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add 5.8; update 4.5
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- [5.5 符号执行](doc/5.5_symbolic.md)
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- [5.6 LLVM](doc/5.6_llvm.md)
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- [5.7 Capstone/Keystone](doc/5.7_cap-keystone.md)
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- [5.8 SAT/SMT](doc/5.8_sat-smt.md)
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- [六、题解篇](doc/6_writeup.md)
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- pwn
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* [5.5 符号执行](doc/5.5_symbolic.md)
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* [5.6 LLVM](doc/5.6_llvm.md)
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* [5.7 Capstone/Keystone](doc/5.7_cap-keystone.md)
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* [5.8 SAT/SMT](doc/5.8_sat-smt.md)
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* [六、题解篇](doc/6_writeup.md)
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* pwn
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* [6.1.1 pwn HCTF2016 brop](doc/6.1.1_pwn_hctf2016_brop.md)
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179
doc/4.5_z3.md
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doc/4.5_z3.md
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# Z3 约束求解器
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- [安装](#安装)
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- [Z3 理论基础](#z3-理论基础)
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- [使用 Z3](#使用-z3)
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- [Z3 在 CTF 中的运用](#z3-在-ctf-中的运用)
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- [参考资料](#参考资料)
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[Z3](https://github.com/Z3Prover/z3) 是一个由微软开发的 Satisfiability Modulo Theories（SMT）求解器。可以用来检查满足一个或多个理论的公式的可满足性，也就是说,它可以自动化地通过内置理论对一阶逻辑多种排列进行可满足性校验。目前其支持的理论有：
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- equality over free 函数和谓词符号
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- 实数和整形运算(有限支持非线性运算)
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- 位向量
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- 阵列
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- 元组/记录/枚举类型和代数（递归）数据类型
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- ...
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因其强大的功能，Z3 已经被用于许多领域中，在安全领域，主要见于符号执行、Fuzzing、二进制逆向、密码学等。另外 Z3 提供了多种语言的接口，这里我们使用 Python。
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## 安装
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在 Linux 环境下，执行下面的命令：
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```
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$ git clone https://github.com/Z3Prover/z3.git
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$ cd z3
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$ python scripts/mk_make.py --python
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$ cd build
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$ make
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$ sudo make install
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```
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另外还可以使用 pip 来安装 Python 接口，这是二进制分析框架 angr 里内置的修改版：
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```
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$ sudo pip install z3-solver
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```
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## Z3 理论基础
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| Op | Mnmonics | Description |
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| --- | --- | --- |
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| 0 | true | 恒真 |
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| 1 | flase | 恒假 |
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| 2 | = | 相等 |
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| 3 | distinct | 不同 |
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| 4 | ite | if-then-else |
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| 5 | and | n元 合取 |
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| 6 | or | n元 析取 |
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| 7 | iff | implication |
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| 8 | xor | 异或 |
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| 9 | not | 否定 |
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| 10 | implies | Bi-implications |
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## 使用 Z3
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先来看一个简单的例子：
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```python
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>>> from z3 import *
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>>> x = Int('x')
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>>> y = Int('y')
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>>> solve(x > 2, y < 10, x + 2*y == 7)
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[y = 0, x = 7]
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```
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首先定义了两个变量 x 和 y，类型是 Z3 内置的整数类型 `Int`，`solve()` 函数会创造一个 solver，然后对括号中的约束条件进行求解，注意在 Z3 默认情况下只会找到满足条件的一组解。
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```python
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>>> simplify(x + y + 2*x + 3)
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3 + 3*x + y
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>>> simplify(x < y + x + 2)
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Not(y <= -2)
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>>> simplify(And(x + 1 >= 3, x**2 + x**2 + y**2 + 2 >= 5))
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And(x >= 2, 2*x**2 + y**2 >= 3)
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>>>
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>>> simplify((x + 1)*(y + 1))
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(1 + x)*(1 + y)
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>>> simplify((x + 1)*(y + 1), som=True)
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1 + x + y + x*y
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```
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`simplify()` 函数用于对表达式进行化简，同时可以设置一些选项来满足不同的要求。更多选项使用 `help_simplify()` 获得。
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同时，Z3 提供了一些函数可以解析表达式：
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```python
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>>> n = x + y >= 3
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>>> "num args: ", n.num_args()
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('num args: ', 2)
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>>> "children: ", n.children()
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('children: ', [x + y, 3])
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>>> "1st child:", n.arg(0)
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('1st child:', x + y)
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>>> "2nd child:", n.arg(1)
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('2nd child:', 3)
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>>> "operator: ", n.decl()
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('operator: ', >=)
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>>> "op name: ", n.decl().name()
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('op name: ', '>=')
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```
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`set_param()` 函数用于对 Z3 的全局变量进行配置，如运算精度，输出格式等等：
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```python
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>>> x = Real('x')
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>>> y = Real('y')
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>>> solve(x**2 + y**2 == 3, x**3 == 2)
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[x = 1.2599210498?, y = -1.1885280594?]
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>>>
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>>> set_param(precision=30)
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>>> solve(x**2 + y**2 == 3, x**3 == 2)
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[x = 1.259921049894873164767210607278?,
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y = -1.188528059421316533710369365015?]
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```
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逻辑运算有 `And`、`Or`、`Not`、`Implies`、`If`，另外 `==` 表示 Bi-implications。
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```python
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>>> p = Bool('p')
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>>> q = Bool('q')
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>>> r = Bool('r')
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>>> solve(Implies(p, q), r == Not(q), Or(Not(p), r))
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[q = False, p = False, r = True]
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>>>
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>>> x = Real('x')
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>>> solve(Or(x < 5, x > 10), Or(p, x**2 == 2), Not(p))
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[x = -1.4142135623?, p = False]
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```
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Z3 提供了多种 Solver，即 `Solver` 类，其中实现了很多 SMT 2.0 的命令，如 `push`, `pop`, `check` 等等。
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```python
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>>> x = Int('x')
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>>> y = Int('y')
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>>> s = Solver() # 创造一个通用 solver
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>>> type(s) # Solver 类
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<class 'z3.z3.Solver'>
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>>> s
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[]
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>>> s.add(x > 10, y == x + 2) # 添加约束到 solver 中
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>>> s
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[x > 10, y == x + 2]
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>>> s.check() # 检查 solver 中的约束是否满足
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sat # satisfiable/满足
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>>> s.push() # 创建一个回溯点，即将当前栈的大小保存下来
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>>> s.add(y < 11)
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>>> s
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[x > 10, y == x + 2, y < 11]
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>>> s.check()
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unsat # unsatisfiable/不满足
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>>> s.pop(num=1) # 回溯 num 个点
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>>> s
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[x > 10, y == x + 2]
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>>> s.check()
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sat
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>>> for c in s.assertions(): # assertions() 返回一个包含所有约束的AstVector
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... print(c)
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...
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x > 10
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y == x + 2
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>>> s.statistics() # statistics() 返回最后一个 check() 的统计信息
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(:max-memory 6.26
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:memory 4.37
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:mk-bool-var 1
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:num-allocs 331960806
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:rlimit-count 7016)
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>>> m = s.model() # model() 返回最后一个 check() 的 model
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>>> type(m) # ModelRef 类
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<class 'z3.z3.ModelRef'>
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>>> m
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[x = 11, y = 13]
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>>> for d in m.decls(): # decls() 返回 model 包含了所有符号的列表
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... print("%s = %s" % (d.name(), m[d]))
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...
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x = 11
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y = 13
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```
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## Z3 在 CTF 中的运用
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## 参考资料
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- [Z3一把梭：用约束求解搞定一类CTF题](https://zhuanlan.zhihu.com/p/30548907)
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- [Z3 API in Python](https://ericpony.github.io/z3py-tutorial/guide-examples.htm)
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- [z3py API](http://z3prover.github.io/api/html/index.html)
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- [Getting Started with Z3: A Guide](https://rise4fun.com/z3/tutorialcontent/guide)
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- [Wiki](https://github.com/Z3Prover/z3/wiki)
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6
doc/5.8_sat-smt.md
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doc/5.8_sat-smt.md
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# SAT/SMT
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- [参考资料](#参考资料)
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## 参考资料
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- [Quick introduction into SAT/SMT solvers and symbolic execution](https://yurichev.com/writings/SAT_SMT_draft-EN.pdf)
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- [5.5 Symbolic Execution 符号执行技术](5.5_symbolic.md)
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- [5.6 LLVM](5.6_llvm.md)
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- [5.7 Capstone/Keystone](5.7_cap-keystone.md)
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- [5.8 SAT/SMT](5.8_sat-smt.md)
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- [SROP 原理](#srop-原理)
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- [Linux 系统调用](#linux-系统调用)
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- [signal 机制](#signal-机制)
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- [SROP](#SROP)
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- [SROP](#srop)
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- [pwnlib.rop.srop](#pwnlibropsrop)
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- [BackdoorCTF2017 Fun Signals](#backdoorctf2017-fun-signals)
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- [参考资料](#参考资料)
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@ -20,8 +20,16 @@ $ ldd /usr/bin/ls
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## 题目解析
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```
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$ file fuckup
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fuckup: ELF 32-bit LSB executable, Intel 80386, version 1 (SYSV), statically linked, stripped
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$ checksec -f fuckup
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RELRO STACK CANARY NX PIE RPATH RUNPATH FORTIFY Fortified Fortifiable FILE
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No RELRO No canary found NX enabled No PIE No RPATH No RUNPATH No 0 0 fuckup
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```
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## Exploit
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完整的 exp 如下，其他文件放在了[github](../src/writeup/6.1.6_pwn_defconctf2015_fuckup)相应文件夹中：
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## 参考资料
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- `man vdso`
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