# `groups-3072`

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## Purpose

RFC 5054 Appendix A 3072-bit safe-prime group with generator `g = 5`. Reachable via `@suaveplan/srp/groups/3072`. A 3072-bit modulus crosses the ~128-bit symmetric-security threshold and is appropriate for deployments that anticipate long secret lifetimes (multi-year auth-token rotation) or that store the verifier database in an environment with a future-quantum-threat tolerance one step above the 2048-bit default.

## Features

- `N_3072` byte-exact to RFC 5054 Appendix A "3072-bit Group".
- `g_3072 = Uint8Array([5])` (RFC 5054 mandates `g = 5` for this size).
- `BIT_LENGTH` literal `3072`.
- Subpath-only — bundle-size cost paid only by importers.

## Usage: Basic Example

```ts
import { N_3072, g_3072, BIT_LENGTH } from "@suaveplan/srp/groups/3072";

console.log(N_3072.byteLength); // 384
console.log(g_3072[0]); // 5
console.log(BIT_LENGTH); // 3072
```

## Usage: Advanced Example

```ts
import { N_3072, g_3072 } from "@suaveplan/srp/groups/3072";
import { defaultHashBridge } from "@suaveplan/srp/hash";
import type { SrpParams } from "@suaveplan/srp/params";

const params: SrpParams = {
    N: N_3072,
    g: g_3072,
    bitLength: 3072,
    hash: defaultHashBridge("SHA256"),
    algorithm: "SHA256",
};
```

## API Reference

| Export       | Type         | Description                |
| ------------ | ------------ | -------------------------- |
| `N_3072`     | `Uint8Array` | 384-byte 3072-bit modulus. |
| `g_3072`     | `Uint8Array` | Generator `0x05`.          |
| `BIT_LENGTH` | `3072`       | Literal bit length.        |

## Implementation Notes

Unlike the 1024/1536/2048-bit groups which all use `g = 2`, RFC 5054 specifies `g = 5` for 3072, 4096, 6144, and 8192-bit groups (the chosen generator depends on the modulus's quadratic-residue structure, picked at RFC-design time so `g` generates a large prime-order subgroup of `Z_N*`). Consumers building `SrpParams` from raw constants MUST use `g_3072` rather than hard-coding `0x02`.

`modPow` over a 3072-bit modulus takes roughly 4x the wall-clock time of the 2048-bit default; expect ~20–80 ms per handshake step. For interactive login this is still well under perceptual latency.