According to C99, Section 6.2.5, "Types":

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.

This behavior is more informally referred to as unsigned integer wrapping. Unsigned integer operations can wrap if the resulting value cannot be represented by the underlying representation of the integer. The following table indicates which operators can result in wrapping:

The following sections examine specific operations that are susceptible to unsigned integer wrap. When operating on small types (smaller than int), integer conversion rules apply. The usual arithmetic conversions may also be applied to (implicitly) convert operands to equivalent types before arithmetic operations are performed. Make sure you understand implicit conversion rules before trying to implement secure arithmetic operations (see INT02-A. Understand integer conversion rules).

Integer values that originate from untrusted sources must not be allowed to wrap if they are used in any of the following ways:

• as an array index
• in any pointer arithmetic
• as a length or size of an object
• as the bound of an array (for example, a loop counter)
• as an argument to a memory allocation function
• in security critical code

Addition

Addition is between two operands of arithmetic type or between a pointer to an object type and an integer type (see ARR37-C. Do not add or subtract an integer to a pointer to a non-array object and ARR38-C. Do not add or subtract an integer to a pointer if the resulting value does not refer to a valid array element for rules about adding a pointer to an integer). Incrementing is equivalent to adding one.

Non-Compliant Code Example

This code may result in an unsigned integer wrap during the addition of the unsigned operands ui1 and ui2. If this behavior is unexpected, the resulting value may be used to allocate insufficient memory for a subsequent operation or in some other manner that could lead to an exploitable vulnerability.

unsigned int ui1, ui2, sum;

sum = ui1 + ui2;

Compliant Solution

This compliant solution tests the suspect addition operation to guarantee there is no possibility of unsigned wrap.

unsigned int ui1, ui2, sum;

if (UINT_MAX - ui1 < ui2) {
  /* handle error condition */
}
sum = ui1 + ui2;

Subtraction

Subtraction is between two operands of arithmetic type, two pointers to qualified or unqualified versions of compatible object types, or between a pointer to an object type and an integer type. See ARR36-C. Do not subtract or compare two pointers that do not refer to the same array, ARR37-C. Do not add or subtract an integer to a pointer to a non-array object, and ARR38-C. Do not add or subtract an integer to a pointer if the resulting value does not refer to a valid array element. for rules about pointer subtraction. Decrementing is equivalent to subtracting one.

Non-Compliant Code Example

This code may result in an unsigned integer wrap during the subtraction of the unsigned operands ui1 and ui2. If this behavior is unanticipated, it may lead to an exploitable vulnerability.

unsigned int ui1, ui2, result;

result = ui1 - ui2;

Compliant Solution

This compliant solution tests the suspect unsigned subtraction operation to guarantee there is no possibility of unsigned wrap.

unsigned int ui1, ui2, result;

if (ui1 < ui2){
   /* handle error condition */
}

result = ui1 - ui2;

Multiplication

Multiplication is between two operands of arithmetic type.

Non-Compliant Code Example

The Mozilla Scalable Vector Graphics (SVG) viewer contains a heap buffer wrap vulnerability resulting from an unsigned integer wrap during the multiplication of the signed int value pen->num_vertices and the size_t value sizeof(cairo_pen_vertex_t) [[VU#551436]]. The signed int operand is converted to unsigned int prior to the multiplication operation (see [INT02-A. Understand integer conversion rules]).

pen->num_vertices = 
  _cairo_pen_vertices_needed(
    gstate->tolerance, 
    radius, 
    &gstate->ctm
  );
pen->vertices = 
  malloc(pen->num_vertices * sizeof(cairo_pen_vertex_t));

The unsigned integer wrap can result in allocating memory of insufficient size.

Compliant Solution

This compliant solution tests the suspect multiplication operation to guarantee that there is no unsigned integer wrap.

pen->num_vertices = 
  _cairo_pen_vertices_needed(
    gstate->tolerance, 
    radius, 
    &gstate->ctm
  );

if (pen->num_vertices > SIZE_MAX/sizeof(cairo_pen_vertex_t)) {
   /* handle error condition */
}
pen->vertices = 
  malloc(pen->num_vertices * sizeof(cairo_pen_vertex_t));

Left Shift Operator

The left shift operator is between two operands of integer type.

Non-Compliant Code Example

This non-compliant code example can result in unsigned wrap left shifting the unsigned operand ui1 by ui2 bits.

unsigned int ui1, ui2, uresult;

uresult = ui1 << ui2;

Compliant Solution

This compliant solution tests the suspect shift operation to guarantee there is no possibility of unsigned wrap. This solution must also be compliant with INT34-C. Do not shift a negative number of bits or more bits than exist in the operand.

unsigned int ui1, ui2, uresult;

if ( (ui2 >= sizeof(unsigned int)*CHAR_BIT) 
  || (ui1 > (UINT_MAX  >> ui2))) ) 
{
  /* handle error condition */
}
else {
  uresult = ui1 << ui2;
}

Exceptions

INT32-EX1. Unsigned integers can exhibit modulo behavior (wrapping) only when this behavior is necessary for the proper execution of the program. It is recommended that the variable declaration be clearly commented as supporting modulo behavior and that each operation on that integer also be clearly commented as supporting modulo behavior.

Risk Assessment

Integer wrap can lead to buffer overflows and the execution of arbitrary code by an attacker.

Automated Detection

Fortify SCA Version 5.0 with CERT C Rule Pack is able to detect violations of this rule.

Related Vulnerabilities

Search for vulnerabilities resulting from the violation of this rule on the CERT website.

A Linux kernel vmsplice exploit, described at [[Wojtczuk 08]], documents a vulnerability and exploit arising from a buffer overflow (caused by unsigned integer wrapping).

References

[[Dowd 06]] Chapter 6, "C Language Issues" (Arithmetic Boundary Conditions, pp. 211-223)
[[ISO/IEC 9899:1999]] Section 6.2.5, "Types," Section 6.5, "Expressions," and Section 7.10, "Sizes of integer types <limits.h>"
[[ISO/IEC PDTR 24772]] "XYY Wrap-around Error"
[[Seacord 05]] Chapter 5, "Integers"
[[Viega 05]] Section 5.2.7, "Integer overflow"
[[VU#551436]]
[[Warren 02]] Chapter 2, "Basics"
[[Wojtczuk 08]]

INT15-A. Use intmax_t or uintmax_t for for formatted IO on programmer-defined integer types      04. Integers (INT)