Whitepaper > Privacy and Zero-Knowledge Technologies

Privacy and Zero-Knowledge Technologies

Quantum-Resistant Steganography

Sierpinski Fractal Hash Keys

Our 3^2187 fractal hash keys provide quantum-resistant encryption with 1046 bits of security.

3^729
Level 3
3^1458
Level 4
3^2187
Level 5

Sensitive Data

Securely store and transmit sensitive information on the blockchain.

Medical Records
2.4 MB
Legal Contracts
1.8 MB
Financial Data
3.2 MB

Security Features

  • Quantum-resistant encryption
  • Perfect forward secrecy
  • Statistical undetectability
  • Blockchain immutability

Our 3^2187 key space provides 1046 bits of security, compared to 256 bits in traditional systems. This makes it resistant to quantum computing attacks.

Process Explanation

1Select Data & Encryption Key

Choose sensitive data and a Sierpinski fractal hash key with 3^2187 complexity for quantum-resistant security.

2Encrypt Data with Fractal Key

The data is encrypted using the fractal key, creating a secure payload that's resistant to quantum attacks.

3Embed in Cover Media

The encrypted data is embedded in the cover image using ternary steganography, making it statistically undetectable.

Ternary Audio Encryption

Waveform Visualization
Frequency Spectrogram

Ternary Modulation Techniques

TFSK

Ternary Frequency Shift Keying varies the carrier frequency based on trit value:

  • Trit -1: f₀-Δf
  • Trit 0: f₀
  • Trit +1: f₀+Δf
TPSK

Ternary Phase Shift Keying shifts the signal phase based on trit value:

  • Trit -1: -π/3
  • Trit 0: 0
  • Trit +1: +π/3
AM

Amplitude Modulation varies the signal amplitude based on trit value:

  • Trit -1: 0.75A
  • Trit 0: A
  • Trit +1: 1.25A

Our ternary audio encryption provides superior information density compared to binary systems, encoding 1.58 bits per symbol. The balanced ternary representation (-1, 0, +1) creates unique spectral patterns that are quantum-resistant and difficult to detect without the correct decryption key.

Quantum-Resistant Security

The 3^2187 Sierpinski fractal hash keys provide approximately 1046 bits of security, compared to the 256 bits offered by traditional binary systems. This exponential increase in key space makes our steganography solution resistant to quantum computing attacks, which can break traditional encryption methods through Shor's algorithm.

When combined with our ternary-based steganographic techniques, we achieve multiple layers of security:

  • The data is encrypted with quantum-resistant fractal keys
  • The encrypted data is hidden within cover media using statistical camouflage
  • The embedding process mimics natural noise patterns
  • Multiple layers of obfuscation prevent statistical analysis
  • The blockchain provides immutable storage and verification
Our approach to steganography is particularly valuable for sensitive applications like medical records, legal contracts, and financial data, where both privacy and integrity are paramount.

6.1 Ternary Sigma Protocols

Implementation Architecture

Built with our Next.js/TypeScript stack:

typescript
1interface TernarySigmaProtocol {
2 // Core protocol types
3 type Trit = -1 | 0 | 1;
4 type Challenge = Trit;
5
6 // Protocol components
7 interface Commitment {
8 value: FieldElement;
9 randomness: FieldElement;
10 }
11
12 interface Proof {
13 commitment: Commitment;
14 challenge: Challenge;
15 response: FieldElement;
16 }
17}
18
19// React component for protocol visualization
20const SigmaProtocolView: React.FC<{
21 proof: TernarySigmaProtocol.Proof;
22}> = ({ proof }) => {
23 return (
24 <StyledProtocolView>
25 <CommitmentPhase data={proof.commitment} />
26 <ChallengePhase value={proof.challenge} />
27 <ResponsePhase value={proof.response} />
28 </StyledProtocolView>
29 );
30};
31
32// Protocol implementation
33class DiscreteLogProof implements TernarySigmaProtocol {
34 private readonly field: TernaryField;
35
36 constructor(field: TernaryField) {
37 this.field = field;
38 }
39
40 async prove(
41 secretKey: FieldElement
42 ): Promise<Proof> {
43 // Offload computation to Web Worker
44 return new Promise((resolve) => {
45 const worker = new Worker('/sigma-worker.ts');
46 worker.postMessage({ secretKey });
47 worker.onmessage = (e) => resolve(e.data);
48 });
49 }
50}

Zero-Knowledge Proof Visualization

Commitment Phase

T1001T1T000110010T10110TT01

Challenge Phase

0TT00TTT010T0011010T1000T10

Response Phase

T0T00111T0T001101T11000TTT1

Color Legend

T (Negative)
0 (Balanced)
1 (Positive)
Our zero-knowledge proof visualization demonstrates the three phases of our ternary sigma protocol: commitment, challenge, and response. The interactive display allows users to explore each phase independently.
All cryptographic operations are implemented with constant-time algorithms and Web Workers to prevent timing attacks while maintaining UI responsiveness.

6.2 Confidential Transactions

Implementation

Using TypeScript for type safety:

typescript
1interface ConfidentialTransaction {
2 // Pedersen commitment components
3 interface PedersenCommitment {
4 value: FieldElement;
5 blinding: FieldElement;
6 }
7
8 // Range proof structure
9 interface RangeProof {
10 commitments: PedersenCommitment[];
11 challenges: Challenge[];
12 responses: FieldElement[];
13 }
14}
15
16// Transaction component with styled-components
17const ConfidentialTxView = styled.div`
18 display: grid;
19 grid-template-columns: repeat(auto-fit, minmax(300px, 1fr));
20 gap: 1.5rem;
21 padding: 2rem;
22 background: ${props => props.theme.colors.background};
23 border-radius: 8px;
24`;
25
26class ConfidentialTxBuilder {
27 async buildTransaction(
28 amount: bigint,
29 recipient: TritAddress
30 ): Promise<ConfidentialTransaction> {
31 // Implementation using Web Workers
32 return new Promise((resolve) => {
33 const worker = new Worker('/tx-builder-worker.ts');
34 worker.postMessage({ amount, recipient });
35 worker.onmessage = (e) => resolve(e.data);
36 });
37 }
38}

6.3 Ring Signatures and Stealth Addresses

Ring Signature Implementation

Leveraging Next.js API routes:

typescript
1interface RingSignature {
2 // Ring structure
3 interface Ring {
4 members: TritAddress[];
5 signature: FieldElement[];
6 keyImage: FieldElement;
7 }
8
9 // Signature generation
10 async function generateSignature(
11 message: Buffer,
12 ring: Ring,
13 secretKey: FieldElement
14 ): Promise<RingSignature>;
15}
16
17// API route for ring signature verification
18export default async function handler(
19 req: NextApiRequest,
20 res: NextApiResponse<RingVerificationResponse>
21) {
22 const { signature, message, ring } = req.body;
23
24 try {
25 const isValid = await verifyRingSignature(signature, message, ring);
26 res.status(200).json({ isValid });
27 } catch (error) {
28 res.status(400).json({ error: error.message });
29 }
30}
31
32// React component for ring visualization
33const RingVisualizer: React.FC<{
34 ring: Ring;
35 signature: RingSignature;
36}> = ({ ring, signature }) => {
37 return (
38 <StyledRing>
39 <RingMembers members={ring.members} />
40 <SignatureDisplay signature={signature} />
41 <KeyImageView image={signature.keyImage} />
42 </StyledRing>
43 );
44};

6.4 Ternary Steganography

Implementation

Built with our React/TypeScript stack:

typescript
1interface TritStego {
2 // Steganographic embedding
3 interface EmbeddingParams {
4 data: Buffer;
5 cover: TritSequence;
6 key: StegKey;
7 }
8
9 // Extraction parameters
10 interface ExtractionParams {
11 stego: TritSequence;
12 key: StegKey;
13 length: number;
14 }
15}
16
17class TritSteganography {
18 // Embed data in ternary sequence
19 async embed(
20 params: EmbeddingParams
21 ): Promise<TritSequence> {
22 return new Promise((resolve) => {
23 const worker = new Worker('/stego-worker.ts');
24 worker.postMessage(params);
25 worker.onmessage = (e) => resolve(e.data);
26 });
27 }
28
29 // Extract hidden data
30 async extract(
31 params: ExtractionParams
32 ): Promise<Buffer> {
33 return new Promise((resolve) => {
34 const worker = new Worker('/stego-worker.ts');
35 worker.postMessage(params);
36 worker.onmessage = (e) => resolve(e.data);
37 });
38 }
39}
40
41// Visualization component
42const StegoVisualizer: React.FC<{
43 original: TritSequence;
44 stego: TritSequence;
45}> = ({ original, stego }) => {
46 return (
47 <StyledStegoView>
48 <SequenceComparison
49 original={original}
50 modified={stego}
51 />
52 <DifferenceHighlight
53 sequences={[original, stego]}
54 />
55 </StyledStegoView>
56 );
57};
Our steganographic implementation leverages the balanced ternary system's natural properties to achieve higher embedding capacity while maintaining statistical undetectability.

Integration with Modern Stack

Our privacy technologies are fully integrated with our technology stack:

  • Next.js server-side rendering for optimal performance
  • React components for interactive visualizations
  • TypeScript for end-to-end type safety
  • Styled-components for consistent UI
  • Web Workers for intensive computations
  • Comprehensive test coverage

Key features:

  • Full TypeScript type checking
  • React hooks for state management
  • Server-side rendering optimization
  • Responsive visualization components
  • Internationalization support
  • Automated security testing