Browse WireGuard specs (1 of 38)

Proofs / WireGuard / The handshake

hs_matching_keys

When a handshake between A and B completes on both sides, A's sending key is B's receiving key and the other way round, and only A's keypair is the initiator's.

spec
36 lines of C
with its headers
99 lines
status
Proved
1 of 38
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The spec

The spec is the C program harness/hs_matching_keys.c, 36 lines, shown whole as it is in the repository at 3c1fc13. It includes harness/hs_laws.h (63 lines). Its first comment states the property in full, with every bound.

C
// Law hs_matching_keys: For devices A and B with any private keys and any preshared key, any clocks (boot clock below
// 2^62 ns) and any randomness, if A's wg_noise_handshake_create_initiation, B's consume_initiation, B's
// create_response, A's consume_response, and wg_noise_handshake_begin_session on both sides all succeed, then the
// sending key of A's new current keypair is the receiving key of B's new next keypair and vice versa, and A's keypair
// is the initiator's and B's is not.
#include "hs_laws.h"

int main(void) {
	// Choose the inputs: the devices and their keys, any clocks
	struct pair p;
	new_pair(&p);
	any_clocks();
	// The handshake
	struct message_handshake_initiation initiation;
	struct message_handshake_response response;
	if (!wg_noise_handshake_create_initiation(&initiation, &p.a_peer.handshake))
		return 0;
	if (wg_noise_handshake_consume_initiation(&initiation, &p.b) == NULL)
		return 0;
	if (!wg_noise_handshake_create_response(&response, &p.b_peer.handshake))
		return 0;
	if (wg_noise_handshake_consume_response(&response, &p.a) == NULL)
		return 0;
	if (!wg_noise_handshake_begin_session(&p.a_peer.handshake, &p.a_peer.keypairs))
		return 0;
	if (!wg_noise_handshake_begin_session(&p.b_peer.handshake, &p.b_peer.keypairs))
		return 0;
	// Check. WireGuard paper, 5.4.5: "(T_i^send = T_r^recv, T_i^recv = T_r^send) := Kdf2(C_i = C_r, ε)"; noise.c,
	// add_new_keypair: the initiator's new keypair becomes current, the responder's becomes next.
	struct noise_keypair *a = p.a_peer.keypairs.current_keypair, *b = p.b_peer.keypairs.next_keypair;
	gp_assert(a != NULL && b != NULL);
	gp_assert(bytes_eq(a->sending.key, b->receiving.key, NOISE_SYMMETRIC_KEY_LEN) != 0);
	gp_assert(bytes_eq(a->receiving.key, b->sending.key, NOISE_SYMMETRIC_KEY_LEN) != 0);
	gp_assert(a->i_am_the_initiator != 0 && b->i_am_the_initiator == 0);
	return 0;
}
harness/hs_laws.h, 63 lines
C
// hs_laws.h: helpers shared by the handshake laws (hs_*): two devices with a peer for each other, set up as the
// kernel sets them up, and any clocks. No models, no algorithms.
#include "quickproof.h"
#include "noise.h"
#include "peer.h"
#include "device.h"
extern u64 wg_shim_boottime_ns;                       // the shim's clocks (patch/wg_shim.c): the laws set them
extern s64 wg_shim_real_sec;
extern long wg_shim_real_nsec;
extern unsigned long wg_shim_allocs;                  // the shim's count of successful kzalloc calls
static u64 any_u64(void) {                            // any 64-bit value
	u64 high = nondet_u32();
	return high << 32 | nondet_u32();
}
static int bytes_eq(const u8 *a, const u8 *b, size_t n) {   // a[0..n-1] == b[0..n-1]
	for (size_t i = 0; i < n; i++)
		if (a[i] != b[i])
			return 0;
	return 1;
}
static void any_clocks(void) {                        // any boot clock below 2^62 ns, any real-time clock
	wg_shim_boottime_ns = any_u64() >> 2;
	wg_shim_real_sec = (s64) any_u64();
	wg_shim_real_nsec = (long) (nondet_u32() % 1000000000u);
}
static void new_device(struct wg_device *wg, struct index_hashtable *indices, struct pubkey_hashtable *keys,
		       const u8 private_key[32]) {    // device.c (kzalloc'd), its private key set as netlink.c sets it
	wg->index_hashtable = indices;
	wg->peer_hashtable = keys;
	indices->head = NULL;
	keys->head = NULL;
	for (size_t i = 0; i < 32; i++)
		wg->static_identity.static_public[i] = 0;
	wg_noise_set_static_identity_private_key(&wg->static_identity, private_key);
}
static void new_peer(struct wg_peer *peer, struct wg_device *wg, const u8 public_key[32], const u8 psk[32]) {
	peer->device = wg;                            // peer.c, wg_peer_create: one reference, no keypairs, a new
	peer->is_dead = false;                        // handshake, listed in the device's public-key table
	peer->keypairs.current_keypair = NULL;
	peer->keypairs.previous_keypair = NULL;
	peer->keypairs.next_keypair = NULL;
	peer->refcount.refcount = 1;
	wg_noise_handshake_init(&peer->handshake, &wg->static_identity, public_key, psk, peer);
	peer->pubkey_next = wg->peer_hashtable->head;
	wg->peer_hashtable->head = peer;
}
struct pair {                                         // devices A and B, each with a peer for the other
	struct wg_device a, b;
	struct index_hashtable a_indices, b_indices;
	struct pubkey_hashtable a_keys, b_keys;
	struct wg_peer a_peer, b_peer;                // a_peer: A's peer for B; b_peer: B's peer for A
};
static void new_pair(struct pair *p) {                // any private keys, any preshared key (the same on both sides)
	u8 a_private[32], b_private[32], psk[32];
	nondet_bytes(a_private, 32);
	nondet_bytes(b_private, 32);
	nondet_bytes(psk, 32);
	wg_noise_init();
	new_device(&p->a, &p->a_indices, &p->a_keys, a_private);
	new_device(&p->b, &p->b_indices, &p->b_keys, b_private);
	new_peer(&p->a_peer, &p->a, p->b.static_identity.static_public, psk);
	new_peer(&p->b_peer, &p->b, p->a.static_identity.static_public, psk);
}

The theorem

QuickProof generated this statement from the spec, in src/contracts/hs_matching_keys.v:

Rocq
Theorem hs_matching_keys : harness_safe whole_prog.

src/contracts/laws.v states it on the spec's own program, whole_prog (the spec linked with the code under test), with its proof:

Rocq
Theorem hs_matching_keys : harness_safe WgNoise.contracts.hs_matching_keys.whole_prog.
Proof. exact (proj1 (proj2 (proj2 (proj2 (proj2 (proj2 (proj2 (proj2 WgNoise.contracts.suite.suite)))))))). Qed.

Read as a statement about runs, it says that no run of the program has undefined behaviour or a failing check, for every value the spec can draw. That reading rests on VST's adequacy theorem, which is not yet instantiated in Rocq (formerly Coq) for QuickProof's environment.

The C files (units) its program links
  • drivers/net/wireguard/noise.c
  • lib/crypto/blake2s.c
  • lib/crypto/chacha.c
  • lib/crypto/chacha-block-generic.c
  • lib/crypto/poly1305.c
  • lib/crypto/poly1305-donna32.c
  • lib/crypto/chacha20poly1305.c
  • lib/crypto/curve25519.c
  • lib/crypto/curve25519-fiat32.c
  • patch/wg_shim.c
  • quickproof/libc/libc.c

What it leaves out

  • What the first comment of the spec excludes, and its bounds.
  • Like every spec of this proof: runs of more than one thread (the locks and RCU are those of one thread), termination (a run that never returns is not a counterexample), and binaries built by a compiler (the theorem is about the code as CompCert defines C for 64-bit x86).
  • The kernel around the code is a shim of plain C for one thread, and the code carries rewrites of idioms that VST cannot handle. Both are tested against the kernel's code, not proved.

The summary page says what the proof as a whole covers.

How it was proved

AI agents wrote the proof, and Rocq checks it. qp verify passes on this repository: this statement is the one generated from the spec at the contract commit, and its proof uses only Rocq's standard axioms and VST's abstract malloc library.