170 lines
9.9 KiB
Plaintext
170 lines
9.9 KiB
Plaintext
(*****************************************************************************
|
|
* Copyright (c) 2005-2010 ETH Zurich, Switzerland
|
|
* 2008-2015 Achim D. Brucker, Germany
|
|
* 2009-2016 Université Paris-Sud, France
|
|
* 2015-2016 The University of Sheffield, UK
|
|
*
|
|
* All rights reserved.
|
|
*
|
|
* Redistribution and use in source and binary forms, with or without
|
|
* modification, are permitted provided that the following conditions are
|
|
* met:
|
|
*
|
|
* * Redistributions of source code must retain the above copyright
|
|
* notice, this list of conditions and the following disclaimer.
|
|
*
|
|
* * Redistributions in binary form must reproduce the above
|
|
* copyright notice, this list of conditions and the following
|
|
* disclaimer in the documentation and/or other materials provided
|
|
* with the distribution.
|
|
*
|
|
* * Neither the name of the copyright holders nor the names of its
|
|
* contributors may be used to endorse or promote products derived
|
|
* from this software without specific prior written permission.
|
|
*
|
|
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
|
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
|
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
|
|
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
|
|
* OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
|
|
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
|
|
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
|
|
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
|
|
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
|
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
|
|
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
|
*****************************************************************************)
|
|
|
|
subsection\<open>Network Address Translation\<close>
|
|
theory
|
|
NAT
|
|
imports
|
|
"../PacketFilter/PacketFilter"
|
|
begin
|
|
|
|
|
|
definition src2pool :: "'\<alpha> set \<Rightarrow> ('\<alpha>::adr,'\<beta>) packet \<Rightarrow> ('\<alpha>,'\<beta>) packet set" where
|
|
"src2pool t = (\<lambda> p. ({(i,s,d,da). (i = id p \<and> s \<in> t \<and> d = dest p \<and> da = content p)}))"
|
|
|
|
definition src2poolAP where
|
|
"src2poolAP t = A\<^sub>f (src2pool t)"
|
|
|
|
definition srcNat2pool :: "'\<alpha> set \<Rightarrow> '\<alpha> set \<Rightarrow> ('\<alpha>::adr,'\<beta>) packet \<mapsto> ('\<alpha>,'\<beta>) packet set" where
|
|
"srcNat2pool srcs transl = {x. src x \<in> srcs} \<triangleleft> (src2poolAP transl)"
|
|
|
|
definition src2poolPort :: "int set \<Rightarrow> (adr\<^sub>i\<^sub>p,'\<beta>) packet \<Rightarrow> (adr\<^sub>i\<^sub>p,'\<beta>) packet set" where
|
|
"src2poolPort t = (\<lambda> p. ({(i,(s1,s2),(d1,d2),da).
|
|
(i = id p \<and> s1 \<in> t \<and> s2 = (snd (src p)) \<and> d1 = (fst (dest p)) \<and>
|
|
d2 = snd (dest p) \<and> da = content p)}))"
|
|
|
|
definition src2poolPort_Protocol :: "int set \<Rightarrow> (adr\<^sub>i\<^sub>p\<^sub>p,'\<beta>) packet \<Rightarrow> (adr\<^sub>i\<^sub>p\<^sub>p,'\<beta>) packet set" where
|
|
"src2poolPort_Protocol t = (\<lambda> p. ({(i,(s1,s2,s3),(d1,d2,d3), da).
|
|
(i = id p \<and> s1 \<in> t \<and> s2 = (fst (snd (src p))) \<and> s3 = snd (snd (src p)) \<and>
|
|
(d1,d2,d3) = dest p \<and> da = content p)}))"
|
|
|
|
definition srcNat2pool_IntPort :: "address set \<Rightarrow> address set \<Rightarrow>
|
|
(adr\<^sub>i\<^sub>p,'\<beta>) packet \<mapsto> (adr\<^sub>i\<^sub>p,'\<beta>) packet set" where
|
|
"srcNat2pool_IntPort srcs transl =
|
|
{x. fst (src x) \<in> srcs} \<triangleleft> (A\<^sub>f (src2poolPort transl))"
|
|
|
|
definition srcNat2pool_IntProtocolPort :: "int set \<Rightarrow> int set \<Rightarrow>
|
|
(adr\<^sub>i\<^sub>p\<^sub>p,'\<beta>) packet \<mapsto> (adr\<^sub>i\<^sub>p\<^sub>p,'\<beta>) packet set" where
|
|
"srcNat2pool_IntProtocolPort srcs transl =
|
|
{x. (fst ( (src x))) \<in> srcs} \<triangleleft> (A\<^sub>f (src2poolPort_Protocol transl))"
|
|
|
|
definition srcPat2poolPort_t :: "int set \<Rightarrow> (adr\<^sub>i\<^sub>p,'\<beta>) packet \<Rightarrow> (adr\<^sub>i\<^sub>p,'\<beta>) packet set" where
|
|
"srcPat2poolPort_t t = (\<lambda> p. ({(i,(s1,s2),(d1,d2),da).
|
|
(i = id p \<and> s1 \<in> t \<and> d1 = (fst (dest p)) \<and> d2 = snd (dest p)\<and> da = content p)}))"
|
|
|
|
definition srcPat2poolPort_Protocol_t :: "int set \<Rightarrow> (adr\<^sub>i\<^sub>p\<^sub>p,'\<beta>) packet \<Rightarrow> (adr\<^sub>i\<^sub>p\<^sub>p,'\<beta>) packet set" where
|
|
"srcPat2poolPort_Protocol_t t = (\<lambda> p. ({(i,(s1,s2,s3),(d1,d2,d3),da).
|
|
(i = id p \<and> s1 \<in> t \<and> s3 = src_protocol p \<and> (d1,d2,d3) = dest p \<and> da = content p)}))"
|
|
|
|
definition srcPat2pool_IntPort :: "int set \<Rightarrow> int set \<Rightarrow> (adr\<^sub>i\<^sub>p,'\<beta>) packet \<mapsto>
|
|
(adr\<^sub>i\<^sub>p,'\<beta>) packet set" where
|
|
"srcPat2pool_IntPort srcs transl =
|
|
{x. (fst (src x)) \<in> srcs} \<triangleleft> (A\<^sub>f (srcPat2poolPort_t transl))"
|
|
|
|
definition srcPat2pool_IntProtocol ::
|
|
"int set \<Rightarrow> int set \<Rightarrow> (adr\<^sub>i\<^sub>p\<^sub>p,'\<beta>) packet \<mapsto> (adr\<^sub>i\<^sub>p\<^sub>p,'\<beta>) packet set" where
|
|
|
|
"srcPat2pool_IntProtocol srcs transl =
|
|
{x. (fst (src x)) \<in> srcs} \<triangleleft> (A\<^sub>f (srcPat2poolPort_Protocol_t transl))"
|
|
|
|
text\<open>
|
|
The following lemmas are used for achieving a normalized output format of packages after
|
|
applying NAT. This is used, e.g., by our firewall execution tool.
|
|
\<close>
|
|
|
|
lemma datasimp: "{(i, (s1, s2, s3), aba).
|
|
\<forall>a aa b ba. aba = ((a, aa, b), ba) \<longrightarrow> i = i1 \<and> s1 = i101 \<and>
|
|
s3 = iudp \<and> a = i110 \<and> aa = X606X3 \<and> b = X607X4 \<and> ba = data}
|
|
= {(i, (s1, s2, s3), aba).
|
|
i = i1 \<and> s1 = i101 \<and> s3 = iudp \<and> (\<lambda> ((a,aa,b),ba). a = i110 \<and> aa = X606X3 \<and>
|
|
b = X607X4 \<and> ba = data) aba}"
|
|
by auto
|
|
|
|
lemma datasimp2: "{(i, (s1, s2, s3), aba).
|
|
\<forall>a aa b ba. aba = ((a, aa, b), ba) \<longrightarrow> i = i1 \<and> s1 = i132 \<and> s3 = iudp \<and>
|
|
s2 = i1 \<and> a = i110 \<and> aa = i4 \<and> b = iudp \<and> ba = data}
|
|
= {(i, (s1, s2, s3), aba).
|
|
i = i1 \<and> s1 = i132 \<and> s3 = iudp \<and> s2 = i1 \<and> (\<lambda> ((a,aa,b),ba). a = i110 \<and>
|
|
aa = i4 \<and> b = iudp \<and> ba = data) aba}"
|
|
by auto
|
|
|
|
lemma datasimp3: "{(i, (s1, s2, s3), aba).
|
|
\<forall> a aa b ba. aba = ((a, aa, b), ba) \<longrightarrow> i = i1 \<and> i115 < s1 \<and> s1 < i124 \<and>
|
|
s3 = iudp \<and> s2 = ii1 \<and> a = i110 \<and> aa = i3 \<and> b = itcp \<and> ba = data}
|
|
= {(i, (s1, s2, s3), aba).
|
|
i = i1 \<and> i115 < s1 \<and> s1 < i124 \<and> s3 = iudp \<and> s2 = ii1 \<and>
|
|
(\<lambda> ((a,aa,b),ba). a = i110 & aa = i3 & b = itcp & ba = data) aba}"
|
|
by auto
|
|
|
|
lemma datasimp4: "{(i, (s1, s2, s3), aba).
|
|
\<forall>a aa b ba. aba = ((a, aa, b), ba) \<longrightarrow> i = i1 \<and> s1 = i132 \<and> s3 = iudp \<and>
|
|
s2 = ii1 \<and> a = i110 \<and> aa = i7 \<and> b = itcp \<and> ba = data}
|
|
= {(i, (s1, s2, s3), aba).
|
|
i = i1 \<and> s1 = i132 \<and> s3 = iudp \<and> s2 = ii1 \<and>
|
|
(\<lambda> ((a,aa,b),ba). a = i110 \<and> aa = i7 \<and> b = itcp \<and> ba = data) aba}"
|
|
by auto
|
|
|
|
lemma datasimp5: " {(i, (s1, s2, s3), aba).
|
|
i = i1 \<and> s1 = i101 \<and> s3 = iudp \<and> (\<lambda> ((a,aa,b),ba). a = i110 \<and> aa = X606X3 \<and>
|
|
b = X607X4 \<and> ba = data) aba}
|
|
= {(i, (s1, s2, s3), (a,aa,b),ba).
|
|
i = i1 \<and> s1 = i101 \<and> s3 = iudp \<and> a = i110 \<and> aa = X606X3 \<and>
|
|
b = X607X4 \<and> ba = data}"
|
|
by auto
|
|
|
|
lemma datasimp6: "{(i, (s1, s2, s3), aba).
|
|
i = i1 \<and> s1 = i132 \<and> s3 = iudp \<and> s2 = i1 \<and>
|
|
(\<lambda> ((a,aa,b),ba). a = i110 \<and> aa = i4 \<and> b = iudp \<and> ba = data) aba}
|
|
= {(i, (s1, s2, s3), (a,aa,b),ba).
|
|
i = i1 \<and> s1 = i132 \<and> s3 = iudp \<and> s2 = i1 \<and> a = i110 \<and>
|
|
aa = i4 \<and> b = iudp \<and> ba = data}"
|
|
by auto
|
|
|
|
lemma datasimp7: "{(i, (s1, s2, s3), aba).
|
|
i = i1 \<and> i115 < s1 \<and> s1 < i124 \<and> s3 = iudp \<and> s2 = ii1 \<and>
|
|
(\<lambda> ((a,aa,b),ba). a = i110 \<and> aa = i3 \<and> b = itcp \<and> ba = data) aba}
|
|
= {(i, (s1, s2, s3), (a,aa,b),ba).
|
|
i = i1 \<and> i115 < s1 \<and> s1 < i124 \<and> s3 = iudp \<and> s2 = ii1
|
|
\<and> a = i110 \<and> aa = i3 \<and> b = itcp \<and> ba = data}"
|
|
by auto
|
|
|
|
lemma datasimp8: "{(i, (s1, s2, s3), aba). i = i1 \<and> s1 = i132 \<and> s3 = iudp \<and> s2 = ii1 \<and>
|
|
(\<lambda> ((a,aa,b),ba). a = i110 \<and> aa = i7 \<and> b = itcp \<and> ba = data) aba}
|
|
= {(i, (s1, s2, s3), (a,aa,b),ba). i = i1 \<and> s1 = i132 \<and> s3 = iudp
|
|
\<and> s2 = ii1 \<and> a = i110 \<and> aa = i7 \<and> b = itcp \<and> ba = data}"
|
|
by auto
|
|
|
|
lemmas datasimps = datasimp datasimp2 datasimp3 datasimp4
|
|
datasimp5 datasimp6 datasimp7 datasimp8
|
|
|
|
lemmas NATLemmas = src2pool_def src2poolPort_def
|
|
src2poolPort_Protocol_def src2poolAP_def srcNat2pool_def
|
|
srcNat2pool_IntProtocolPort_def srcNat2pool_IntPort_def
|
|
srcPat2poolPort_t_def srcPat2poolPort_Protocol_t_def
|
|
srcPat2pool_IntPort_def srcPat2pool_IntProtocol_def
|
|
end
|