(* Title: HOL/Auth/TLS
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1997 University of Cambridge
Inductive relation "tls" for the baby TLS (Transport Layer Security) protocol.
This protocol is essentially the same as SSL 3.0.
Abstracted from "The TLS Protocol, Version 1.0" by Tim Dierks and Christopher
Allen, Transport Layer Security Working Group, 21 May 1997,
INTERNET-DRAFT draft-ietf-tls-protocol-03.txt. Section numbers below refer
to that memo.
An RSA cryptosystem is assumed, and X.509v3 certificates are abstracted down
to the trivial form {A, publicKey(A)}privateKey(Server), where Server is a
global signing authority.
A is the client and B is the server, not to be confused with the constant
Server, who is in charge of all public keys.
The model assumes that no fraudulent certificates are present, but it does
assume that some private keys are to the spy.
REMARK. The event "Notes A {|Agent B, Nonce PMS|}" appears in ClientCertKeyEx,
CertVerify, ClientFinished to record that A knows M. It is a note from A to
herself. Nobody else can see it. In ClientCertKeyEx, the Spy can substitute
his own certificate for A's, but he cannot replace A's note by one for himself.
The Note event avoids a weakness in the public-key model. Each
agent's state is recorded as the trace of messages. When the true client (A)
invents PMS, he encrypts PMS with B's public key before sending it. The model
does not distinguish the original occurrence of such a message from a replay.
In the shared-key model, the ability to encrypt implies the ability to
decrypt, so the problem does not arise.
*)
TLS = Public +
consts
(*Pseudo-random function of Section 5*)
PRF :: "nat*nat*nat => nat"
(*Client, server write keys implicitly include the MAC secrets.*)
clientK, serverK :: "nat*nat*nat => key"
certificate :: "[agent,key] => msg"
defs
certificate_def
"certificate A KA == Crypt (priK Server) {|Agent A, Key KA|}"
rules
inj_PRF "inj PRF"
(*clientK is collision-free and makes symmetric keys*)
inj_clientK "inj clientK"
isSym_clientK "isSymKey (clientK x)" (*client write keys are symmetric*)
(*serverK is similar*)
inj_serverK "inj serverK"
isSym_serverK "isSymKey (serverK x)" (*server write keys are symmetric*)
(*Clashes with pubK and priK are impossible, but this axiom is needed.*)
clientK_range "range clientK <= Compl (range serverK)"
consts tls :: event list set
inductive tls
intrs
Nil (*Initial trace is empty*)
"[]: tls"
Fake (*The spy, an active attacker, MAY say anything he CAN say.*)
"[| evs: tls; B ~= Spy;
X: synth (analz (sees Spy evs)) |]
==> Says Spy B X # evs : tls"
SpyKeys (*The spy may apply PRF, clientK & serverK to available nonces*)
"[| evsSK: tls;
Says Spy B {|Nonce NA, Nonce NB, Nonce M|} : set evsSK |]
==> Says Spy B {| Nonce (PRF(M,NA,NB)),
Key (clientK(NA,NB,M)),
Key (serverK(NA,NB,M)) |} # evsSK : tls"
ClientHello
(*(7.4.1.2)
XA represents CLIENT_VERSION, CIPHER_SUITES and COMPRESSION_METHODS.
It is uninterpreted but will be confirmed in the FINISHED messages.
As an initial simplification, SESSION_ID is identified with NA
and reuse of sessions is not supported.
May assume NA ~: range PRF because CLIENT RANDOM is 32 bytes
while MASTER SECRET is 48 byptes (6.1)*)
"[| evsCH: tls; A ~= B; Nonce NA ~: used evsCH; NA ~: range PRF |]
==> Says A B {|Agent A, Nonce NA, Number XA|} # evsCH : tls"
ServerHello
(*7.4.1.3 of the TLS Internet-Draft
XB represents CLIENT_VERSION, CIPHER_SUITE and COMPRESSION_METHOD.
NA is returned in its role as SESSION_ID.
SERVER CERTIFICATE (7.4.2) is always present.
CERTIFICATE_REQUEST (7.4.4) is implied.*)
"[| evsSH: tls; A ~= B; Nonce NB ~: used evsSH; NB ~: range PRF;
Says A' B {|Agent A, Nonce NA, Number XA|} : set evsSH |]
==> Says B A {|Nonce NA, Nonce NB, Number XB,
certificate B (pubK B)|}
# evsSH : tls"
ClientCertKeyEx
(*CLIENT CERTIFICATE (7.4.6) and KEY EXCHANGE (7.4.7).
The client, A, chooses PMS, the PREMASTER SECRET.
She encrypts PMS using the supplied KB, which ought to be pubK B.
We assume PMS ~: range PRF because a clash betweem the PMS
and another MASTER SECRET is highly unlikely (even though
both items have the same length, 48 bytes).
The Note event records in the trace that she knows PMS
(see REMARK at top).*)
"[| evsCX: tls; A ~= B; Nonce PMS ~: used evsCX; PMS ~: range PRF;
Says B' A {|Nonce NA, Nonce NB, Number XB, certificate B KB|}
: set evsCX |]
==> Says A B {|certificate A (pubK A), Crypt KB (Nonce PMS)|}
# Notes A {|Agent B, Nonce PMS|}
# evsCX : tls"
CertVerify
(*The optional CERTIFICATE VERIFY (7.4.8) message contains the
specific components listed in the security analysis, F.1.1.2.
It adds the pre-master-secret, which is also essential!
Checking the signature, which is the only use of A's certificate,
assures B of A's presence*)
"[| evsCV: tls; A ~= B;
Says B' A {|Nonce NA, Nonce NB, Number XB, certificate B KB|}
: set evsCV;
Notes A {|Agent B, Nonce PMS|} : set evsCV |]
==> Says A B (Crypt (priK A)
(Hash{|Nonce NB, certificate B KB, Nonce PMS|}))
# evsCV : tls"
(*Finally come the FINISHED messages (7.4.8), confirming XA and XB
among other things. The master-secret is PRF(PMS,NA,NB).
Either party may sent its message first.*)
(*The occurrence of Notes A {|Agent B, Nonce PMS|} stops the
rule's applying when the Spy has satisfied the "Says A B" by
repaying messages sent by the true client; in that case, the
Spy does not know PMS and could not sent CLIENT FINISHED. One
could simply put A~=Spy into the rule, but one should not
expect the spy to be well-behaved.*)
ClientFinished
"[| evsCF: tls;
Says A B {|Agent A, Nonce NA, Number XA|} : set evsCF;
Says B' A {|Nonce NA, Nonce NB, Number XB, certificate B KB|}
: set evsCF;
Notes A {|Agent B, Nonce PMS|} : set evsCF;
M = PRF(PMS,NA,NB) |]
==> Says A B (Crypt (clientK(NA,NB,M))
(Hash{|Nonce M,
Nonce NA, Number XA, Agent A,
Nonce NB, Number XB, Agent B|}))
# evsCF : tls"
(*Keeping A' and A'' distinct means B cannot even check that the
two messages originate from the same source. *)
ServerFinished
"[| evsSF: tls;
Says A' B {|Agent A, Nonce NA, Number XA|} : set evsSF;
Says B A {|Nonce NA, Nonce NB, Number XB,
certificate B (pubK B)|}
: set evsSF;
Says A'' B {|certificate A KA, Crypt (pubK B) (Nonce PMS)|}
: set evsSF;
M = PRF(PMS,NA,NB) |]
==> Says B A (Crypt (serverK(NA,NB,M))
(Hash{|Nonce M,
Nonce NA, Number XA, Agent A,
Nonce NB, Number XB, Agent B|}))
# evsSF : tls"
(**Oops message??**)
end