# WIA-SEC-012: Homomorphic Encryption Standard
## PHASE 2, 3, & 4 - ADVANCED APPLICATIONS

**Standard ID:** WIA-SEC-012
**Version:** 1.0.0
**Status:** Draft
**Last Updated:** 2025-12-25

---

# PHASE 2 - SECURE MULTI-PARTY COMPUTATION

## 1. MPC PROTOCOLS

### 1.1 Introduction to MPC

Secure Multi-Party Computation (MPC) enables multiple parties to jointly compute a function over their inputs while keeping those inputs private. When combined with homomorphic encryption, MPC provides strong privacy guarantees with practical efficiency.

### 1.2 Protocol Components

#### 1.2.1 Participant Roles

**Data Owner**
- Provides encrypted input data
- Holds secret key for decryption
- Controls data access permissions

**Compute Party**
- Performs computations on encrypted data
- No access to plaintext data
- Returns encrypted results

**Result Recipient**
- Receives encrypted computation results
- May or may not be data owner
- Decrypts final results with appropriate keys

#### 1.2.2 Communication Model

**Synchronous Model:**
```typescript
interface SyncMPCProtocol {
  round: number;
  participants: ParticipantId[];
  broadcast(message: EncryptedMessage): Promise<void>;
  receive(): Promise<EncryptedMessage[]>;
  nextRound(): Promise<void>;
}
```

**Asynchronous Model:**
```typescript
interface AsyncMPCProtocol {
  send(to: ParticipantId, message: EncryptedMessage): Promise<void>;
  receive(from: ParticipantId): Promise<EncryptedMessage>;
  barrier(): Promise<void>;
}
```

### 1.3 Common MPC Patterns

#### 1.3.1 Secure Sum Protocol

**Use Case:** Calculate sum of private values without revealing individual contributions

**Protocol:**
```
Input: n parties, each with private value xᵢ
Output: Sum Σxᵢ without revealing individual xᵢ

1. Party 1 generates key pair (pk, sk)
2. Each party i encrypts: Enc(xᵢ) using pk
3. Compute: Enc(sum) = Enc(x₁) + Enc(x₂) + ... + Enc(xₙ)
4. Party 1 decrypts: sum = Dec(Enc(sum), sk)
5. Broadcast sum to all parties
```

**Implementation:**
```typescript
async function secureSum(
  values: Map<ParticipantId, number>,
  coordinator: ParticipantId
): Promise<number> {
  const he = new WIAHomomorphic({ scheme: 'BFV' });
  const { publicKey, secretKey } = await he.generateKeys();

  // Each party encrypts their value
  const encryptedValues = new Map();
  for (const [party, value] of values.entries()) {
    encryptedValues.set(party, await he.encrypt(value, publicKey));
  }

  // Homomorphic addition
  let encryptedSum = encryptedValues.values().next().value;
  for (const encrypted of Array.from(encryptedValues.values()).slice(1)) {
    encryptedSum = await he.add(encryptedSum, encrypted);
  }

  // Coordinator decrypts
  return await he.decrypt(encryptedSum, secretKey);
}
```

#### 1.3.2 Secure Average Protocol

**Protocol Extension:**
```typescript
async function secureAverage(
  values: Map<ParticipantId, number>
): Promise<number> {
  const sum = await secureSum(values, coordinator);
  const count = values.size;
  return sum / count;
}
```

#### 1.3.3 Secure Comparison

**Problem:** Compare two encrypted values without revealing them

**Solution using DGK Protocol:**
```typescript
async function secureCompare(
  encA: Ciphertext,
  encB: Ciphertext,
  threshold: number
): Promise<boolean> {
  // Use DGK (Damgård-Geisler-Krøigaard) protocol
  // Returns Enc(1) if a > b, Enc(0) otherwise
  const diff = await subtract(encA, encB);
  const signBit = await extractSign(diff);
  return await decrypt(signBit, secretKey) === 1;
}
```

### 1.4 Threshold Cryptography

#### 1.4.1 Threshold Encryption

**Concept:** Secret key is split among n parties, requiring t parties to decrypt

**Key Generation:**
```typescript
interface ThresholdKeyGen {
  n: number;              // Total parties
  t: number;              // Threshold (t ≤ n)
  publicKey: PublicKey;
  shares: SecretKeyShare[];  // n shares
}

async function generateThresholdKeys(
  n: number,
  t: number
): Promise<ThresholdKeyGen> {
  // Shamir secret sharing on secret key
  // Generate polynomial of degree t-1
  // Distribute shares to n parties
}
```

**Threshold Decryption:**
```typescript
async function thresholdDecrypt(
  ciphertext: Ciphertext,
  shares: SecretKeyShare[],  // At least t shares
  t: number
): Promise<Plaintext> {
  if (shares.length < t) {
    throw new Error('Insufficient shares for decryption');
  }

  // Combine shares using Lagrange interpolation
  const partialDecryptions = shares.map(share =>
    partialDecrypt(ciphertext, share)
  );

  return combinePartialDecryptions(partialDecryptions);
}
```

#### 1.4.2 Use Cases

**Distributed Key Management:**
- No single point of failure
- Require consensus for decryption
- Protection against insider threats

**Secure Auctions:**
- Bids encrypted and stored
- Decryption requires t auctioneers
- Winner determined without revealing all bids

**Cryptocurrency Wallets:**
- Multi-signature wallets
- Corporate treasury management
- Recovery mechanisms

---

# PHASE 3 - PRIVACY-PRESERVING MACHINE LEARNING

## 2. PPML FUNDAMENTALS

### 2.1 Overview

Privacy-Preserving Machine Learning (PPML) enables training and inference on sensitive data without exposing the data to model operators or inference servers.

### 2.2 Training vs Inference

**Private Training:**
- Train models on encrypted training data
- Protect sensitive training datasets
- Higher computational cost (10-1000x slower)

**Private Inference:**
- Evaluate models on encrypted input data
- Protect user queries and results
- Moderate computational cost (10-100x slower)

### 2.3 Linear Models

#### 2.3.1 Linear Regression

**Model:** y = w₁x₁ + w₂x₂ + ... + wₙxₙ + b

**Encrypted Training:**
```typescript
async function trainLinearRegression(
  encryptedFeatures: Ciphertext[][],  // Each row is encrypted feature vector
  encryptedLabels: Ciphertext[],
  learningRate: number,
  epochs: number
): Promise<Ciphertext[]> {  // Encrypted weights

  let encWeights = await initializeWeights(featureCount);

  for (let epoch = 0; epoch < epochs; epoch++) {
    for (let i = 0; i < encryptedFeatures.length; i++) {
      // Compute prediction: ŷ = w·x
      const encPrediction = await dotProduct(encWeights, encryptedFeatures[i]);

      // Compute error: e = ŷ - y
      const encError = await subtract(encPrediction, encryptedLabels[i]);

      // Update weights: w = w - α·e·x
      const encGradient = await scalarMultiply(
        await multiply(encError, encryptedFeatures[i]),
        learningRate
      );
      encWeights = await subtract(encWeights, encGradient);
    }
  }

  return encWeights;
}
```

**Encrypted Inference:**
```typescript
async function predictLinear(
  encryptedInput: Ciphertext[],
  encryptedWeights: Ciphertext[],
  encryptedBias: Ciphertext
): Promise<Ciphertext> {
  const encDotProduct = await dotProduct(encryptedInput, encryptedWeights);
  return await add(encDotProduct, encryptedBias);
}
```

#### 2.3.2 Logistic Regression

**Challenge:** Sigmoid function not directly computable in HE

**Solution:** Polynomial approximation
```typescript
function sigmoidApproximation(x: number): number {
  // 3rd degree polynomial approximation
  // sigmoid(x) ≈ 0.5 + 0.197x - 0.004x³
  return 0.5 + 0.197 * x - 0.004 * Math.pow(x, 3);
}

async function encryptedSigmoid(
  encX: Ciphertext
): Promise<Ciphertext> {
  const encXCubed = await multiply(
    await multiply(encX, encX),
    encX
  );

  const term1 = await scalarAdd(zero, 0.5);
  const term2 = await scalarMultiply(encX, 0.197);
  const term3 = await scalarMultiply(encXCubed, -0.004);

  return await add(await add(term1, term2), term3);
}
```

### 2.4 Neural Networks

#### 2.4.1 Activation Functions

**ReLU Approximation:**
```typescript
async function encryptedReLU(encX: Ciphertext): Promise<Ciphertext> {
  // Approximate using polynomial: max(0, x) ≈ polynomial
  // Degree-2 approximation: ReLU(x) ≈ x² / (1 + x²)

  const encXSquared = await multiply(encX, encX);
  const encOnePlusXSquared = await scalarAdd(encXSquared, 1);

  // Use polynomial division approximation
  return await approximateDivision(encXSquared, encOnePlusXSquared);
}
```

**Tanh and Sigmoid:** Use Chebyshev or Taylor series approximations

#### 2.4.2 Fully Connected Layer

```typescript
async function encryptedDenseLayer(
  encInput: Ciphertext[],      // Input vector
  encWeights: Ciphertext[][],  // Weight matrix
  encBias: Ciphertext[]        // Bias vector
): Promise<Ciphertext[]> {

  const output: Ciphertext[] = [];

  for (let i = 0; i < encWeights.length; i++) {
    // Compute weighted sum: output[i] = Σ(weights[i][j] * input[j]) + bias[i]
    let encSum = encBias[i];

    for (let j = 0; j < encInput.length; j++) {
      const encProduct = await multiply(encWeights[i][j], encInput[j]);
      encSum = await add(encSum, encProduct);
    }

    output.push(encSum);


## Annex E — Implementation Notes for PHASE-2-API-INTERFACE

The following implementation notes document field experience from pilot
deployments and are non-normative. They are republished here so that early
adopters can read them in context with the rest of PHASE-2-API-INTERFACE.

- **Operational scope** — implementations SHOULD declare their operational
  scope (single-tenant, multi-tenant, federated) in the OpenAPI document so
  that downstream auditors can score the deployment against the correct
  conformance tier in Annex A.
- **Schema evolution** — additive changes (new optional fields, new error
  codes) are non-breaking; renaming or removing fields, even in error
  payloads, MUST trigger a minor version bump.
- **Audit retention** — a 7-year retention window is sufficient to satisfy
  ISO/IEC 17065:2012 audit expectations in most jurisdictions; some
  regulators require longer retention, in which case the deployment policy
  MUST extend the retention window rather than relying on this PHASE's
  defaults.
- **Time synchronization** — sub-second deadlines depend on synchronized
  clocks. NTPv4 with stratum-2 servers is sufficient for most deadlines
  expressed in this PHASE; PTP is recommended for sites that require
  deterministic interlocks.
- **Error budget reporting** — implementations SHOULD publish a monthly
  error-budget summary (latency p95, error rate, violation hours) in the
  format defined by the WIA reporting profile to facilitate cross-vendor
  comparison without exposing tenant-specific data.

These notes are not requirements; they are a reference for field teams
mapping their existing operations onto WIA conformance.

## Annex F — Adoption Roadmap

The adoption roadmap for this PHASE document is non-normative and is intended to set expectations for early implementers about the relative stability of each section.

- **Stable** (sections marked normative with `MUST` / `MUST NOT`) — semantic versioning applies; breaking changes require a major version bump and at minimum 90 days of overlap with the prior major version on all WIA-published reference implementations.
- **Provisional** (sections in this Annex and Annex D) — items are tracked openly and may be promoted to normative status without a major version bump if community feedback supports promotion.
- **Reference** (test vectors, simulator behaviour, the reference TypeScript SDK) — versioned independently of this document so that mistakes in reference material can be corrected without amending the published PHASE document.

Implementers SHOULD subscribe to the WIA Standards GitHub release notifications to track promotions between these tiers. Comments on the roadmap are accepted via the GitHub issues tracker on the WIA-Official organization.

The roadmap is reviewed at every minor version of this PHASE document, and the review outcomes are recorded in the version-history table at the start of the document.

## Annex G — Test Vectors and Conformance Evidence

This annex describes how implementations capture and publish conformance
evidence for PHASE-2-API-INTERFACE. The procedure is non-normative; it standardizes the
shape of evidence so that auditors and downstream integrators can compare
implementations without re-running the full test matrix.

- **Test vectors** — every normative requirement in this PHASE has at least
  one positive vector and one negative vector under
  `tests/phase-vectors/phase-2-api-interface/`. Implementations claiming
  conformance MUST run all vectors in CI and publish the resulting
  pass/fail matrix in their compliance package.
- **Evidence package** — the compliance package is a tarball containing
  the SBOM (CycloneDX 1.5 or SPDX 2.3), the OpenAPI document, the test
  vector matrix, and a signed manifest. Signatures use Sigstore (DSSE
  envelope, Rekor transparency log entry) so that downstream consumers
  can verify provenance without trusting a private CA.
- **Quarterly recheck** — implementations re-publish the evidence package
  every quarter even if no source change occurred, so that consumers can
  detect environmental drift (compiler updates, dependency updates, OS
  updates) without polling vendor changelogs.
- **Cross-vendor crosswalk** — the WIA Standards working group maintains a
  crosswalk that maps each vector to the equivalent assertion in adjacent
  industry programs (where one exists), so an implementer that already
  certifies under one program can show conformance to PHASE-2-API-INTERFACE with
  reduced incremental effort.
- **Negative-result reporting** — vendors MUST report negative results
  with the same fidelity as positive ones. A test that is skipped without
  recorded justification is treated by auditors as a failure.

These conventions are intended to make conformance evidence portable and
machine-readable so that adoption of PHASE-2-API-INTERFACE does not require bespoke
auditor tooling.