Georgy Nosenko - An introduction to the use SMT solvers for software security

SMT Solvers for Software Security

George Nosenko,
Security researcher at Digital Security


#whoami

• Member of DSecRG.
• System Developer
• Reverse Engineer
• Security Researcher

© 2002—2013, Digital Security

SMT Solvers in very simple terms

What is a SMT Solver?

Just like the first time using a SMT
constraint solver


What is a SMT Solver?

 Solver is a program
 You ask a question
“What is the meaning of life?”
 Solver tries to answer
“42”



How can I ask a question?

 Question is a logical formula
b+2 = c, f(read(write(a,b,3), c-2)) ≠ f(c-b+1)
 SMT-LIB: Language for expressing formulas
http://smtlib.org/
 All solvers understand this language



What solver should I choose?

There are many SMT-solvers (over 20)
CVC3, CVC4, STP, Alt-Ergo, Yices, Z3, etc
Z3 is my choice
 Efficient SMT solver
 Open Source Project: http://z3.codeplex.com
 Python, C/C++, .NET binding
 Available online
 Support Windows & Linux


SAT or not SAT? Ask a question.

 structure of formula
 declaration
 precondition
 postcondition
 answer
 sat, unsat, unknown
 satisfiability
 validity
 model
Taint Nobody Got Time for Crash

(declare-const work Int)
(declare-const sleep Int)
(declare-const fun Int)
(assert (>= work 40))
(assert (>= sleep 42))
(assert (>= fun work))
(assert (= (+ work (+ sleep fun)) 168))
(check-sat)
(get-model)
sat (model (sleep: 42, fun: 63, work 63)
http://rise4fun.com/Z3/pLpMc


Properties of SMT solvers

 Mathematical precision
 Expressive power
 Data model
 Efficient implementation
Support Bit-vector & Array


Applications
 Bug Hunting
 Fuzzing (whitebox or blackbox)
 Program Verification & Analysis
 Exploit Generation
 PoC, AEG, APEG
 Automate generate payload
 Protection Analysis
 Obfuscation
 Crypto Analysis
 Malware Analysis


What’s the point?

Idea: convert portions of code into logical formulas,
and use SMT solver to prove properties about them
add eax, ebx
xor ebx, ebx
sub ecx, 0x123
setz bl
add eax, ebx

Is this snippet equivalent to “add eax, ebx”?

sub
bl, bl
What value must EAX have at the beginning
movzx ebx, bl
add
ebx, 0xbbbbbbbb of this snippet in order for EAX to be
0x12345678 after the snippet executes?
add
eax, ebx
http://recon.cx/2012/schedule/attachments/52_semantics-based-methods.pdf
Taint Nobody Got Time for Crash


BV Operations in SMT-LIB 2.0

=/bvcomp
distinct
ite

bvand
bvor
bvxor
bvnot
bvnand
bvnor
bvxnor
bvneg

bvadd
bvmul
bvudiv
bvurem
bvsub
bvsdiv
bvsrem
bvsmod
bvshl
bvlshr
bvashr

bvult
bvule
bvugt
bvuge
bvslt
bvsle
bvsgt
bvsge

concat
extract
bvshl
bvlshr
bvashr
repeat
zero_extend
sign_extend
rotate_left
rotate_right

Slides - SMT Workshop 2013


Array Operations in SMT-LIB 2.0: select-store axioms
1. Expression (select a i) returns the value stored at position i of the array a;
2. And (store a i v) returns a new array identical to a, but on position i it
contains the value v.
(declare-const x Int)
(declare-const y Int)
(declare-const a1 (Array Int Int))
(assert (= (select a1 x) x))
(assert (= (store a1 x y) a1))
(check-sat)



Binary Analysis Platform: http://bap.ece.cmu.edu/

BIL code for add %rax, %rbx
addr 0x0 @asm "add %rax,%rbx"
label pc_0x0
T_t1:u64 = R_RBX:u64
T_t2:u64 = R_RAX:u64
R_RBX:u64 = R_RBX:u64 + T_t2:u64
R_CF:bool = R_RBX:u64 < T_t1:u64
R_OF:bool = high:bool((T_t1:u64 ^ ~T_t2:u64) & (T_t1:u64 ^ R_RBX:u64))
R_AF:bool = 0x10:u64 == (0x10:u64 & (R_RBX:u64 ^ T_t1:u64^T_t2:u64))
R_PF:bool =
~low:bool(let T_acc:u64 := R_RBX:u64 >> 4:u64 ^ R_RBX:u64 in
let T_acc:u64 := T_acc:u64 >> 2:u64 ^ T_acc:u64 in
T_acc:u64 >> 1:u64 ^ T_acc:u64)
R_SF:bool = high:bool(R_RBX:u64) R_ZF:bool = 0:u64 == R_RBX:u64



Bug Hunting


Bug Hunting

Vulnerability related with Integer

 CWE-190,191,192,194,196







May cause:
Bypass sanity check
Buffer Overflow
Dangling Pointer
Use after free
Application specific


Bug Hunting

Integer Overflow in Linux Kernel. CVE-2013-2596


Bug Hunting

Integer Overflow in Linux Kernel. CVE-2013-2596
static int fb_mmap(struct file *file, struct vm_area_struct * vma){
if (!info) return -ENODEV;
...
off = vma->vm_pgoff << PAGE_SHIFT;
fb = info->fbops;
if (!fb)
return -ENODEV;
...
/* frame buffer memory */
start = info->fix.smem_start;
len = PAGE_ALIGN((start & ~PAGE_MASK) + info->fix.smem_len);
if (off >= len) {
/* memory mapped io */
off -= len;
...
start = info->fix.mmio_start;
len = PAGE_ALIGN((start & ~PAGE_MASK) + info>fix.mmio_len);
}
mutex_unlock(&info->mm_lock);
start &= PAGE_MASK;
if ((vma->vm_end - vma->vm_start + off) > len)
return -EINVAL;
...
fb_pgprotect(file, vma, off);
if (io_remap_pfn_range(vma, vma->vm_start, off >> PAGE_SHIFT,
vma->vm_end - vma->vm_start, vma>vm_page_prot))
return -EAGAIN;
return 0;
}

Bug Hunting

How does Motochopper work?
1728 open("/dev/graphics/fb0", O_RDWR) = 6
...
1728 mmap2(NULL, 4096, PROT_READ|PROT_WRITE, MAP_SHARED, 6, 0) = 0x400f2000
...
1728 munmap(0x4015b000, 9433088)
= 0
1728 mmap2(NULL, 9437184, PROT_READ|PROT_WRITE, MAP_SHARED, 6, 0) = 0x4015b000
1728 munmap(0x4015b000, 9437184)
= 0
1728 mmap2(NULL, 9441280, PROT_READ|PROT_WRITE, MAP_SHARED, 6, 0) = -1 EINVAL (Invalid
argument)
1728 mmap2(NULL,
1728 mmap2(NULL,
(Out of memory)
1728 mmap2(NULL,
(Out of memory)
...
(Out of memory)
1728 mmap2(NULL,

NAME

2415919104, PROT_READ|PROT_WRITE, MAP_SHARED, 6, 0x70900) = -1 ENOMEM
2231369728, PROT_READ|PROT_WRITE, MAP_SHARED, 6, 0x7b900) = -1 ENOMEM
2214592512, PROT_READ|PROT_WRITE, MAP_SHARED, 6, 0x7c900) = -1 ENOMEM

2113929216, PROT_READ|PROT_WRITE, MAP_SHARED, 6, 0x82900) = 0x4015b000

mmap2 - map files or devices into memory
#include <sys/mman.h>
void *mmap2(void *addr, size_t length, int prot,
int flags, int fd, off_t pgoffset);


Bug Hunting

Integer Overflow in OpenSSH. CVE-2002-0639


Bug Hunting

input_userauth_info_response(){
...
u_int nresp;
...
nresp = packet_get_int();
if (nresp > 0) {
response = xmalloc(nresp * sizeof(char*));
for (i = 0; i < nresp; i++)
response[i] = packet_get_string(NULL);
}
packet_check_eom();
}


Bug Hunting

(declare-const

sizeof (_ BitVec 32))

(declare-const

nresp

(_ BitVec 32))

(declare-const

mult

(_ BitVec 32))

(assert ( =
4

sizeof

(assert ( = mult
nresp*sizeof

(_ bv4 32)))

(bvmul nresp sizeof)))

(assert ( bvugt

nresp

(assert ( bvult
nresp

mult nresp))

(get-model)


;

(_ bv0 32) )) ; nresp > 0

(assert ( = mult (_ bv256 32)))
nresp*sizeof = 256
(check-sat)

; sizeof (char*) =

; nresp*sizeof <
;

Bug Hunting

Verification & Static analyze with SMT
 Single collaborative framework
 It’s not heuristic bug-finding
 It allows user to manipulate
 Functional specification
 Prove that source code satisfies
specification
 Expands with plug-ins
 ACSL is a behavioral
specification language


Bug Hunting

Jessie: verification tools for C programs

 Jessie is a plug-in for the Frama-C
 Functional Checking
 Safety Checking
 Memory Safety
 Integer Overflow
 Checking Termination

Bug Hunting

Jessie: Integer Overflow Safety
#pragma JessieTerminationPolicy(user)
//@ requires n >= 0 && valid_range(t,0,n−1);
int binary_search(long t[], int n, long v) {
int l = 0, u = n-1;
//@ loop invariant 0 <= l && u <= n−1;
while (l <= u) {
int m = l + (u - l) / 2; //int m = (l + u) / 2;
if (t[m] < v)
l = m + 1;
else if (t[m] > v)
u = m - 1;
else return m;
}
return -1;
}

> frama-c -jessie binary-search.c


Bug Hunting

Immunity Debugger & SMT: Infrastructure

SequenceAnalyzer – Models x86 as operations over a set of SMT primitives.
Solver – Ctypes interface to the CVC3 SMT solver API. Supports a variety of
theories including quantifier free, bit-vector arithmetic, linear arithmetic etc.
CodeGraph/PathGenerator – Purely static CFG building and path generation.
PathWalker – SMT based path traversal. Each conditional jump is checked for
feasibility and the path discarded if not SAT.
BugChecker – Subclasses provide the check_ins method which will be passed the
SMT context representing the current path.


Bug Hunting

Immunity Debugger & SMT: !find_int_overwlow.py


SMT in protection analysis

PROTECTION ANALYSIS



Using SMT to defeat simple hashing algorithms
def round_hash(a, b, c, d):
out = [ ]
for i, n in enumerate((a, b, c, d)):
nn = 0
for j in range(32):
nn |= (rotl(n, SCRAMBLE_TABLE[(i << 2)+j]) & 1) << j
nn ^= XOR_TABLE[i]
out.append(nn)
out[0] = rotl(out[0], ROT_TABLE[0])
return out
a ^= c
b ^= d
for i in range(128):
a, b, c, d = round_hash(a, b, c, d)



Automated KeyGen Generation. Kao’s Toy Project



Automated KeyGen Generation. Kao’s Toy Project
 Lift the checking algorithm to BIL
./toil -binrange ~/toyproject.exe 0x401105 0x401111 -o checkUnlockCode.il

 Convert BIL to single static assignment form (SSA), unroll loop
./iltrans -il checkUnlockCode.il -to-ssa -simp-ssa -to-cfg -unroll 31 -rm-cycles
-rm-indirect-ast -to-ast -normalize-mem -flatten-mem -pp-ast checkUnlockUnroll.il
egrep -v '^cjmp.*$' checkUnlockUnroll.il > checkUnlockUnrollOpt.il

 Convert BIL to SMT-formula
./topredicate -il checkUnlockUnrollOpt.il -noopt -solver z3 -stp-out checkLoop.smt
line 18: assert --> define-fun alg () (Array (_ BitVec 32) (_ BitVec 8))
line 921: false --> ?mem_array_83_670



Create precondition and postcondition


AEG

Automatic Exploit Generation

 Automatically craft an input that redirects control
flow
Loosely defined as “Given a program and a vulnerability,
automatically craft an input that redirects control flow to
malicious code”

 Automated Payload Creation


AEG

Automatically craft an input that hijacks control flow

 Get the trace to vulnerable code
 Convert the trace into set of constraints
Freach
 Generate the set of conditions that make code exploitable
Fexploit = Cval U Caddr
 Solve (Freach U Fexploit)
 SMT-solver defines required input

AEG

Freach =
{ t0= eax + ebx, zf ==1 }
Cval =
{ eax = 0xdeadbeef }
Caddr =
{ t1= ebp + 4, t1 = ebp +ecx }


AEG

Freach =
{t0 = eax + ebx, zf == 1}
Cval =
{ eax = 0xdeadbeef }
Caddr =
{t1 = ebp + 4, t1 = ebp + ecx}
Input ={eax = 0xdeadbeef,
ebx = 0x21524111, ecx = 4}

(declare-const t0 (_ BitVec 32))
(declare-const t1 (_ BitVec 32))
(declare-const eax (_ BitVec 32))
(declare-const ebx (_ BitVec 32))
(declare-const ecx (_ BitVec 32))
(declare-const ebp (_ BitVec 32))
; Freach = {zf = 1, t0 = eax + ebx}
(assert (= t0 (bvadd eax ebx)))
; t0 = eax + ebx
(assert (= t0 #x00000000))
; zf = 1
; Cval = { eax = 0xDEADBEEF }
(assert (= eax #xdeadbeef))
; eax = 0xDEADBEEF
; Caddr = { t1 = ebp + 4, t1 = ebp + ecx}
(assert
(and
(= t1 (bvadd ebp #x00000004)) ; t1 = ebp + 4
(= t1 (bvadd ebp ecx)))
; t2 = ebp + ecx
)
sat (model
(define-fun ecx () (_ BitVec 32) #x00000004)
(define-fun eax () (_ BitVec 32) #xdeadbeef)
(define-fun ebx () (_ BitVec 32) #x21524111)
)

http://rise4fun.com/Z3/j2Y

Automate Generation Payload

Automated Payload Creation
 Data Execution Prevention (DEP)
 Windows 8 ROP mitigation enforces policies on who/where can call VirtualAlloc() or
VirtualProtect() to enable memory executable at run-time
 IOS already totally forbid code injection: Writable pages have NX permission & only signed
pages are executable
 Return Oriented Programming
 fun at first time, then hurt
 hundreds and thousands of ROP-gadgets
 “bad characters"
 find a suitable gadget can be difficult
 research efforts aimed at solving the problem of automatic generation ROP-chains



An interesting example from 0verckl0ck
Given:


we can write into eax, but only ASCII printable char



we have ROP-gadgets like these:

add eax, 0xc9f4458b;
add eax, 0x0fcf;
add eax, 0x1337;
Goal:

add eax, 0xdeadbeef;
add eax, 0x13b2;
add eax, 0x42;



make eax = 0xb00bdead



determine the initial value eax



find the minimum sequence of calls gadgets



An interesting example from 0verckl0ck

source: http://rise4fun.com/Z3Py/OrzP
assert( init_eax + g1*0xc9f4458b +
g2*0xdeadbeef +
g3*0x0fcf +
g4*0x13b2 +
g5*0x1337 +
g6*0x42 = 0xb00bdead)
assert(ascii_printable( init_eax ) )
sum (g1,g2,g3,g4,g5,g6) --> min
answer:
0x522e707c + 3*0xc9f4458b + 8*0x13b2 = 0xb00bdead


Finding gadgets with specific samntics

http://www.immunitysec.com/downloads/sean_ruxcon2010.pdf


Immunity Debugger: !find_gadget

This script looks for a sequence that satisfies
the constraints we specify



OptiROP



ROPC: https://github.com/pakt/ropc



ROPC : Type of gadgets that ROPC find &use
Name

Input

NopG

_

_

nop

LoadConstG

OutReg, Value

_

OutReg  Value

MoveRegG

InReg, OutReg

_

OutReg  InReg

ArithmeticG

InReg1, InReg2, OutReg

op

OutReg <- InReg1 op InReg2

StoreMemG

AddrReg, InReg

# Bytes, Offset

M[AddrReg+Offset]<-InReg

LoadMemReg

AddrReg, OutReg

# Bytes, Offset

OutRegM[AddrReg+Offset]

ArithmeticStoreG

InReg, AddrReg

# Bytes, Offset, op

M[AddrReg+Offset] op  InReg

ArithmeticLoadG

OutReg, AddrReg


Parameters

# Bytes, Offset, op

Semantic Definition

OutReg op  M[AddrReg+Offset


ROPC-LLVM: https://github.com/programa-stic/ropcllvm



Questions ?


Georgy Nosenko - An introduction to the use SMT solvers for software security

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