# `groups-2048`

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  - [groups-1024](./1024/groups-1024.md) — <!-- begin:auto-docs --> _(no submodules)_- [1536](./1536/groups-1536.md) — <!-- begin:auto-docs --> _(no submodules)_  - [groups-1536](./1536/groups-1536.md) — <!-- begin:auto-docs --> _(no submodules)_- [3072](./3072/groups-3072.md) — <!-- begin:auto-docs --> _(no submodules)_  - [groups-3072](./3072/groups-3072.md) — <!-- begin:auto-docs --> _(no submodules)_- [4096](./4096/groups-4096.md) — <!-- begin:auto-docs --> _(no submodules)_  - [groups-4096](./4096/groups-4096.md) — <!-- begin:auto-docs --> _(no submodules)_- [6144](./6144/groups-6144.md) — <!-- begin:auto-docs --> _(no submodules)_  - [groups-6144](./6144/groups-6144.md) — <!-- begin:auto-docs --> _(no submodules)_- [8192](./8192/groups-8192.md) — <!-- begin:auto-docs --> _(no submodules)_  - [groups-8192](./8192/groups-8192.md) — <!-- begin:auto-docs --> _(no submodules)_- [groups-2048](./groups-2048.md) — <!-- begin:auto-docs --> _(no submodules)_- groups-1024 — <!-- begin:auto-docs --> _(no submodul…
- [groups-1024](./1024/groups-1024.md) — <!-- begin:auto-docs --> _(no submodules)_- [1536](./1536/groups-1536.md) — <!-- begin:auto-docs --> _(no submodules)_- [groups-1536](./1536/groups-1536.md) — <!-- begin:auto-docs --> _(no submodules)_- [3072](./3072/groups-3072.md) — <!-- begin:auto-docs --> _(no submodules)_- [groups-3072](./3072/groups-3072.md) — <!-- begin:auto-docs --> _(no submodules)_- [4096](./4096/groups-4096.md) — <!-- begin:auto-docs --> _(no submodules)_- [groups-4096](./4096/groups-4096.md) — <!-- begin:auto-docs --> _(no submodules)_- [6144](./6144/groups-6144.md) — <!-- begin:auto-docs --> _(no submodules)_- [groups-6144](./6144/groups-6144.md) — <!-- begin:auto-docs --> _(no submodules)_- [8192](./8192/groups-8192.md) — <!-- begin:auto-docs --> _(no submodules)_- [groups-8192](./8192/groups-8192.md) — <!-- begin:auto-docs --> _(no submodules)_- [groups-2048](./groups-2048.md) — <!-- begin:auto-docs --> _(no submodules)_- [groups-1024](./1024/groups-1024.md) — <!-- begin:auto-docs --> _(no submodules)_- [1536](./1536/groups-1536.md) — <!-- begin:auto-docs --> _(no submodules)_- [groups-1536](./1536/groups-1536.md) — <!-- begin:auto-docs --> _(no submodules)_- [3072](./3072/groups-3072.md) — <!-- begin:auto-docs --> _(no submodules)_- [groups-3072](./3072/groups-3072.md) — <!-- begin:auto-docs --> _(no submodules)_- [4096](./4096/groups-4096.md) — <!-- begin:auto-docs --> _(no submodules)_- [groups-4096](./4096/groups-4096.md) — <!-- begin:auto-docs --> _(no submodules)_- [6144](./6144/groups-6144.md) — <!-- begin:auto-docs --> _(no submodules)_- [groups-6144](./6144/groups-6144.md) — <!-- begin:auto-docs --> _(no submodules)_- [8192](./8192/groups-8192.md) — <!-- begin:auto-docs --> _(no submodules)_- [groups-8192](./8192/groups-8192.md) — <!-- begin:auto-docs --> _(no submodules)_- [groups-2048](./groups-2048.md) — <!-- begin:auto-docs --> _(no submodules)_- groups-1024 — <!-- begin:aut…
- [groups-1024](./1024/groups-1024.md) — <!-- begin:auto-docs --> _(no submodules)_- [1536](./1536/groups-1536.md) — <!-- begin:auto-docs --> _(no submodules)_- [groups-1536](./1536/groups-1536.md) — <!-- begin:auto-docs --> _(no submodules)_- [3072](./3072/groups-3072.md) — <!-- begin:auto-docs --> _(no submodules)_- [groups-3072](./3072/groups-3072.md) — <!-- begin:auto-docs --> _(no submodules)_- [4096](./4096/groups-4096.md) — <!-- begin:auto-docs --> _(no submodules)_- [groups-4096](./4096/groups-4096.md) — <!-- begin:auto-docs --> _(no submodules)_- [6144](./6144/groups-6144.md) — <!-- begin:auto-docs --> _(no submodules)_- [groups-6144](./6144/groups-6144.md) — <!-- begin:auto-docs --> _(no submodules)_- [8192](./8192/groups-8192.md) — <!-- begin:auto-docs --> _(no submodules)_- [groups-8192](./8192/groups-8192.md) — <!-- begin:auto-docs --> _(no submodules)_- [groups-2048](./groups-2048.md) — <!-- begin:auto-docs --> _(no submodules)_- groups-1024 — <!-- begin:auto-docs --> _(no submodu…
- [groups-1024](./1024/groups-1024.md) — <!-- begin:auto-docs --> _(no submodules)_- [1536](./1536/groups-1536.md) — <!-- begin:auto-docs --> _(no submodules)_  - [groups-1536](./1536/groups-1536.md) — <!-- begin:auto-docs --> _(no submodules)_- [3072](./3072/groups-3072.md) — <!-- begin:auto-docs --> _(no submodules)_  - [groups-3072](./3072/groups-3072.md) — <!-- begin:auto-docs --> _(no submodules)_- [4096](./4096/groups-4096.md) — <!-- begin:auto-docs --> _(no submodules)_  - [groups-4096](./4096/groups-4096.md) — <!-- begin:auto-docs --> _(no submodules)_- [6144](./6144/groups-6144.md) — <!-- begin:auto-docs --> _(no submodules)_  - [groups-6144](./6144/groups-6144.md) — <!-- begin:auto-docs --> _(no submodules)_- [8192](./8192/groups-8192.md) — <!-- begin:auto-docs --> _(no submodules)_  - [groups-8192](./8192/groups-8192.md) — <!-- begin:auto-docs --> _(no submodules)_- [groups-2048](./groups-2048.md) — <!-- begin:auto-docs --> _(no submodules)_
## Purpose

The bundled 2048-bit safe-prime group from RFC 5054 Appendix A. This is the default SRP-6a group every consumer of `@suaveplan/srp` gets without any additional import: `N_2048` is a 256-byte modulus, `g_2048` is the single byte `0x02`, and `BIT_LENGTH` is the literal `2048`. RFC 5054 deliberately bundles a small set of fixed safe primes to side-step trust-on-first-use over arbitrary moduli; we ship the 2048-bit one as the default because it sits at the contemporary security floor while keeping a 2048-bit `modPow` cheap enough (~5–20 ms) for an interactive login.

## Features

- `N_2048` byte-exact to RFC 5054 Appendix A "2048-bit Group" literal.
- `g_2048` equal to `Uint8Array([2])`.
- `BIT_LENGTH` literal-typed `2048`.
- Frozen `Uint8Array`s — consumers cannot mutate the shared constant.
- Reachable from the root `@suaveplan/srp` barrel AND from `@suaveplan/srp/groups`.

## Usage: Basic Example

```ts
import { N_2048, g_2048, BIT_LENGTH } from "@suaveplan/srp/groups";

console.log(N_2048.byteLength); // 256
console.log(g_2048[0]); // 2
console.log(BIT_LENGTH); // 2048
```

## Usage: Advanced Example

```ts
import { N_2048, g_2048 } from "@suaveplan/srp/groups";
import { defaultHashBridge } from "@suaveplan/srp/hash";
import { params2048Sha256 } from "@suaveplan/srp/params";

const params = params2048Sha256(defaultHashBridge("SHA256"));
// params.N is the same shared reference as N_2048.
// Use this params object for client + server handshakes.
```

## API Reference

| Export       | Type           | Description                                                    |
| ------------ | -------------- | -------------------------------------------------------------- |
| `N_2048`     | `Uint8Array`   | 256-byte modulus from RFC 5054 Appendix A.                     |
| `g_2048`     | `Uint8Array`   | Single-byte generator `0x02`.                                  |
| `BIT_LENGTH` | `2048`         | Literal bit length of `N_2048`.                                |

## Implementation Notes

The modulus is encoded as a hex literal in source rather than embedded as a base64 blob so a human reader can diff it against RFC 5054 Appendix A line-by-line. The hex string is split into eight 64-char chunks matching the eight rows the RFC prints. The byte-exact unit test (`groups-2048.test.ts`) reconstructs the same hex from the `Uint8Array`, uppercases it, and asserts equality against the same literal.

`g_2048` is `Uint8Array([2])` rather than a `bigint` because every place SRP mixes group elements into a hash uses `PAD(g)` over the group modulus; expressing `g` as a one-byte buffer up-front avoids a runtime `bigint`-to-bytes conversion at every hash site. The single-byte representation also matches the byte-shape every `Uint8Array`-keyed helper in this package expects.

The `BIT_LENGTH` literal is typed `2048` (not `number`) so consumers narrowing on the constant get a literal type back. This matters in test files where we assert that the bundled group is exactly the RFC's 2048-bit choice and not, say, a future 3072-bit upgrade.