multiplication.

Components & Requirements

10 components required for this project.

#	Component	Purpose	Qty
1	Python 3.10+	Implementation language (easy big integers)	x1
2	sympy (for prime generation)	Large prime number generation	x1
3	pytest	NIST test vectors for validation	x1
4	Hypothesis library	Property-based testing (encrypt then decrypt)	x1
5	bitstring	Bit-level manipulation	x1
6	Timing analysis tools	Side-channel vulnerability research	x1
7	NIST FIPS standards	Algorithm specification documents	x1
8	PyCryptodome (reference)	Reference implementation for test comparison	x1
9	SageMath (optional)	Elliptic curve mathematics	x1
10	Jupyter	Mathematical exploration	x1

Step-by-Step Implementation

Follow these 3 steps carefully.

1

AES-256 Block Cipher Implementation

AES operates on 4×4 byte state matrices. Key expansion: generate 14 round keys from 256-bit master key using Rijndael key schedule. Each of 14 rounds applies 4 transformations: SubBytes (16-entry S-box substitution), ShiftRows (rotate each row left by its index), MixColumns (GF(2^8) matrix multiplication — most complex step), AddRoundKey (XOR with round key). Implement GF(2^8) arithmetic: multiplication uses XTIMES function and Russian peasant multiplication.

2

RSA Key Generation and Operations

Key generation: generate two large primes p, q (512 bits each for 1024-bit RSA). n = p×q. φ(n) = (p-1)(q-1). Choose e (typically 65537, must be coprime to φ(n)). Compute d = e^-1 mod φ(n) using Extended Euclidean Algorithm. Public key: (n, e). Private key: (n, d). Encrypt: C = M^e mod n. Decrypt: M = C^d mod n. Miller-Rabin primality test for large primes. Chinese Remainder Theorem for efficient decryption.

3

SHA-256 Hash Function

SHA-256 processes messages in 512-bit (64-byte) blocks. Preprocessing: append

Code & Implementation

Core code for aes.py:

aes.py
  Python

Testing & Troubleshooting

Test Cryptography Library Implementation by verifying each subsystem individually before full integration.

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Troubleshooting Tips

Verify power voltages, check ground connections, use serial monitor for debug.

Real-World Applications

*Secure messaging application development

*Digital signature system for documents

*Certificate authority implementation

*Password manager encryption

*Blockchain cryptography education

*VPN tunnel establishment

*Secure file storage system

*Academic cryptography course

Extensions & Next Steps

Implement post-quantum cryptography (Kyber, Dilithium)
Build a TLS 1.3 handshake implementation
Add zero-knowledge proof implementation (ZKP)
Implement threshold cryptography (Shamir Secret Sharing)
Build an authenticated encryption with associated data (AEAD) mode

Interactive Playground

Coming Soon

An interactive simulator will be available here — simulate circuits and run code in-browser without hardware.

Frequently Asked Questions

Why should I never implement cryptography for production use?

Cryptographic implementations are notoriously difficult to make secure against side-channel attacks (timing attacks — code branches that leak secret information through timing, power analysis, cache timing). Naive Python AES implementations are orders of magnitude slower than optimized C implementations and vulnerable to timing attacks (dict lookups take variable time based on cache state). For production: always use well-audited libraries (PyCryptodome, cryptography.io). This implementation is educational only — to understand the mathematics, not deploy.

What is the difference between symmetric and asymmetric encryption?

Symmetric (AES): same key for encryption and decryption. Very fast (GHz throughput). Key distribution problem: how to securely share the key? Asymmetric (RSA): public key encrypts, private key decrypts. Secure key exchange without prior shared secret. Very slow (10,000× slower than AES). In practice: use asymmetric to exchange a symmetric session key, then switch to symmetric for bulk data. This hybrid approach is used in TLS/HTTPS: RSA/ECDH for key agreement, AES-256-GCM for data encryption.

Introduction