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docs/security-stack/security/srp/src/groups/3072/groups-3072.md

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+# `groups-3072`
+
+<!-- begin:auto-docs -->
+_(no submodules)_
+<!-- end:auto-docs -->
+## 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.