From d19c25abbdb9220a84322dd1e7a9a8c931b1ed51 Mon Sep 17 00:00:00 2001 From: Francesco Mecca Date: Fri, 3 Apr 2020 18:12:32 +0200 Subject: [PATCH] symbolic execution done --- tesi/conv.py | 2 +- tesi/referenze/blexim.txt | 777 ++++++++++++++++++++++++++++++++++++++ tesi/tesi.pdf | Bin 377155 -> 384600 bytes tesi/tesi_unicode.org | 125 ++++++ 4 files changed, 903 insertions(+), 1 deletion(-) create mode 100644 tesi/referenze/blexim.txt diff --git a/tesi/conv.py b/tesi/conv.py index ce5fd8b..20477f4 100644 --- a/tesi/conv.py +++ b/tesi/conv.py @@ -3,7 +3,7 @@ import re from sys import argv allsymbols = json.load(open('./unicode-latex.json')) -mysymbols = ['≡', '≠', '≼', '→', '←', '⊀', '⋠', '≺', '∀', '∈', 'ε','₀', '₂', '₁', '₃', 'ₐ', 'ₖ', 'ₘ', 'ₙ', 'ᵢ', 'ⁱ', '⋮', 'ₛ', 'ₜ', '≃', '⇔', '∧', '∅', 'ℕ', 'ⱼ', 'ʲ', '⊥', 'π'] +mysymbols = ['≡', '≠', '≼', '→', '←', '⊀', '⋠', '≺', '∀', '∈', 'ε','₀', '₂', '₁', '₃', 'ₐ', 'ₖ', 'ₘ', 'ₙ', 'ᵢ', 'ⁱ', '⋮', 'ₛ', 'ₜ', '≃', '⇔', '∧', '∅', 'ℕ', 'ⱼ', 'ʲ', '⊥', 'π', 'α', 'β', '∞', 'σ', '≤', '⊈', '∧', '∨', '∃', '⇒' ] extrasymbols = {'〚': '\llbracket', '〛': '\rrbracket'} symbols = {s: allsymbols[s] for s in mysymbols} diff --git a/tesi/referenze/blexim.txt b/tesi/referenze/blexim.txt new file mode 100644 index 0000000..98e7bfa --- /dev/null +++ b/tesi/referenze/blexim.txt @@ -0,0 +1,777 @@ + + ==Phrack Inc.== + + Volume 0x0b, Issue 0x3c, Phile #0x0a of 0x10 + + +|=--------------------=[ Basic Integer Overflows ]=----------------------=| +|=-----------------------------------------------------------------------=| +|=-------------------=[ by blexim ]=-------------------=| + +1: Introduction + 1.1 What is an integer? + 1.2 What is an integer overflow? + 1.3 Why can they be dangerous? + +2: Integer overflows + 2.1 Widthness overflows + 2.1.1 Exploiting + 2.2 Arithmetic overflows + 2.2.1 Exploiting + +3: Signedness bugs + 3.1 What do they look like? + 3.1.1 Exploiting + 3.2 Signedness bugs caused by integer overflows + +4: Real world examples + 4.1 Integer overflows + 4.2 Signedness bugs + + +--[ 1.0 Introduction + +In this paper I'm going to describe two classes of programming bugs which +can sometimes allow a malicious user to modify the execution path of an +affected process. Both of these classes of bug work by causing variables +to contain unexpected values, and so are not as "direct" as classes which +overwrite memory, e.g. buffer overflows or format strings. All the +examples given in the paper are in C, so a basic familiarity with C is +assumed. A knowledge of how integers are stored in memory is also useful, +but not essential. + + +----[ 1.1 What is an integer? + +An integer, in the context of computing, is a variable capable of +representing a real number with no fractional part. Integers are typically +the same size as a pointer on the system they are compiled on (i.e. on a 32 +bit system, such as i386, an integer is 32 bits long, on a 64 bit system, +such as SPARC, an integer is 64 bits long). Some compilers don't use +integers and pointers of the same size however, so for the sake of +simplicity all the examples refer to a 32 bit system with 32 bit integers, +longs and pointers. + +Integers, like all variables are just regions of memory. When we talk +about integers, we usually represent them in decimal, as that is the +numbering system humans are most used to. Computers, being digital, cannot +deal with decimal, so internally to the computer integers are stored in +binary. Binary is another system of representing numbers which uses only +two numerals, 1 and 0, as opposed to the ten numerals used in decimal. As +well as binary and decimal, hexadecimal (base sixteen) is often used in +computing as it is very easy to convert between binary and hexadecimal. + +Since it is often necessary to store negative numbers, there needs to be a +mechanism to represent negative numbers using only binary. The way this is +accomplished is by using the most significant bit (MSB) of a variable to +determine the sign: if the MSB is set to 1, the variable is interpreted as +negative; if it is set to 0, the variable is positive. This can cause some +confusion, as will be explained in the section on signedness bugs, because +not all variables are signed, meaning they do not all use the MSB to +determine whether they are positive or negative. These variable are known +as unsigned and can only be assigned positive values, whereas variables +which can be either positive or negative are called unsigned. + + +----[ 1.2 What is an integer overflow? + +Since an integer is a fixed size (32 bits for the purposes of this paper), +there is a fixed maximum value it can store. When an attempt is made to +store a value greater than this maximum value it is known as an integer +overflow. The ISO C99 standard says that an integer overflow causes +"undefined behaviour", meaning that compilers conforming to the standard +may do anything they like from completely ignoring the overflow to aborting +the program. Most compilers seem to ignore the overflow, resulting in an +unexpected or erroneous result being stored. + + +----[ 1.3 Why can they be dangerous? + +Integer overflows cannot be detected after they have happened, so there is +not way for an application to tell if a result it has calculated previously +is in fact correct. This can get dangerous if the calculation has to do +with the size of a buffer or how far into an array to index. Of course +most integer overflows are not exploitable because memory is not being +directly overwritten, but sometimes they can lead to other classes of bugs, +frequently buffer overflows. As well as this, integer overflows can be +difficult to spot, so even well audited code can spring surprises. + + + +--[ 2.0 Integer overflows + +So what happens when an integer overflow does happen? ISO C99 has this to +say: + + "A computation involving unsigned operands can never overflow, + because a result that cannot be represented by the resulting unsigned + integer type is reduced modulo the number that is one greater than + the largest value that can be represented by the resulting type." + +NB: modulo arithmetic involves dividing two numbers and taking the +remainder, +e.g. + 10 modulo 5 = 0 + 11 modulo 5 = 1 +so reducing a large value modulo (MAXINT + 1) can be seen as discarding the +portion of the value which cannot fit into an integer and keeping the rest. +In C, the modulo operator is a % sign. + + +This is a bit wordy, so maybe an example will better demonstrate the +typical "undefined behaviour": + +We have two unsigned integers, a and b, both of which are 32 bits long. We +assign to a the maximum value a 32 bit integer can hold, and to b we assign +1. We add a and b together and store the result in a third unsigned 32 bit +integer called r: + + a = 0xffffffff + b = 0x1 + r = a + b + +Now, since the result of the addition cannot be represented using 32 bits, +the result, in accordance with the ISO standard, is reduced modulo +0x100000000. + + r = (0xffffffff + 0x1) % 0x100000000 + r = (0x100000000) % 0x100000000 = 0 + +Reducing the result using modulo arithmetic basically ensures that only the +lowest 32 bits of the result are used, so integer overflows cause the +result to be truncated to a size that can be represented by the variable. +This is often called a "wrap around", as the result appears to wrap around +to 0. + + +----[ 2.1 Widthness overflows + +So an integer overflow is the result of attempting to store a value in a +variable which is too small to hold it. The simplest example of this can +be demonstrated by simply assigning the contents of large variable to a +smaller one: + + /* ex1.c - loss of precision */ + #include + + int main(void){ + int l; + short s; + char c; + + l = 0xdeadbeef; + s = l; + c = l; + + printf("l = 0x%x (%d bits)\n", l, sizeof(l) * 8); + printf("s = 0x%x (%d bits)\n", s, sizeof(s) * 8); + printf("c = 0x%x (%d bits)\n", c, sizeof(c) * 8); + + return 0; + } + /* EOF */ + +The output of which looks like this: + + nova:signed {48} ./ex1 + l = 0xdeadbeef (32 bits) + s = 0xffffbeef (16 bits) + c = 0xffffffef (8 bits) + +Since each assignment causes the bounds of the values that can be stored in +each type to be exceeded, the value is truncated so that it can fit in the +variable it is assigned to. + +It is worth mentioning integer promotion here. When a calculation +involving operands of different sizes is performed, the smaller operand is +"promoted" to the size of the larger one. The calculation is then +performed with these promoted sizes and, if the result is to be stored in +the smaller variable, the result is truncated to the smaller size again. +For example: + + int i; + short s; + + s = i; + +A calculation is being performed with different sized operands here. What +happens is that the variable s is promoted to an int (32 bits long), then +the contents of i is copied into the new promoted s. After this, the +contents of the promoted variable are "demoted" back to 16 bits in order to +be saved in s. This demotion can cause the result to be truncated if it is +greater than the maximum value s can hold. + +------[ 2.1.1 Exploiting + +Integer overflows are not like most common bug classes. They do not allow +direct overwriting of memory or direct execution flow control, but are much +more subtle. The root of the problem lies in the fact that there is no way +for a process to check the result of a computation after it has happened, +so there may be a discrepancy between the stored result and the correct +result. Because of this, most integer overflows are not actually +exploitable. Even so, in certain cases it is possible to force a crucial +variable to contain an erroneous value, and this can lead to problems later +in the code. + +Because of the subtlety of these bugs, there is a huge number of situations +in which they can be exploited, so I will not attempt to cover all +exploitable conditions. Instead, I will provide examples of some +situations which are exploitable, in the hope of inspiring the reader in +their own research :) + +Example 1: + + /* width1.c - exploiting a trivial widthness bug */ + #include + #include + + int main(int argc, char *argv[]){ + unsigned short s; + int i; + char buf[80]; + + if(argc < 3){ + return -1; + } + + i = atoi(argv[1]); + s = i; + + if(s >= 80){ /* [w1] */ + printf("Oh no you don't!\n"); + return -1; + } + + printf("s = %d\n", s); + + memcpy(buf, argv[2], i); + buf[i] = '\0'; + printf("%s\n", buf); + + return 0; + } + + +While a construct like this would probably never show up in real life code, +it serves well as an example. Take a look at the following inputs: + + nova:signed {100} ./width1 5 hello + s = 5 + hello + nova:signed {101} ./width1 80 hello + Oh no you don't! + nova:signed {102} ./width1 65536 hello + s = 0 + Segmentation fault (core dumped) + +The length argument is taken from the command line and held in the integer +i. When this value is transferred into the short integer s, it is +truncated if the value is too great to fit into s (i.e. if the value is +greater than 65535). Because of this, it is possible to bypass the bounds +check at [w1] and overflow the buffer. After this, standard stack smashing +techniques can be used to exploit the process. + + +----[ 2.2 Arithmetic overflows + +As shown in section 2.0, if an attempt is made to store a value in an +integer which is greater than the maximum value the integer can hold, the +value will be truncated. If the stored value is the result of an +arithmetic operation, any part of the program which later uses the result +will run incorrectly as the result of the arithmetic being incorrect. +Consider this example demonstrating the wrap around shown earlier: + + /* ex2.c - an integer overflow */ + #include + + int main(void){ + unsigned int num = 0xffffffff; + + printf("num is %d bits long\n", sizeof(num) * 8); + printf("num = 0x%x\n", num); + printf("num + 1 = 0x%x\n", num + 1); + + return 0; + } + /* EOF */ + +The output of this program looks like this: + + nova:signed {4} ./ex2 + num is 32 bits long + num = 0xffffffff + num + 1 = 0x0 + +Note: +The astute reader will have noticed that 0xffffffff is decimal -1, so it +appears that we're just doing +1 + (-1) = 0 +Whilst this is one way at looking at what's going on, it may cause some +confusion since the variable num is unsigned and therefore all arithmetic +done on it will be unsigned. As it happens, a lot of signed arithmetic +depends on integer overflows, as the following demonstrates (assume both +operands are 32 bit variables): + +-700 + 800 = 100 +0xfffffd44 + 0x320 = 0x100000064 + +Since the result of the addition exceeds the range of the variable, the +lowest 32 bits are used as the result. These low 32 bits are 0x64, which +is equal to decimal 100. + + +Since an integer is signed by default, an integer overflow can cause a +change in signedness which can often have interesting effects on subsequent +code. Consider the following example: + + /* ex3.c - change of signedness */ + #include + + int main(void){ + int l; + + l = 0x7fffffff; + + printf("l = %d (0x%x)\n", l, l); + printf("l + 1 = %d (0x%x)\n", l + 1 , l + 1); + + return 0; + } + /* EOF */ + +The output of which is: + + nova:signed {38} ./ex3 + l = 2147483647 (0x7fffffff) + l + 1 = -2147483648 (0x80000000) + +Here the integer is initialised with the highest positive value a signed +long integer can hold. When it is incremented, the most significant bit +(indicating signedness) is set and the integer is interpreted as being +negative. + +Addition is not the only arithmetic operation which can cause an integer to +overflow. Almost any operation which changes the value of a variable can +cause an overflow, as demonstrated in the following example: + + /* ex4.c - various arithmetic overflows */ + #include + + int main(void){ + int l, x; + + l = 0x40000000; + + printf("l = %d (0x%x)\n", l, l); + + x = l + 0xc0000000; + printf("l + 0xc0000000 = %d (0x%x)\n", x, x); + + x = l * 0x4; + printf("l * 0x4 = %d (0x%x)\n", x, x); + + x = l - 0xffffffff; + printf("l - 0xffffffff = %d (0x%x)\n", x, x); + + return 0; + } + /* EOF */ + +Output: + + nova:signed {55} ./ex4 + l = 1073741824 (0x40000000) + l + 0xc0000000 = 0 (0x0) + l * 0x4 = 0 (0x0) + l - 0xffffffff = 1073741825 (0x40000001) + +The addition is causing an overflow in exactly the same way as the first +example, and so is the multiplication, although it may seem different. In +both cases the result of the arithmetic is too great to fit in an integer, +so it is reduced as described above. The subtraction is slightly +different, as it is causing an underflow rather than an overflow: an +attempt is made to store a value lower than the minimum value the integer +can hold, causing a wrap around. In this way we are able to force an +addition to subtract, a multiplication to divide or a subtraction to add. + +------[ 2.2.1 Exploiting + +One of the most common ways arithmetic overflows can be exploited is when a +calculation is made about how large a buffer must be allocated. Often a +program must allocate space for an array of objects, so it uses the +malloc(3) or calloc(3) routines to reserve the space and calculates how +much space is needed by multiplying the number of elements by the size of +an object. As has been previously shown, if we are able to control either +of these operands (number of elements or object size) we may be able to +mis-size the buffer, as the following code fragment shows: + + int myfunction(int *array, int len){ + int *myarray, i; + + myarray = malloc(len * sizeof(int)); /* [1] */ + if(myarray == NULL){ + return -1; + } + + for(i = 0; i < len; i++){ /* [2] */ + myarray[i] = array[i]; + } + + return myarray; + } + +This seemingly innocent function could bring about the downfall of a system +due to its lack of checking of the len parameter. The multiplication at +[1] can be made to overflow by supplying a high enough value for len, so we +can force the buffer to be any length we choose. By choosing a suitable +value for len, we can cause the loop at [2] to write past the end of the +myarray buffer, resulting in a heap overflow. This could be leveraged into +executing arbitrary code on certain implementations by overwriting malloc +control structures, but that is beyond the scope of this article. + +Another example: + + int catvars(char *buf1, char *buf2, unsigned int len1, + unsigned int len2){ + char mybuf[256]; + + if((len1 + len2) > 256){ /* [3] */ + return -1; + } + + memcpy(mybuf, buf1, len1); /* [4] */ + memcpy(mybuf + len1, buf2, len2); + + do_some_stuff(mybuf); + + return 0; + } + +In this example, the check at [3] can be bypassed by using suitable values +for len1 and len2 that will cause the addition to overflow and wrap around +to a low number. For example, the following values: + + len1 = 0x104 + len2 = 0xfffffffc + +when added together would result in a wrap around with a result of 0x100 +(decimal 256). This would pass the check at [3], then the memcpy(3)'s at +[4] would copy data well past the end of the buffer. + + + +--[ 3 Signedness Bugs + +Signedness bugs occur when an unsigned variable is interpreted as signed, +or when a signed variable is interpreted as unsigned. This type of +behaviour can happen because internally to the computer, there is no +distinction between the way signed and unsigned variables are stored. +Recently, several signedness bugs showed up in the FreeBSD and OpenBSD +kernels, so there are many examples readily available. + + +----[ 3.1 What do they look like? + +Signedness bugs can take a variety of forms, but some of the things to look +out for are: +* signed integers being used in comparisons +* signed integers being used in arithmetic +* unsigned integers being compared to signed integers + +Here is classic example of a signedness bug: + + int copy_something(char *buf, int len){ + char kbuf[800]; + + if(len > sizeof(kbuf)){ /* [1] */ + return -1; + } + + return memcpy(kbuf, buf, len); /* [2] */ + } + +The problem here is that memcpy takes an unsigned int as the len parameter, +but the bounds check performed before the memcpy is done using signed +integers. By passing a negative value for len, it is possible to pass the +check at [1], but then in the call to memcpy at [2], len will be interpeted +as a huge unsigned value, causing memory to be overwritten well past the +end of the buffer kbuf. + +Another problem that can stem from signed/unsigned confusion occurs when +arithmetic is performed. Consider the following example: + + int table[800]; + + int insert_in_table(int val, int pos){ + if(pos > sizeof(table) / sizeof(int)){ + return -1; + } + + table[pos] = val; + + return 0; + } + +Since the line + table[pos] = val; +is equivalent to + *(table + (pos * sizeof(int))) = val; +we can see that the problem here is that the code does not expect a +negative operand for the addition: it expects (table + pos) to be greater +than table, so providing a negative value for pos causes a situation which +the program does not expect and can therefore not deal with. + +------[ 3.1.1 Exploiting + +This class of bug can be problematic to exploit, due to the fact that +signed integers, when interpreted as unsigned, tend to be huge. For +example, -1 when represented in hexadecimal is 0xffffffff. When +interpreted as unsiged, this becomes the greatest value it is possible to +represent in an integer (4,294,967,295), so if this value is passed to +mempcpy as the len parameter (for example), memcpy will attempt to copy 4GB +of data to the destination buffer. Obviously this is likely to cause a +segfault or, if not, to trash a large amount of the stack or heap. +Sometimes it is possible to get around this problem by passing a very low +value for the source address and hope, but this is not always possible. + + + +----[ 3.2 Signedness bugs caused by integer overflows + +Sometimes, it is possible to overflow an integer so that it wraps around to +a negative number. Since the application is unlikely to expect such a +value, it may be possible to trigger a signedness bug as described above. + +An example of this type of bug could look like this: + + int get_two_vars(int sock, char *out, int len){ + char buf1[512], buf2[512]; + unsigned int size1, size2; + int size; + + if(recv(sock, buf1, sizeof(buf1), 0) < 0){ + return -1; + } + if(recv(sock, buf2, sizeof(buf2), 0) < 0){ + return -1; + } + + /* packet begins with length information */ + memcpy(&size1, buf1, sizeof(int)); + memcpy(&size2, buf2, sizeof(int)); + + size = size1 + size2; /* [1] */ + + if(size > len){ /* [2] */ + return -1; + } + + memcpy(out, buf1, size1); + memcpy(out + size1, buf2, size2); + + return size; + } + +This example shows what can sometimes happen in network daemons, especially +when length information is passed as part of the packet (in other words, it +is supplied by an untrusted user). The addition at [1], used to check that +the data does not exceed the bounds of the output buffer, can be abused by +setting size1 and size2 to values that will cause the size variable to wrap +around to a negative value. Example values could be: + size1 = 0x7fffffff + size2 = 0x7fffffff + (0x7fffffff + 0x7fffffff = 0xfffffffe (-2)). +When this happens, the bounds check at [2] passes, and a lot more of the +out buffer can be written to than was intended (in fact, arbitrary memory +can be written to, as the (out + size1) dest parameter in the second memcpy +call allows us to get to any location in memory). + +These bugs can be exploited in exactly the same way as regular signedness +bugs and have the same problems associated with them - i.e. negative values +translate to huge positive values, which can easily cause segfaults. + + + +--[ 4 Real world examples + +There are many real world applications containing integer overflows and +signedness bugs, particularly network daemons and, frequently, in operating +system kernels. + +----[ 4.1 Integer overflows + +This (non-exploitable) example was taken from a security module for linux. +This code runs in the kernel context: + + int rsbac_acl_sys_group(enum rsbac_acl_group_syscall_type_t call, + union rsbac_acl_group_syscall_arg_t arg) + { + ... + switch(call) + { + case ACLGS_get_group_members: + if( (arg.get_group_members.maxnum <= 0) /* [A] */ + || !arg.get_group_members.group + ) + { + ... + rsbac_uid_t * user_array; + rsbac_time_t * ttl_array; + + user_array = vmalloc(sizeof(*user_array) * + arg.get_group_members.maxnum); /* [B] */ + if(!user_array) + return -RSBAC_ENOMEM; + ttl_array = vmalloc(sizeof(*ttl_array) * + arg.get_group_members.maxnum); /* [C] */ + if(!ttl_array) + { + vfree(user_array); + return -RSBAC_ENOMEM; + } + + err = + rsbac_acl_get_group_members(arg.get_group_members.group, + user_array, + ttl_array, + + arg.get_group_members.max + num); + ... + } + +In this example, the bounds checking at [A] is not sufficient to prevent +the integer overflows at [B] and [C]. By passing a high enough (i.e. +greater than 0xffffffff / 4) value for arg.get_group_members.maxnum, we +can cause the multiplications at [B] and [C] to overflow and force the +buffers ttl_array and user_array to be smaller than the application +expects. Since rsbac_acl_get_group_members copies user controlled data +to these buffers, it is possible to write past the end of the user_array +and ttl_array buffers. In this case, the application used vmalloc() to +allocate the buffers, so an attempt to write past the end of the buffers +will simply raise an error, so it cannot be exploited. Even so, it +provides an example of what these bugs can look like in real code. + +Another example of a recent real world integer overflow vulnerability +was the problem in the XDR RPC library (discovered by ISS X-Force). In this +case, user supplied data was used in the calculation of the size of a +dynamically allocated buffer which was filled with user supplied data. The +vulnerable code was this: + + bool_t + xdr_array (xdrs, addrp, sizep, maxsize, elsize, elproc) + XDR *xdrs; + caddr_t *addrp; /* array pointer */ + u_int *sizep; /* number of elements */ + u_int maxsize; /* max numberof elements */ + u_int elsize; /* size in bytes of each element */ + xdrproc_t elproc; /* xdr routine to handle each element */ + { + u_int i; + caddr_t target = *addrp; + u_int c; /* the actual element count */ + bool_t stat = TRUE; + u_int nodesize; + + ... + + c = *sizep; + if ((c > maxsize) && (xdrs->x_op != XDR_FREE)) + { + return FALSE; + } + nodesize = c * elsize; /* [1] */ + + ... + + *addrp = target = mem_alloc (nodesize); /* [2] */ + + ... + + for (i = 0; (i < c) && stat; i++) + { + stat = (*elproc) (xdrs, target, LASTUNSIGNED); /* [3] */ + target += elsize; + } + +As you can see, by supplying large values for elsize and c (sizep), it +was possible to cause the multiplication at [1] to overflow and cause +nodesize to be much smaller than the application expected. Since +nodesize was then used to allocate a buffer at [2], the buffer could be +mis-sized leading to a heap overflow at [3]. For more information on this +hole, see the CERT advisory listed in the appendix. + + +----[ 4.2 Signedness bugs + +Recently, several signedness bugs were brought to light in the freebsd +kernel. These allowed large portions of kernel memory to be read by +passing +negative length paramters to various syscalls. The getpeername(2) function +had such a problem and looked like this: + + static int + getpeername1(p, uap, compat) + struct proc *p; + register struct getpeername_args /* { + int fdes; + caddr_t asa; + int *alen; + } */ *uap; + int compat; + { + struct file *fp; + register struct socket *so; + struct sockaddr *sa; + int len, error; + + ... + + error = copyin((caddr_t)uap->alen, (caddr_t)&len, sizeof (len)); + if (error) { + fdrop(fp, p); + return (error); + } + + ... + + len = MIN(len, sa->sa_len); /* [1] */ + error = copyout(sa, (caddr_t)uap->asa, (u_int)len); + if (error) + goto bad; + gotnothing: + error = copyout((caddr_t)&len, (caddr_t)uap->alen, sizeof (len)); + bad: + if (sa) + FREE(sa, M_SONAME); + fdrop(fp, p); + return (error); + } + +This is a classic example of a signedness bug - the check at [1] did not +take into account the fact that len could be negative, in which case the +MIN macro would always return len. When this negative len parameter was +passed to copyout, it was interpretted as a huge positive integer which +caused copyout to copy up to 4GB of kernel memory to user space. + + +--[ Conclusion + +Integer overflows can be extremely dangerous, partly because it is +impossible to detect them after they have happened. If an integer overflow +takes place, the application cannot know that the calculation it has +performed is incorrect, and it will continue under the assumption that it +is. Even though they can be difficult to exploit, and frequently cannot be +exploited at all, they can cause unepected behaviour, which is never a good +thing in a secure system. + + +--[ Appendix + +CERT advisory on the XDR bug: +http://www.cert.org/advisories/CA-2002-25.html +FreeBSD advisory: http://online.securityfocus.com/advisories/4407 + + +|=[ EOF ]=---------------------------------------------------------------=| + diff --git a/tesi/tesi.pdf b/tesi/tesi.pdf index 19973f641568b779bd4618b39444d1d00fa107d3..7089d0d15c5445f1bd7446f06e6846d6b64e429b 100644 GIT binary patch delta 148121 zcmZshQ*bU!v~6SC+Ocihwr$(~V%xTDCp)&y9ou$t|8vgkt?H_N?6)=6oTG<=FxPu9 z8}<=ESlE+|Dk%XY*c)+MkXxFLl-kC!k*G-z z(?IWU%L^rva&wKawhx1SRn=9O^innMG>soWsh*}^hbz?_w=w!si6_MA)zu6%=W5iC zwq~)iV)p79TPtHnLw0;Ap9;jNzm{7@y@}A%#~+U?2Ec$B@e9@|th*U+lM?m`insZD z@kv##AwhBrO3|ks?_{ZT-!It=c4oMQYx)Bb;DC+g!NjK~L(I(fC@lxn_*ZWgMySlM8f}X4#AH3f;|-qWgnh^Fj$wrB|OT)<4d%^A4fIfkgb?k 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6f70226..336adb1 100644 --- a/tesi/tesi_unicode.org +++ b/tesi/tesi_unicode.org @@ -636,6 +636,131 @@ pattern is not exhaustive or some patterns are shadowed by precedent ones. Symbolic execution is a widely used techniques in the field of computer security. +It allows to analyze different execution paths of a program +simultanously while tracking which inputs trigger the execution of +different parts of the program. +Inputs are modelled symbolically rather than taking "concrete" values. +A symbolic execution engine keeps track of expressions and variables +in terms of these symbolic symbols and attaches logical constraints to every +branch that is being followed. +Symbolic execution engines are used to track bugs by modelling the +domain of all possible inputs of a program, detecting infeasible +paths, dead code and proving that two code segments are equivalent. + +Let's take as example this signedness bug that was found in the +FreeBSD kernel and allowed, when calling the getpeername function, to +read portions of kernel memory. +#+BEGIN_SRC +int compat; +{ + struct file *fp; + register struct socket *so; + struct sockaddr *sa; + int len, error; + + ... + + len = MIN(len, sa->sa_len); /* [1] */ + error = copyout(sa, (caddr_t)uap->asa, (u_int)len); + if (error) + goto bad; + + ... + +bad: + if (sa) + FREE(sa, M_SONAME); + fdrop(fp, p); + return (error); +} +#+END_SRC + +The tree of the execution when the function is evaluated considering +/int len/ our symbolic variable α, sa->sa_len as symbolic variable β +and π as the set of constraints on a symbolic variable: + +#+BEGIN_SRC +[1] compat (...) { π_{α}: -∞ < α < ∞ } + | +[2] min (σ₁, σ₂) { π_{σ}: -∞ < (σ₁,σ₂) < ∞ ; π_{α}: -∞ < α < β ; π_{β}: ...} + | +[3] cast(u_int) (...) { π_{σ}: 0 ≤ (σ) < ∞ ; π_{α}: -∞ < α < β ; π_{β}: ...} + | + ... // rest of the execution +#+END_SRC +We can see that at step 3 the set of possible values of the scrutinee +α is bigger than the set of possible values of the input σ to the +/cast/ directive, that is: π_{α} ⊈ π_{σ}. For this reason the /cast/ may fail when α is /len/ +negative number, outside the domain π_{σ}. In C this would trigger undefined behaviour (signed +overflow) that made the exploitation possible. + +Every step of evaluation can be modelled as the following transition: +#+BEGIN_SRC +(π_{σ}, (πᵢ)ⁱ) → (π'_{σ}, (π'ᵢ)ⁱ) +#+END_SRC +if we express the π constraints as logical formulas we can model the +execution of the program in terms of Hoare Logic. +State of the computation is a Hoare triple {P}C{Q} where P and Q are +respectively the /precondition/ and the /postcondition/ that +constitute the assertions of the program. C is the directive being +executed. +The language of the assertions P is: +#+BEGIN_SRC +P ::= true | false | a < b | P₁ ∧ P₂ | P₁ ∨ P₂ | ~P +#+END_SRC +where a and b are numbers. +In the Hoare rules assertions could also take the form of +#+BEGIN_SRC +P ::= ∀i. P | ∃i. P | P₁ ⇒ P₂ +#+END_SRC +where i is a logical variable, but assertions of these kinds increases +the complexity of the symbolic engine. +Execution follows the rules of Hoare logic: +- Empty statement : +\begin{verbatim} +———————————— +{P}/skip/{P} +\end{verbatim} +- Assignment statement : The truthness of P[a/x] is equivalent to the + truth of {P} after the assignment. +\begin{verbatim} +———————————— +{P[a/x]}x:=a{P} +\end{verbatim} + +- Composition : c₁ and c₂ are directives that are executed in order; + {Q} is the /midcondition/. +\begin{verbatim} +{P}c₁{R}, {R}c₂{Q} +—————————————————— + {P}c₁;c₂{Q} +\end{verbatim} + +- Conditional : +\begin{verbatim} + {P∧b}c₁{Q}, {P∧~b}c₂{Q} +———————————————————————— +{P}if b then c₁ else c₂{Q} +\end{verbatim} + +- Loop : {P} is the loop invariant. After the loop is finished /P/ + holds and ~b caused the loop to end. +\begin{verbatim} + {P∧b}c{P} +———————————————————————— +{P}while b do c{P∧~b} +\end{verbatim} + +Even if the semantics of symbolic execution engines are well defined, +the user may run into different complications when applying such +analysis to non trivial codebases. +For example, depending on the domain, loop termination is not +guaranteed. Even when termination is guaranteed, looping causes +exponential branching that may lead to path explosion or state +explosion. +Reasoning about all possible executions of a program is not always +feasible and in case of explosion usually symbolic execution engines +implement heuristics to reduce the size of the search space. ** Translation validation Translators, such as translators and code generators, are huge pieces of