Symphonic Cipher

Intent-Modulated Conlang + Harmonic Verification System

A mathematically rigorous authentication protocol that combines:

Private conlang (constructed language) dictionary mapping
Modality-driven harmonic synthesis
Key-driven Feistel permutation
Studio engineering DSP pipeline
AI-based feature extraction and verification
RWP v3 cryptographic envelope

Overview

The Symphonic Cipher authenticates commands by encoding them as audio waveforms with specific harmonic signatures. Different “intent modalities” (STRICT, ADAPTIVE, PROBE) produce different overtone patterns that can be verified through FFT analysis.

Architecture

[Conlang Phrase] → [Token IDs] → [Feistel Permutation] → [Harmonic Synthesis]
        ↓
[DSP Chain: Gain → EQ → Compression → Reverb → Panning]
        ↓
[RWP v3 Envelope: HMAC-SHA256 + Nonce + Timestamp]
        ↓
[Verification: MAC Check + Harmonic Analysis + AI Classification]

Mathematical Foundation

1. Dictionary Mapping (Section 2)

Bijection between lexical tokens and integer IDs:

∀τ ∈ D: id(τ) ∈ {0, ..., |D|-1}

2. Modality Encoding (Section 3)

Each modality M determines which overtones are emitted via mask M(M):

Modality	Mask M(M)	Description
STRICT	{1, 3, 5}	Odd harmonics (binary intent)
ADAPTIVE	{1, 2, 3, 4, 5}	Full series (non-binary intent)
PROBE	{1}	Fundamental only

3. Per-Message Secret (Section 4)

K_msg = HMAC_{k_master}(ASCII("msg_key" || n))

4. Feistel Permutation (Section 5)

4-round balanced Feistel network:

L^(r+1) = R^(r)
R^(r+1) = L^(r) ⊕ F(R^(r), k^(r))

5. Harmonic Synthesis (Section 6)

x(t) = Σᵢ Σₕ∈M(M) (1/h) sin(2π(f₀ + vᵢ'·Δf)·h·t)

Where:

f₀ = 440 Hz (base frequency)
Δf = 30 Hz (frequency step per token ID)

6. DSP Pipeline (Sections 3.2-3.10)

Gain Stage: v₁ = g · v₀, where g = 10^(G_dB/20)
Mic Pattern Filter: v₂[i] = v₁[i] · (a + (1-a)·cos(θᵢ - θ_axis))
Parametric EQ: Biquad IIR filter with peak/shelf modes
Compressor: Piecewise-linear gain reduction with attack/release
Convolution Reverb: z[n] = (x * h)[n]
Stereo Panning: Constant-power law L/R distribution

7. RWP v3 Envelope (Section 7)

C = "v3." || σ || AAD_canon || t || n || b64url(x)
sig = HMAC_{k_master}(C)

Installation

pip install -r requirements.txt

Usage

Basic Example

from symphonic_cipher import SymphonicCipher, Modality

# Create cipher with auto-generated key
cipher = SymphonicCipher()

# Encode a conlang phrase
envelope = cipher.encode(
    phrase="korah aelin dahru",
    modality=Modality.ADAPTIVE,
    tongue="KO"
)

# Verify envelope
success, message = cipher.verify(envelope)
print(f"Verified: {success}")

With DSP Processing

from symphonic_cipher import SymphonicCipher, Modality
from symphonic_cipher.dsp import DSPChain

# Create cipher and DSP chain
cipher = SymphonicCipher()
dsp = DSPChain()

# Configure studio engineering stages
dsp.configure_compressor(threshold_db=-20, ratio=4.0)
dsp.configure_reverb(wet_mix=0.2)
dsp.configure_panning(pan_position=0.3)

# Encode and process
envelope, components = cipher.encode(
    "korah aelin",
    modality=Modality.STRICT,
    return_components=True
)

# Get raw audio and process through DSP
import numpy as np
import base64
audio = np.frombuffer(
    base64.urlsafe_b64decode(envelope['payload'] + '=='),
    dtype=np.float32
)
stereo = dsp.process(audio)

AI Verification

from symphonic_cipher.ai_verifier import (
    FeatureExtractor,
    HarmonicVerifier,
    IntentClassifier
)

# Extract features
extractor = FeatureExtractor()
features = extractor.extract(audio_signal)

# Harmonic verification
verifier = HarmonicVerifier()
report = verifier.verify(audio_signal, "ADAPTIVE")
print(f"Result: {report.result.value}")

# AI classification
classifier = IntentClassifier()
is_authentic, confidence = classifier.classify(features)

Running the Demo

python demo.py

This demonstrates all components:

Dictionary mapping
Modality encoding
Feistel permutation
Harmonic synthesis
DSP chain processing
RWP v3 envelope
Feature extraction
Harmonic verification
AI classification
End-to-end flow

Running Tests

pytest symphonic_cipher/tests/ -v

Security Properties

HMAC-SHA256 Integrity: Envelope tampering is detected
Nonce-based Replay Protection: Each message uses unique nonce
Timestamp Expiry: Messages expire after 60 seconds
Key-driven Permutation: Token order is secret without key
Harmonic Verification: Modality must match declared intent
AI Liveness Detection: Synthetic/replay audio is flagged

Constants

Symbol	Value	Description
f₀	440 Hz	Base frequency (A4)
Δf	30 Hz	Frequency step per token ID
H_max	5	Maximum overtone index
SR	44,100 Hz	Sample rate
T_sec	0.5 s	Waveform duration
R	4	Feistel rounds
τ_max	60,000 ms	Replay window
ε_f	2 Hz	Frequency tolerance
ε_a	0.15	Amplitude tolerance

Conlang Vocabulary

Default vocabulary:

Token	ID	Frequency
korah	0	440 Hz
aelin	1	470 Hz
dahru	2	500 Hz
melik	3	530 Hz
sorin	4	560 Hz
tivar	5	590 Hz
ulmar	6	620 Hz
vexin	7	650 Hz

Extended vocabulary supports negative IDs (e.g., “shadow” = -1 → 410 Hz).

License

MIT License

References

HMAC-SHA256: RFC 2104
Feistel Networks: Luby-Rackoff, 1988
Biquad Filters: Audio EQ Cookbook
MFCC: Davis & Mermelstein, 1980