1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
|
; This books demonstrates how we could model network state and an attacker that
; would be a "Man in the middle" between a client and a server. This file is
; one of two that perform this modeling. The second file, network-state.lisp,
; is similar to this file, but it uses more advanced features of ACL2 (like
; defn, defaggregate, etc.).
; The concepts in this book are based off Rager's JFKr model, which can be
; found in books/projects/security/jfkr/jfkr.lisp and is explained in "An
; Executable Model for JFKr", by David Rager, which was included in the 2009
; ACL2 Workshop.
; Copyright David Rager 2012.
; License: (An MIT/X11-style license)
;
; Permission is hereby granted, free of charge, to any person obtaining a
; copy of this software and associated documentation files (the "Software"),
; to deal in the Software without restriction, including without limitation
; the rights to use, copy, modify, merge, publish, distribute, sublicense,
; and/or sell copies of the Software, and to permit persons to whom the
; Software is furnished to do so, subject to the following conditions:
;
; The above copyright notice and this permission notice shall be included in
; all copies or substantial portions of the Software.
;
; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
; AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
; FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
; DEALINGS IN THE SOFTWARE.
; Suppose we have the following english description of a protocol.
; There are two actors, a client/initiator and a server/responder. In this
; case, the server is providing a simple service -- it looks for a request on
; the network (presumably sent to the responder), squares the number included
; within the request, and sends the result back on the network.
; The server will keep track of the number of requests that it has served.
(in-package "ACL2")
(include-book "std/testing/must-fail" :dir :system)
(defconst *initial-number-to-square* 8)
(defconst *initial-result* :unknown)
(defun initialize-client ()
(list *initial-number-to-square*
*initial-result*))
(defconst *initial-client-state*
(initialize-client))
(defun valid-client-state (st)
(declare (xargs :guard t))
(and (true-listp st)
(equal (length st) 2)
(integerp (car st))
(or (integerp (cadr st))
(equal (cadr st) :unknown))))
(defun get-number-to-square-from-client-state (st)
(declare (xargs :guard (valid-client-state st)))
(car st))
(defun get-answer-from-client-state (st)
(declare (xargs :guard (valid-client-state st)))
(cadr st))
(defconst *intial-number-of-requests-served* 0)
(defun initialize-server ()
(list *intial-number-of-requests-served*))
(defun valid-server-state (st)
(declare (xargs :guard t))
(and (true-listp st)
(equal (length st) 1)
(integerp (car st))
(>= (car st) 0)))
(defconst *initial-server-state*
(initialize-server))
(defun initialize-network ()
nil)
(defun valid-message (msg)
(declare (xargs :guard t))
(and (true-listp msg)
(equal (len msg) 3)))
(defun valid-message-list (msg-list)
(declare (xargs :guard t))
(cond ((atom msg-list)
(null msg-list))
(t (and (valid-message (car msg-list))
(valid-message-list (cdr msg-list))))))
(defun valid-network (st)
(declare (xargs :guard t))
(valid-message-list st))
(defun server-function (x)
(expt x 2))
(defconst *client-id* :client)
(defconst *server-id* :server)
(defun make-message (sender dest msg)
(declare (xargs :guard t))
(list sender dest msg))
(defun retrieve-network-message (receiver network-st)
; Returns the message and a new network state, which does not include the new
; message
(declare (xargs :guard (and (or (equal receiver *client-id*)
(equal receiver *server-id*))
(valid-network network-st))))
(cond ((atom network-st)
(mv nil nil))
((equal (cadar network-st) receiver)
(mv (car network-st) (cdr network-st)))
(t (mv-let (msg network-st-recursive)
(retrieve-network-message receiver (cdr network-st))
(mv msg (cons (car network-st)
network-st-recursive))))))
(defun client-make-message-1 (value-to-square)
(declare (xargs :guard t))
(make-message *client-id* *server-id* (list :request value-to-square)))
(defun client-step1 (client-st network-st)
(declare (xargs :guard (and (valid-client-state client-st)
(valid-network network-st))))
(mv client-st
(cons
(client-make-message-1
(get-number-to-square-from-client-state client-st))
network-st)))
(defun print-states (client-st server-st network-st)
(prog2$
(cw "Client state is: ~x0~%" client-st)
(prog2$
(cw "Server state is: ~x0~%" server-st)
(cw "Network state is: ~x0~%" network-st))))
#+demo-only ; skipped during book certification
(let ((client-st (initialize-client))
(server-st (initialize-server))
(network-st (initialize-network)))
(mv-let (client-st network-st)
(client-step1 client-st network-st)
(print-states client-st server-st network-st)))
(defun get-input-from-client-request (msg)
(declare (xargs :guard (valid-message msg)
:verify-guards nil))
(cadr (caddr msg)))
(defun server-make-message-1 (result)
(declare (xargs :guard t))
(make-message *server-id* *client-id*
(list :answer result)))
(defun server-step1 (server-st network-st)
(declare (xargs :guard (and (valid-server-state server-st)
(valid-network network-st))
:verify-guards nil))
(mv-let (message network-st)
(retrieve-network-message *server-id* network-st)
(mv (list (+ 1 (car server-st))) ; todo abstract server state
(cons
(server-make-message-1
(server-function (get-input-from-client-request message)))
network-st))))
#+demo-only
(let ((client-st (initialize-client))
(server-st (initialize-server))
(network-st (initialize-network)))
(mv-let (client-st network-st)
(client-step1 client-st network-st)
(mv-let (server-st network-st)
(server-step1 server-st network-st)
(print-states client-st server-st
network-st))))
(defun client-step2 (client-st network-st)
(mv-let (message network-st)
(retrieve-network-message *client-id* network-st)
(mv (list (car client-st)
(cadr (caddr message))) ; todo make an assoc off :answer
network-st)))
#+demo-only
(let ((client-st (initialize-client))
(server-st (initialize-server))
(network-st (initialize-network)))
(mv-let (client-st network-st)
(client-step1 client-st network-st)
(mv-let (server-st network-st)
(server-step1 server-st network-st)
(mv-let (client-st network-st)
(client-step2 client-st
network-st)
(print-states client-st server-st
network-st)))))
(defun man-in-the-middle-attacks-once (network-st)
; Changes the number requested
(mv-let (original-message network-st)
(retrieve-network-message *server-id* network-st)
(cons (client-make-message-1 (1+ (cadr (caddr original-message))))
network-st)))
#+demo-only
(let ((client-st (initialize-client))
(server-st (initialize-server))
(network-st (initialize-network)))
(mv-let (client-st network-st)
(client-step1 client-st network-st)
(let ((network-st (man-in-the-middle-attacks-once network-st)))
(mv-let (server-st network-st)
(server-step1 server-st network-st)
(print-states client-st server-st network-st)))))
#+demo-only
(let ((client-st (initialize-client))
(server-st (initialize-server))
(network-st (initialize-network)))
(mv-let (client-st network-st)
(client-step1 client-st network-st)
(prog2$
(print-states client-st server-st network-st)
(mv-let (server-st network-st)
(server-step1 server-st
(man-in-the-middle-attacks-once network-st))
(print-states client-st server-st network-st)))))
(defthm honest-square-is-good-concrete
(let ((client-st (initialize-client)) ; not symbolic, because it has concrete initialization
(server-st (initialize-server))
(network-st (initialize-network)))
(mv-let (client-st network-st)
(client-step1 client-st network-st)
(mv-let (server-st network-st)
(server-step1 server-st network-st)
(declare (ignore server-st))
(mv-let (client-st network-st)
(client-step2 client-st network-st)
(declare (ignore network-st))
(equal (expt (get-number-to-square-from-client-state client-st) 2)
(get-answer-from-client-state client-st)))))))
(defthm honest-square-is-good-symbolic-simulation
(implies (and (valid-client-state client-st) ; is symbolic
(valid-server-state server-st)
(valid-network network-st))
(mv-let (client-st network-st)
(client-step1 client-st network-st)
(mv-let (server-st network-st)
(server-step1 server-st network-st)
(declare (ignore server-st))
(mv-let (client-st network-st)
(client-step2 client-st network-st)
(declare (ignore network-st))
(equal (expt (get-number-to-square-from-client-state client-st) 2)
(get-answer-from-client-state client-st)))))))
(encapsulate (((attack1 *) => *))
(local (defun attack1 (x) (declare (ignore x))
nil)))
(encapsulate (((attack2 *) => *))
(local (defun attack2 (x) (declare (ignore x))
nil)))
(must-fail
; Technically being unable to prove this theorem in ACL2 doesn't mean that the
; theorem isn't valid. However, if we believed the theorem to be valid, we
; would relentlessly examine the feedback from ACL2 until we figured out how to
; make ACL2 agree with our belief. But, we happen to know that the theorem
; isn't true, so we leave it as is.
(defthm |bad-square-is-good?-with-single-attack|
(implies
(and (valid-client-state client-st) ; is symbolic
(valid-server-state server-st)
(valid-network network-st))
(mv-let (client-st network-st)
(client-step1 client-st network-st)
(mv-let (server-st network-st)
(server-step1 server-st (attack1 network-st))
(declare (ignore server-st))
(mv-let (client-st network-st)
(client-step2 client-st network-st)
(declare (ignore network-st))
(equal (expt (get-number-to-square-from-client-state client-st) 2)
(get-answer-from-client-state client-st))))))))
(must-fail
; Technically being unable to prove this theorem in ACL2 doesn't mean that the
; theorem isn't valid. However, if we believed the theorem to be valid, we
; would relentlessly examine the feedback from ACL2 until we figured out how to
; make ACL2 agree with our belief. But, we happen to know that the theorem
; isn't true, so we leave it as is.
(defthm |bad-square-is-good?-with-double-attack|
(implies
(and (valid-client-state client-st) ; is symbolic
(valid-server-state server-st)
(valid-network network-st))
(mv-let (client-st network-st)
(client-step1 client-st (attack1 network-st))
(mv-let (server-st network-st)
(server-step1 server-st (attack2 network-st))
(declare (ignore server-st))
(mv-let (client-st network-st)
(client-step2 client-st network-st)
(declare (ignore network-st))
(equal (expt (get-number-to-square-from-client-state client-st) 2)
(get-answer-from-client-state client-st))))))))
|
