PCEA — Prime Circular Encryption Algorithm

Pure-Python, zero-dependency library implementing the prime-circular base number encryption algorithm for neural architecture state.

Purpose

Encrypts neural architecture state using the relationship between the current state and the previous (last) state. No external dependencies. Framework-agnostic: operates on flat integer sequences — callers pre-quantize their framework's weight or activation tensors.

Algorithm

For each index i in the state:

1. Select prime p = PRIME_CIRCLE[i % 53] (circular indexing over 53 primes: 2, 3, 5, …, 241)
2. Decompose state[i] into bijective base-p digits — each digit in {1, …, p}
3. Extract key digits from last_state[i % L] in standard base p
4. Shift each digit additively mod p, staying within {1, …, p}
5. Reconstruct the encrypted value

Bijective base-p encoding guarantees that encrypted values always have the same digit count as the originals. Decryption is the additive inverse and requires the same last_state.

encrypt: e_j = ((v_j - 1 + k_j) mod p) + 1
decrypt: v_j = ((e_j - 1 - k_j) mod p) + 1

Usage

from pcea import encrypt_state, decrypt_state, PCEAInstance

# Stateless (caller manages last_state)
state      = [1000, 2000, 3000]   # pre-quantized integers
last_state = [500,  600,  700]

encrypted  = encrypt_state(state, last_state)
recovered  = decrypt_state(encrypted, last_state)
assert recovered == state

# Stateful (instance advances last_state automatically)
enc = PCEAInstance(seed=[1, 2, 3])
dec = PCEAInstance(seed=[1, 2, 3])

e1 = enc.encrypt([100, 200, 300])
e2 = enc.encrypt([400, 500, 600])

assert dec.decrypt(e1) == [100, 200, 300]
assert dec.decrypt(e2) == [400, 500, 600]

Install

pip install .          # runtime — no dependencies
pip install ".[dev]"   # adds pytest

Author

Erin Patrick Spencer — interdependentway.org