# `groups-8192`

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## Purpose

RFC 5054 Appendix A 8192-bit safe-prime group with generator `g = 19`. Reachable via `@suaveplan/srp/groups/8192`. The largest bundled group RFC 5054 specifies. Use only when verifier-database lifetime extends beyond the practical horizon of precomputed-discrete-log attacks against bundled primes; for almost every contemporary deployment the 2048-bit default is sufficient and the 8192-bit group's ~64x `modPow` slowdown is not justified.

## Features

- `N_8192` byte-exact to RFC 5054 Appendix A "8192-bit Group".
- `g_8192 = Uint8Array([19])` — RFC 5054 mandates `g = 19` for this size.
- `BIT_LENGTH` literal `8192`.
- Subpath-only.

## Usage: Basic Example

```ts
import { N_8192, g_8192, BIT_LENGTH } from "@suaveplan/srp/groups/8192";

console.log(N_8192.byteLength); // 1024
console.log(g_8192[0]); // 19
console.log(BIT_LENGTH); // 8192
```

## Usage: Advanced Example

```ts
import { N_8192, g_8192 } from "@suaveplan/srp/groups/8192";
import { defaultHashBridge } from "@suaveplan/srp/hash";
import type { SrpParams } from "@suaveplan/srp/params";

const params: SrpParams = {
    N: N_8192,
    g: g_8192,
    bitLength: 8192,
    hash: defaultHashBridge("SHA256"),
    algorithm: "SHA256",
};
```

## API Reference

| Export       | Type         | Description                 |
| ------------ | ------------ | --------------------------- |
| `N_8192`     | `Uint8Array` | 1024-byte 8192-bit modulus. |
| `g_8192`     | `Uint8Array` | Generator `0x13` (19).      |
| `BIT_LENGTH` | `8192`       | Literal bit length.         |

## Implementation Notes

An 8192-bit `modPow` typically costs hundreds of milliseconds on contemporary hardware. Interactive login flows MUST NOT use this group on the request critical path; instead schedule the handshake off the perceptual deadline (e.g. background-thread the auth call, show a placeholder for the duration). The benchmark suite skips 8192 by default because the per-iteration cost dominates the warmup statistics.

The generator `g = 19` is unique to this size in RFC 5054. Consumers building `SrpParams` from raw constants MUST use `g_8192` rather than hard-coding `0x02` or `0x05`.