# `server-start`

## Purpose

Begin the SRP-6a handshake on the server side. Loads the stored verifier `v` (alongside the user's `(I, salt)`), draws a `≥ 256`-bit private exponent `b`, and emits the server public value `B = (k * v + g^b) mod N` per RFC 5054 §2.5.4. The augmented form (multiplying `k` into the verifier) is what distinguishes SRP-6a from SRP-6. The function re-draws `b` if the resulting `B mod N == 0`, up to 16 attempts.

## Features

- 256-bit private exponent — matches RFC 5054 §2.5.4 minimum.
- `k = H(N | PAD(g))` precomputed once per call (could be memoized externally for further savings).
- `B ≡ 0 mod N` re-draw with 16-attempt safety cap.
- Returns `B` zero-padded to `byteLength(N)`.
- Emits `srp.handshake_duration_ms{role=server,phase=start}` and on abort `srp.outcome_total{role=server,outcome=public_key_invalid}` + `srp.errors_total{code=SRP.PUBLIC_KEY_INVALID}`.

## Usage: Basic Example

```ts
import { serverStartHandshake } from "@suaveplan/srp/server";
import { params2048Sha256 } from "@suaveplan/srp/params";
import { nobleHashBridge } from "@suaveplan/srp/hash";
import { computeVerifier } from "@suaveplan/srp/verifier";

const params = params2048Sha256(nobleHashBridge("SHA256"));
const salt = new Uint8Array(16);
const { v } = computeVerifier("alice", "password123", salt, params);
const rng = {
    nextUint32: () => 0,
    nextFloat: () => 0,
    nextBytes: (n: number) => crypto.getRandomValues(new Uint8Array(n)),
};
const { b, B } = serverStartHandshake(v, rng, params);
console.log(b.byteLength, B.byteLength); // 32 256
```

## Usage: Advanced Example

```ts
import { serverStartHandshake } from "@suaveplan/srp/server";
import { params2048Sha256 } from "@suaveplan/srp/params";
import { nobleHashBridge } from "@suaveplan/srp/hash";
import { computeVerifier } from "@suaveplan/srp/verifier";
import type { Rng } from "@suaveplan/types";

const params = params2048Sha256(nobleHashBridge("SHA256"));
const salt = new Uint8Array(16);
const { v } = computeVerifier("alice", "password123", salt, params);

// Synthetic deterministic RNG to demonstrate reproducibility.
function seededRng(seed: number): Rng {
    let state = seed >>> 0;
    return {
        nextUint32: () => {
            state = (state * 1664525 + 1013904223) >>> 0;
            return state;
        },
        nextFloat: () => 0.5,
    };
}
const r1 = serverStartHandshake(v, seededRng(42), params);
const r2 = serverStartHandshake(v, seededRng(42), params);
console.log(Buffer.from(r1.B).equals(Buffer.from(r2.B))); // true
```

## API Reference

### `serverStartHandshake(v, rng, params): { b, B }`

Returns `{ b, B }`. `b` is 32 bytes of fresh entropy from `rng`; `B` is `params.N.byteLength` bytes, zero-padded.

## Implementation Notes

`kvModN = (k * v) mod N` is computed once at the top of the function and reused inside the re-draw loop because it does not depend on `b`. The only loop-variant work is `g^b mod N` (the `modPow` call) and the final `((kvModN + gb) mod N)`. This matters because the dominant cost is `modPow`; pulling `k*v` out of the loop saves wall time on the (vanishingly unlikely) re-draw path.

The re-draw cap is the same `16` as the client side. Per RFC 5054 §2.5.4 the requirement is "MUST abort if `B ≡ 0 mod N`"; the cap converts that into a finite-bound failure rather than an unbounded loop on a pathological RNG.