Homomorphic Math & Encrypted Counters

One of the greatest limitations of traditional encrypted databases is the inability to compute mathematical aggregates (SUM, AVG, INC) without sending all records back to the client or decrypting on the server.

FLASH DB solves this using Additive Homomorphic Masked Groups (FlashHomomorphic).

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How Additive Homomorphism Works

When a numerical field (e.g. balance, salary, score) is configured as a counter policy:

1. Client-Side Additive Encryption

For each document: $$C_i = (M_i + \text{Mask}(RecordId, FieldName)) \pmod P$$ Where:

• $M_i$ is the plaintext integer or float (scaled by $10^2$).
• $\text{Mask}$ is a cryptographically derived pseudorandom offset known only to the client.
• $P$ is a large 64-bit safe prime modulus ($2^{64} - 59$).

2. Server-Side Blind Aggregation

The server can add thousands of encrypted balances together without decrypting any of them: $$C_{\text{total}} = \sum_{i=1}^{N} C_i \pmod P$$

3. Client-Side Decryption of Final Result

The client receives only the aggregated ciphertext $C_{\text{total}}$: $$\text{PlainSum} = \left( C_{\text{total}} - \sum_{i=1}^{N} \text{Mask}_i \right) \pmod P$$

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Usage Example

1. Declare Field Policy as 'counter'

import { FlashClient } from 'flash-zk';

const client = new FlashClient({
  secretKey: 'master-key',
  fieldPolicy: {
    balance: 'counter'
  }
});

const accounts = await client.collection('accounts');

await accounts.insertMany([
  { accountId: 'ACC-01', balance: 1500.50 },
  { accountId: 'ACC-02', balance: 2400.25 },
  { accountId: 'ACC-03', balance: 900.00 }
]);

2. Run Aggregations

const stats = await accounts.aggregate([
  {
    $group: {
      _id: null,
      totalBalance: { $sum: '$balance' }
    }
  }
]);

console.log(stats[0].totalBalance); // 4800.75