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hpke.curveprime.auth_psk__skR.oneshot.coll.cv
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(* Mechanised cryptographic proofs for HPKE using CryptoVerif.
Following as close as possible the notation of the specification at
https://cfrg.github.io/draft-irtf-cfrg-hpke/draft-irtf-cfrg-hpke.html
Generate individual model files with:
./run false
Generate and run (takes a while and writes a lot of files to disk):
./run
Run individual model with (example file):
f=hpke.curveprime.base.oneshot; mkdir -p $f; cryptoverif -oproof $f/$f.proof -o $f $f.cv
2019-2020, Benjamin Lipp, INRIA Paris, Prosecco
*)
(* BEGIN m4 variables are processed that are given as arguments. *)
(* mode_auth_psk is es,ss,psk:
- secrecy as long as skR and psk are not both compromised
- auth as long as skS and psk are not both compromised *)
(* TODO Use to put success only when needed *)
(* END *)
(* BEGIN process m4 variables created from input variables. *)
(* END *)
(* BEGIN other m4 macros. *)
(* The macro m4_out_game outputs the current game to a file.
The file name contains a number that is increased at each output. *)
(* END *)
proof {
out_game "g00.out.cv";
insert after "in(ch1_2\\["
"let extract_auth_input(psk: psk_t, concat2G(dh1: G_t, dh2: G_t)) = x1_1 in";
out_game "g01.out.cv";
crypto rom(ExtractAuth_inner);
simplify;
out_game "g02.out.cv";
crypto prf(Expand) **;
simplify;
out_game "g03.out.cv";
crypto truncate(truncate_to_Nn) **;
crypto truncate(truncate_to_Nk) **;
simplify;
out_game "g05.out.cv";
crypto int_ctxt(Seal_inner) **;
success;
simplify;
out_game "g06.out.cv";
crypto ind_cpa(Seal_inner) **;
simplify;
success
}
(* TODO make sure the channel names are all unique *)
channel c_start, c_setup, c_config_init, c_init, c_resp.
channel c_config_init_sw, c_init_sw.
channel c_init_send, c_init_send_config.
channel c_resp_mult.
channel c_resp_send_config.
channel c_msgs_send_config, c_msgs_send, c_msgs_recv, c_msgs_recv_finish.
channel c_corrupt_skS, c_corrupt_skR, c_corrupt_psk, c_corrupt_skS_psk.
(* This session index is not part of the specification but assumed
by the model. In an implementation, a session index is likely needed
to match subsequent messages to a session and thus the appropriate
decryption context. The session index could be explicit, or implicit,
i.e. a TCP connection. *)
(*type session_index_t [large,fixed].
table sent_seqs(session_index_t, nonce_t).
table rcvd_seqs(session_index_t, nonce_t).*)
type psk_t [large,fixed].
const default_psk: psk_t.
fun psk_to_bitstring(psk_t): bitstring [data].
const default_pskID: bitstring.
const default_pskID_hash: bitstring.
(* We believe an equation like
equation Hash(default_pskID) = default_pskID_hash.
is not necessary, because the default psk is only used in modes where
the psk in not used and thus a formal link between default_psk and
default_pskID is not necessary. *)
const default_pkSm: bitstring.
type expand_t [large,fixed].
(* This covers the maximum length of HKDF-Expand's output. For
RFC 5869, this is 255*Nh. *)
type key_t [large,fixed].
type nonce_t [large,fixed].
(* Application constants *)
const app_info: bitstring.
expand Xor(
nonce_t,
xor,
nonce_zero (* also used for seq that starts at zero *)
).
(* DH-based KEM *)
(* For P-256 and P-521
- to model Unmarshal(), use a left-hand-side pattern matching of Marshal
- TODO figure out if Marshal and G_to_bitstring are actually the same:
I think they are the same, because looking at the F* specs for
P256 and Curve25519, the scalarmult function is returning an
encoded point.
*)
type G_t [bounded,large].
fun Marshal(G_t): bitstring [data].
fun G_to_bitstring(G_t): bitstring [data].
type Z_t [bounded,large].
expand DH_good_group(
G_t,
Z_t,
g,
exp,
exp_1,
mult
).
proba P_GDH.
expand GDH(
(* types *)
G_t, (* Group elements *)
Z_t, (* Exponents *)
(* variables *)
g, (* a generator of the group *)
exp, (* exponentiation function *)
exp_1, (* a symbol that replaces exp after game transformation *)
mult, (* multiplication function for exponents *)
(* probabilities *)
P_GDH (* probability of breaking the GDH assumption *)
).
const default_pkS: G_t.
equation Marshal(default_pkS) = default_pkSm.
letfun DH(exponent: Z_t, group_element: G_t) =
exp(group_element, exponent).
letfun pk(exponent: Z_t) =
exp(g, exponent).
letfun GenerateKeyPair() =
new z: Z_t;
(z, exp(g, z)).
(* Key Derivation Function *)
type hash_key_t [fixed].
type hash_output_t [large,fixed].
fun hash_output_to_bitstring(hash_output_t): bitstring [data].
proba P_hash. (* probability of breaking collision resistance *)
expand CollisionResistant_hash(
(* types *)
hash_key_t, (* key of the hash function, models the choice of *)
(* the hash function *)
bitstring, (* input that gets hashed *)
hash_output_t, (* output type of the hash function *)
(* functions *)
Hash_inner, (* name of the hash function: *)
(* hash(hashkey_t, bitstring): hash_output_t *)
(* processes *)
Hash_oracle, (* name of the oracle that will make available the *)
(* hash key to the attacker *)
(* parameters *)
P_hash (* probability of breaking collision resistance *)
).
letfun Hash(key_hash: hash_key_t, input: bitstring) =
hash_output_to_bitstring(Hash_inner(key_hash, input)).
(*
Extract(salt, IKM):
Extract a pseudorandom key of fixed length from
input keying material IKM and an optional octet string salt.
Extract(salt, IKM) is HMAC-Hash(salt, IKM)
*)
type extract_input_t.
fun extract_input(psk_t, bitstring): extract_input_t [data].
type extract_auth_input_t.
fun extract_auth_input(psk_t, bitstring): extract_auth_input_t [data].
type extract_output_t [large,fixed]. (* size: Nh bytes *)
expand ROM_hash_1(
(* types *)
hash_key_t,
extract_input_t,
extract_output_t,
(* functions *)
Extract_inner,
(* processes *)
Extract_oracle,
(* parameters *)
N_qExtract (* number of queries to the oracle by the adversary *)
).
expand ROM_hash_1(
(* types *)
hash_key_t,
extract_auth_input_t,
extract_output_t,
(* functions *)
ExtractAuth_inner,
(* processes *)
ExtractAuth_oracle,
(* parameters *)
N_qExtractAuth (* number of queries to the oracle by the adversary *)
).
letfun Extract(key_extract: hash_key_t, psk: psk_t, zz: bitstring) =
Extract_inner(key_extract, extract_input(psk, zz)).
letfun ExtractAuth(key_extract_auth: hash_key_t, psk: psk_t, zz: bitstring) =
ExtractAuth_inner(key_extract_auth, extract_auth_input(psk, zz)).
(*
Expand(PRK, info, L):
Expand a pseudorandom key PRK using optional string info into L bytes
of output keying material.
*)
proba P_PRF.
expand PRF_large(
extract_output_t,
bitstring,
expand_t,
Expand,
P_PRF
).
def truncate(input_t, output_t, truncate_f) {
param N.
fun truncate_f(input_t): output_t.
(* If we truncate a uniformly distributed random value,
we obtain a uniformly distributed random value *)
equiv(truncate(truncate_f))
foreach i<=N do h <-R input_t;
O_trunc() := return(truncate_f(h))
<=(0)=>
foreach i<=N do k <-R output_t;
O_trunc() := return(k).
}
expand truncate(
expand_t,
nonce_t,
truncate_to_Nn
).
expand truncate(
expand_t,
key_t,
truncate_to_Nk
).
(* Nh: The output size of the Hash and Extract functions *)
expand truncate(
expand_t,
extract_output_t,
truncate_to_Nh
).
letfun Expand_Nk(key: extract_output_t, input: bitstring) =
truncate_to_Nk(Expand(key, input)).
letfun Expand_Nn(key: extract_output_t, input: bitstring) =
truncate_to_Nn(Expand(key, input)).
letfun Expand_Nh(key: extract_output_t, input: bitstring) =
truncate_to_Nh(Expand(key, input)).
(* An AEAD encryption algorithm *)
proba P_cpa.
proba P_ctxt.
expand AEAD_nonce(
(* types *)
key_t,
bitstring, (* plaintext *)
bitstring, (* ciphertext *)
bitstring, (* additional data *)
nonce_t,
(* functions *)
Seal_inner,
Open_inner,
injbot, (* injection from plaintext to bitstringbot:
(* injbot(plaintext): bitstringbot *)
Zero, (* returns a plaintext of same length, consisting of zeros:
(* Zero(plaintext): plaintext *)
(* probabilities *)
P_cpa,
P_ctxt
).
letfun Seal(key: key_t, nonce: nonce_t, aad: bitstring, pt: bitstring) =
Seal_inner(pt, aad, key, nonce).
letfun Open(key: key_t, nonce: nonce_t, aad: bitstring, ct: bitstring) =
Open_inner(ct, aad, key, nonce).
(***********************************************************************
The following is part of boolean_choice.cvl
inspired by some CryptoVerif examples and Bruno Blanchet
***********************************************************************)
def boolean_choice(value_t, test) {
fun test(bool, value_t, value_t) : value_t.
equation forall x:value_t, y:value_t; test(true, x, y) = x.
equation forall x:value_t, y:value_t; test(false, x, y) = y.
(* Knowing the equations defined above, this can be deduced, but
CryptoVerif can’t do this on its own. *)
equation forall x:value_t, b:bool; test(b,x,x) = x.
}
(* Zero needs to be defined already, typically by the AEAD scheme that’s
* expanded somewhere before.
*)
def boolean_choice_for_encryption(value_t, Zero, test) {
expand boolean_choice(value_t, test).
(* Knowing the equations defined above, this can be deduced, but
CryptoVerif can’t do this on its own. *)
equation forall x:value_t, y:value_t, b:bool; Zero(test(b,x,y)) = test (b,Zero(x),Zero(y)).
}
(* Define a function for choosing from two attacker-provided plaintexts based
on a bit. Also, defines some equations on it so CryptoVerif is able
to reason about it. *)
expand boolean_choice_for_encryption(
(* types *)
bitstring, (* type of the values *)
(* functions *)
Zero, (* the Zero function provided by the encryption scheme. *)
(* Needed for some equations about the function. *)
test (* Name of the choice function: *)
(* test(bool, bitstring, bitstring): bitstring *)
).
(* 5.1. DH-Based KEM *)
type Encap_res_t.
fun Encap_success(bitstring, bitstring): Encap_res_t [data].
const Encap_fail: Encap_res_t.
equation forall zz: bitstring, enc: bitstring;
Encap_success(zz, enc) <> Encap_fail.
letfun Encap(pkR: G_t) =
let (skE: Z_t, pkE: G_t) = GenerateKeyPair() in
(
let zz: bitstring = G_to_bitstring(DH(skE, pkR)) in
let enc: bitstring = Marshal(pkE) in
Encap_success(zz, enc)
) else (
Encap_fail
).
type Decap_res_t.
fun Decap_success(bitstring): Decap_res_t [data].
const Decap_fail: Decap_res_t.
equation forall zz: bitstring; Decap_success(zz) <> Decap_fail.
letfun Decap(enc: bitstring, skR: Z_t) =
let Marshal(pkE: G_t) = enc in
(
Decap_success(G_to_bitstring(DH(skR, pkE)))
) else (
Decap_fail
).
fun concat2G(G_t, G_t): bitstring [data].
type AuthEncap_res_t.
fun AuthEncap_success(bitstring, bitstring): AuthEncap_res_t [data].
const AuthEncap_fail: AuthEncap_res_t.
equation forall zz: bitstring, enc: bitstring;
AuthEncap_success(zz, enc) <> AuthEncap_fail.
letfun AuthEncap(pkR: G_t, skS: Z_t) =
let (skE: Z_t, pkE: G_t) = GenerateKeyPair() in
(
let zz: bitstring = concat2G(DH(skE, pkR), DH(skS, pkR)) in
let enc: bitstring = Marshal(pkE) in
AuthEncap_success(zz, enc)
) else (
AuthEncap_fail
).
type AuthDecap_res_t.
fun AuthDecap_success(bitstring): AuthDecap_res_t [data].
const AuthDecap_fail: AuthDecap_res_t.
equation forall zz: bitstring; AuthDecap_success(zz) <> AuthDecap_fail.
letfun AuthDecap(enc: bitstring, skR: Z_t, pkS: G_t) =
let Marshal(pkE: G_t) = enc in
(
AuthDecap_success(concat2G(DH(skR, pkE), DH(skR, pkS)))
) else (
AuthDecap_fail
).
(* Encryption Context *)
type mode_t [fixed].
const mode_base: mode_t.
const mode_psk: mode_t.
const mode_auth: mode_t.
const mode_auth_psk: mode_t.
type two_bytes [fixed].
const kem_id: two_bytes.
const kdf_id: two_bytes.
const aead_id: two_bytes.
fun concat2bitstring(bitstring, bitstring): bitstring [data].
fun concat3(two_bytes, two_bytes, two_bytes): bitstring [data].
fun concat7(mode_t, bitstring, bitstring, bitstring,
bitstring, bitstring, bitstring): bitstring [data].
const hpke_key: bitstring.
const hpke_nonce: bitstring.
const hpke_exp: bitstring.
type context_t [large,fixed].
(* key, nonce, seq, exporter_secret *)
fun Context(key_t, nonce_t, nonce_t, extract_output_t): context_t [data].
type Context_new_seq_res_t.
fun Context_new_seq_success(context_t): Context_new_seq_res_t [data].
const Context_new_seq_fail: Context_new_seq_res_t.
equation forall ctx: context_t;
Context_new_seq_success(ctx) <> Context_new_seq_fail.
letfun Context_new_seq(ctx: context_t, seq: nonce_t) =
let Context(key: key_t, nonce: nonce_t, seq_old: nonce_t, exporter_secret_old: extract_output_t) = ctx in
(
Context_new_seq_success(Context(key, nonce, seq, exporter_secret_old))
) else (
Context_new_seq_fail
).
letfun VerifyMode(mode: mode_t, psk: psk_t, pskID: bitstring, pkSm: bitstring) =
let got_psk: bool = not(psk = default_psk) && not(pskID = default_pskID) in
let no_psk: bool = (psk = default_psk) && (pskID = default_pskID) in
let got_pkSm: bool = not(pkSm = default_pkSm) in
let no_pkSm: bool = (pkSm = default_pkSm) in
if (mode = mode_base && (got_psk || got_pkSm)) then (false) else (
if (mode = mode_psk && (no_psk || got_pkSm)) then (false) else (
if (mode = mode_auth && (got_psk || no_pkSm) ) then (false) else (
if (mode = mode_auth_psk && (no_psk || no_pkSm) ) then (false) else (
true)))).
(* We provide pskID_hash and info_hash as parameters to simplify
the model. They are either way the same for all protocol
executions in this model, and then the random oracle doesn't
blow up inside KeySchedule. *)
type KeyScheduleAuth_res_t.
fun KeyScheduleAuth_success(context_t): KeyScheduleAuth_res_t [data].
const KeyScheduleAuth_fail: KeyScheduleAuth_res_t.
equation forall ctx: context_t;
KeyScheduleAuth_success(ctx) <> KeyScheduleAuth_fail.
letfun KeyScheduleAuth(key_hash: hash_key_t, key_extract: hash_key_t,
mode: mode_t, pkR: G_t,
zz: bitstring, enc: bitstring, info_hash: bitstring,
psk: psk_t, pskID: bitstring, pskID_hash: bitstring, pkSm: bitstring) =
if VerifyMode(mode, psk, pskID, pkSm) then
(
let pkRm: bitstring = Marshal(pkR) in
let ciphersuite: bitstring = concat3(kem_id, kdf_id, aead_id) in
let context: bitstring = concat7(mode, ciphersuite, enc, pkRm, pkSm,
pskID_hash, info_hash) in
(* secret is a reserved keyword in CryptoVerif *)
let secrett: extract_output_t = ExtractAuth(key_extract, psk, zz) in
let key: key_t = Expand_Nk(secrett, concat2bitstring(hpke_key, context)) in
let nonce: nonce_t = Expand_Nn(secrett, concat2bitstring(hpke_nonce, context)) in
let exporter_secret: extract_output_t = Expand_Nh(secrett, concat2bitstring(hpke_exp, context)) in
KeyScheduleAuth_success(Context(key, nonce, nonce_zero, exporter_secret))
) else (
KeyScheduleAuth_fail
).
(* Authentication using an Asymmetric Key *)
type SetupAuthI_res_t.
fun SetupAuthI_success(bitstring, context_t): SetupAuthI_res_t [data].
const SetupAuthI_fail: SetupAuthI_res_t.
equation forall enc: bitstring, ctx: context_t;
SetupAuthI_success(enc, ctx) <> SetupAuthI_fail.
letfun SetupAuthI(key_hash: hash_key_t, key_extract: hash_key_t,
pkR: G_t, info_hash: bitstring, skS: Z_t) =
let AuthEncap_success(
zz: bitstring, enc: bitstring) = AuthEncap(pkR, skS) in
(
let pkSm: bitstring = Marshal(pk(skS)) in
let KeyScheduleAuth_success(ctx: context_t) = KeyScheduleAuth(key_hash, key_extract, mode_auth, pkR, zz, enc, info_hash, default_psk, default_pskID, default_pskID_hash, pkSm) in
(
SetupAuthI_success(enc, ctx)
) else (
SetupAuthI_fail
)
) else (
SetupAuthI_fail
).
type SetupAuthR_res_t.
fun SetupAuthR_success(context_t): SetupAuthR_res_t [data].
const SetupAuthR_fail: SetupAuthR_res_t.
equation forall ctx: context_t;
SetupAuthR_success(ctx) <> SetupAuthR_fail.
letfun SetupAuthR(key_hash: hash_key_t, key_extract: hash_key_t,
enc: bitstring, skR: Z_t, info_hash: bitstring, pkS: G_t) =
let AuthDecap_success(zz: bitstring) = AuthDecap(enc, skR, pkS) in
(
let pkSm: bitstring = Marshal(pkS) in
let KeyScheduleAuth_success(ctx: context_t) = KeyScheduleAuth(key_hash, key_extract, mode_auth, pk(skR), zz, enc, info_hash, default_psk, default_pskID, default_pskID_hash, pkSm) in
(
SetupAuthR_success(ctx)
) else (
SetupAuthR_fail
)
) else (
SetupAuthR_fail
).
(* Authentication using both a PSK and an Asymmetric Key *)
type SetupAuthPSKI_res_t.
fun SetupAuthPSKI_success(bitstring, context_t): SetupAuthPSKI_res_t [data].
const SetupAuthPSKI_fail: SetupAuthPSKI_res_t.
equation forall enc: bitstring, ctx: context_t;
SetupAuthPSKI_success(enc, ctx) <> SetupAuthPSKI_fail.
letfun SetupAuthPSKI(key_hash: hash_key_t, key_extract: hash_key_t,
pkR: G_t, info_hash: bitstring,
psk: psk_t, pskID: bitstring, pskID_hash: bitstring, skS: Z_t) =
let AuthEncap_success(
zz: bitstring, enc: bitstring) = AuthEncap(pkR, skS) in
(
let pkSm: bitstring = Marshal(pk(skS)) in
let KeyScheduleAuth_success(ctx: context_t) = KeyScheduleAuth(key_hash, key_extract, mode_auth_psk, pkR, zz, enc, info_hash, psk, pskID, pskID_hash, pkSm) in
(
SetupAuthPSKI_success(enc, ctx)
) else (
SetupAuthPSKI_fail
)
) else (
SetupAuthPSKI_fail
).
type SetupAuthPSKR_res_t.
fun SetupAuthPSKR_success(context_t): SetupAuthPSKR_res_t [data].
const SetupAuthPSKR_fail: SetupAuthPSKR_res_t.
equation forall ctx: context_t;
SetupAuthPSKR_success(ctx) <> SetupAuthPSKR_fail.
letfun SetupAuthPSKR(key_hash: hash_key_t, key_extract: hash_key_t,
enc: bitstring, skR: Z_t, info_hash: bitstring,
psk: psk_t, pskID: bitstring, pskID_hash: bitstring, pkS: G_t) =
let AuthDecap_success(zz: bitstring) = AuthDecap(enc, skR, pkS) in
(
let pkSm: bitstring = Marshal(pkS) in
let KeyScheduleAuth_success(ctx: context_t) = KeyScheduleAuth(key_hash, key_extract, mode_auth_psk, pk(skR), zz, enc, info_hash, psk, pskID, pskID_hash, pkSm) in
(
SetupAuthPSKR_success(ctx)
) else (
SetupAuthPSKR_fail
)
) else (
SetupAuthPSKR_fail
).
(* Encryption and Decryption *)
letfun Context_Nonce(nonce: nonce_t, seq: nonce_t) =
(* We suppose that seq has already the length of the nonce, by
assigning it the type nonce_t. *)
xor(nonce, seq).
type Context_Seal_res_t.
fun Context_Seal_success(bitstring): Context_Seal_res_t [data].
const Context_Seal_fail: Context_Seal_res_t.
equation forall ct: bitstring;
Context_Seal_success(ct) <> Context_Seal_fail.
letfun Context_Seal(context: context_t, aad: bitstring,
pt: bitstring) =
let Context(key: key_t, nonce: nonce_t, seq: nonce_t, exporter_secret_unused: extract_output_t) = context in
(
let ct: bitstring = Seal(key, Context_Nonce(nonce, seq), aad, pt) in
(* TODO model increment seq (probably outside of this function)
self.seq += 1 *)
Context_Seal_success(ct)
) else (
Context_Seal_fail
).
type Context_Open_res_t.
fun Context_Open_success(bitstring): Context_Open_res_t [data].
const Context_Open_fail: Context_Open_res_t.
equation forall pt: bitstring;
Context_Open_success(pt) <> Context_Open_fail.
letfun Context_Open(context: context_t, aad: bitstring,
ct: bitstring) =
let Context(key: key_t, nonce: nonce_t, seq: nonce_t, exporter_secret_unused: extract_output_t) = context in
(
let injbot(pt: bitstring) = Open(key, Context_Nonce(nonce, seq),
aad, ct) in
(
(* TODO model increment seq (probably outside of this function)
self.seq += 1 *)
Context_Open_success(pt)
) else (
Context_Open_fail
)
) else (
Context_Open_fail
).
type Context_Export_res_t.
fun Context_Export_success(expand_t): Context_Export_res_t [data].
const Context_Export_fail: Context_Export_res_t.
equation forall exported: expand_t;
Context_Export_success(exported) <> Context_Export_fail.
(* Context_Export directly outputs the maximum length (for HKDF it is
255*Hashlen) and the truncation is left to the user.
This simplifies the model, as we can re-use the same Expand function. *)
letfun Context_Export(context: context_t, exporter_context: bitstring) =
let Context(key: key_t, nonce: nonce_t, seq: nonce_t, exporter_secret_here: extract_output_t) = context in
(
let exported: expand_t = Expand(exporter_secret_here, exporter_context) in
Context_Export_success(exported)
) else (
Context_Export_fail
).
(* Single-Shot APIs *)
type SealAuth_res_t.
fun SealAuth_success(bitstring, bitstring): SealAuth_res_t [data].
const SealAuth_fail: SealAuth_res_t.
equation forall enc: bitstring, ct: bitstring;
SealAuth_success(enc, ct) <> SealAuth_fail.
letfun SealAuth(key_hash: hash_key_t, key_extract: hash_key_t,
pkR: G_t, info_hash: bitstring, aad: bitstring,
pt: bitstring, skS: Z_t) =
let SetupAuthI_success(enc: bitstring, ctx: context_t) =
SetupAuthI(key_hash, key_extract, pkR, info_hash, skS) in
(
let Context_Seal_success(ct: bitstring) = Context_Seal(ctx, aad, pt) in
(
SealAuth_success(enc, ct)
) else (
SealAuth_fail
)
) else (
SealAuth_fail
).
type OpenAuth_res_t.
fun OpenAuth_success(Context_Open_res_t): OpenAuth_res_t [data].
const OpenAuth_fail: OpenAuth_res_t.
equation forall ctx_open: Context_Open_res_t;
OpenAuth_success(ctx_open) <> OpenAuth_fail.
letfun OpenAuth(key_hash: hash_key_t, key_extract: hash_key_t,
enc: bitstring, skR: Z_t, info_hash: bitstring,
aad: bitstring, ct: bitstring, pkS: G_t) =
let SetupAuthR_success(ctx: context_t) =
SetupAuthR(key_hash, key_extract, enc, skR, info_hash, pkS) in
(
OpenAuth_success(Context_Open(ctx, aad, ct))
) else (
OpenAuth_fail
).
type SealAuthPSK_res_t.
fun SealAuthPSK_success(bitstring, bitstring): SealAuthPSK_res_t [data].
const SealAuthPSK_fail: SealAuthPSK_res_t.
equation forall enc: bitstring, ct: bitstring;
SealAuthPSK_success(enc, ct) <> SealAuthPSK_fail.
letfun SealAuthPSK(key_hash: hash_key_t, key_extract: hash_key_t,
pkR: G_t, info_hash: bitstring, aad: bitstring,
pt: bitstring, psk: psk_t, pskID: bitstring, pskID_hash: bitstring,
skS: Z_t) =
let SetupAuthPSKI_success(enc: bitstring, ctx: context_t) =
SetupAuthPSKI(key_hash, key_extract, pkR, info_hash, psk, pskID, pskID_hash, skS) in
(
let Context_Seal_success(ct: bitstring) = Context_Seal(ctx, aad, pt) in
(
SealAuthPSK_success(enc, ct)
) else (
SealAuthPSK_fail
)
) else (
SealAuthPSK_fail
).
type OpenAuthPSK_res_t.
fun OpenAuthPSK_success(Context_Open_res_t): OpenAuthPSK_res_t [data].
const OpenAuthPSK_fail: OpenAuthPSK_res_t.
equation forall ctx_open: Context_Open_res_t;
OpenAuthPSK_success(ctx_open) <> OpenAuthPSK_fail.
letfun OpenAuthPSK(key_hash: hash_key_t, key_extract: hash_key_t,
enc: bitstring, skR: Z_t, info_hash: bitstring,
aad: bitstring, ct: bitstring,
psk: psk_t, pskID: bitstring, pskID_hash: bitstring, pkS: G_t) =
let SetupAuthPSKR_success(ctx: context_t) =
SetupAuthPSKR(key_hash, key_extract,
enc, skR, info_hash, psk, pskID, pskID_hash, pkS) in
(
OpenAuthPSK_success(Context_Open(ctx, aad, ct))
) else (
OpenAuthPSK_fail
).
(* TODO make sure the params used are all unique *)
param N_initiators_base, N_initiators_base_sw.
param N_initiators_auth, N_initiators_auth_sw.
param N_initiators_psk, N_initiators_psk_sw.
param N_initiators_auth_psk, N_initiators_auth_psk_sw.
param N_initiators_mult.
param N_initiators_mult_send.
param N_responders_base, N_responders_base_sw.
param N_responders_auth, N_responders_auth_sw.
param N_responders_psk, N_responders_psk_sw.
param N_responders_auth_psk, N_responders_auth_psk_sw.
param N_initiators_psk_adv, N_responders_psk_adv.
param N_initiators_auth_psk_adv, N_responders_auth_psk_adv.
param N_responders_mult.
param N_responders_mult_recv.
param N_responders_mult_send.
param N_msgs_send, N_msgs_recv.
(* In one-shot, the initiator does not receive the encryption
context from the API. This means it cannot send subsequent messages.
*)
letfun has_secrecy(pkX: G_t, pkR: G_t) =
pkX = pkR
.
letfun has_auth() =
(* skS and psk cannot both be compromised, in particular the psk
cannot be compromised, thus KCI is not an issue. *)
true
.
const exp_ctx_1: bitstring.
const exp_ctx_2: bitstring.
event rcvd(
bool, (* clean_session *)
mode_t,
G_t, (* pkR *)
G_t, (* pkS *)
bitstring, (* pskID *)
bitstring, (* info *)
bitstring, (* aad *)
bitstring (* plaintext *)
).
event sent(
mode_t,
G_t, (* pkR *)
G_t, (* pkS *)
bitstring, (* pskID *)
bitstring, (* info *)
bitstring, (* aad *)
bitstring (* plaintext *)
).
let Initiator_Auth(key_hash: hash_key_t, key_extract: hash_key_t, info_hash: bitstring,
b_I: bool, pkR: G_t, skS: Z_t, pkS: G_t) =
! i_N_initiators <= N_initiators_auth
in(c_config_init, (pkX: G_t, pt1: bitstring, pt2: bitstring,
aad: bitstring));
if Zero(pt1) = Zero(pt2) then
let bit: bool = if has_secrecy(pkX, pkR) then b_I else false in
let pt: bitstring = test(bit, pt1, pt2) in
let SealAuth_success(enc: bitstring, ct: bitstring) =
SealAuth(key_hash, key_extract, pkX, info_hash, aad, pt, skS) in
event sent(mode_auth, pkX, pkS, default_pskID, app_info, aad, pt);
out(c_init, (enc, ct, aad))
.
let Responder_Auth(key_hash: hash_key_t, key_extract: hash_key_t, info_hash: bitstring,
skR: Z_t, pkR: G_t, pkS: G_t) =
! i_N_responders <= N_responders_auth
in(c_resp, (enc: bitstring, ct: bitstring, aad: bitstring));
let bool_has_auth: bool = has_auth() in
let OpenAuth_success(Context_Open_success(pt: bitstring)) =
OpenAuth(key_hash, key_extract, enc, skR, info_hash, aad, ct, pkS) in
event rcvd(bool_has_auth, mode_auth, pkR, pkS, default_pskID, app_info, aad, pt);
out(c_resp, ())
.
let Initiator_Auth_swap(key_hash: hash_key_t, key_extract: hash_key_t, info_hash: bitstring,
pkR: G_t, skS: Z_t, pkS: G_t) =
! i_N_initiators <= N_initiators_auth_sw
in(c_config_init, (pkX: G_t, pt: bitstring, aad: bitstring));
(* oneshot *)
let SealAuth_success(enc: bitstring, ct: bitstring) =
SealAuth(key_hash, key_extract, pkX, info_hash, aad, pt, skS) in
out(c_init, (enc, ct, aad))
.
let Responder_Auth_swap(key_hash: hash_key_t, key_extract: hash_key_t, info_hash: bitstring,
skR: Z_t, pkR: G_t, pkS: G_t) =
! i_N_responders <= N_responders_auth_sw
in(c_resp, (enc: bitstring, ct: bitstring, aad: bitstring));
let OpenAuth_success(Context_Open_success(pt: bitstring)) =
OpenAuth(key_hash, key_extract, enc, skR, info_hash, aad, ct, pkS) in
out(c_resp, ())
.
let Initiator_Auth_PSK(key_hash: hash_key_t, key_extract: hash_key_t, info_hash: bitstring,
b_I: bool, pkR: G_t, skS: Z_t, pkS: G_t, psk: psk_t, pskID: bitstring, pskID_hash: bitstring) =
! i_N_initiators <= N_initiators_auth_psk
in(c_config_init, (pkX: G_t, pt1: bitstring, pt2: bitstring,
aad: bitstring));
if pkX = pkR then
if Zero(pt1) = Zero(pt2) then