Subclause 6.2.5, paragraph 9, of the C Standard [ISO/IEC 9899:2011] states:

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 called 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:

Although unsigned left shift << can result in wrapping, modulo behavior is permitted by this standard because of common usage, because this behavior is usually expected by the programmer and because the behavior is well defined.

The following sections examine specific operations that are susceptible to unsigned integer wrap. When operating on small integer types (smaller than int), integer promotions are applied. The usual arithmetic conversions may also be applied to (implicitly) convert operands to equivalent types before arithmetic operations are performed. Programmers should understand integer conversion rules before trying to implement secure arithmetic operations. (See INT02-C. Understand integer conversion rules.)

Integer values 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 ARR30-C. Do not form or use out of bounds pointers or array subscripts for information about adding a pointer to an integer.) Incrementing is equivalent to adding 1.

Noncompliant Code Example

This noncompliant code example may result in an unsigned integer wrap during the addition of the unsigned operands ui_a and ui_b. 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 can lead to an exploitable vulnerability.

void func(unsigned int ui_a, unsigned int ui_b) {
  unsigned int usum = ui_a + ui_b;

  /* ... */
}

Compliant Solution (Precondition Test)

This compliant solution performs a precondition test of the operands of the addition to guarantee there is no possibility of unsigned wrap:

#include <limits.h>
 
void func(unsigned int ui_a, unsigned int ui_b) {
  unsigned int usum;
  if (UINT_MAX - ui_a < ui_b) {
    /* Handle error condition */
  } else {
    usum = ui_a + ui_b;
  }

  /* ... */
}

Compliant Solution (Postcondition Test)

This compliant solution performs a postcondition test to ensure that the result of the unsigned addition operation usum is not less than the first operand:

void func(unsigned int ui_a, unsigned int ui_b) {
  unsigned int usum = ui_a + ui_b;
  if (usum < ui_a) {
    /* Handle error condition */
  }

  /* ... */
}

Subtraction

Subtraction is between two operands of arithmetic type, between 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 ARR30-C. Do not form or use out of bounds pointers or array subscripts for information about pointer subtraction.) Decrementing is equivalent to subtracting 1.

Noncompliant Code Example

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

void func(unsigned int ui_a, unsigned int ui_b) {
  unsigned int udiff = ui_a - ui_b;

  /* ... */
}

Compliant Solution (Precondition Test)

This compliant solution performs a precondition test of the unsigned operands of the subtraction operation to guarantee there is no possibility of unsigned wrap:

void func(unsigned int ui_a, unsigned int ui_b) {
  unsigned int udiff;
  if (ui_a < ui_b){
    /* Handle error condition */
  } else {
    udiff = ui_a - ui_b;
  }

  /* ... */
}

Compliant Solution (Postcondition Test)

This compliant solution performs a postcondition test that the result of the unsigned subtraction operation udiff is not greater than the minuend:

void func(unsigned int ui_a, unsigned int ui_b) {
  unsigned int udiff = ui_a - ui_b;
  if (udiff > ui_a) {
    /* Handle error condition */
  }

  /* ... */
}

Multiplication

Multiplication is between two operands of arithmetic type.

Noncompliant Code Example

The Mozilla Foundation Security Advisory 2007-01 describes a heap buffer overflow vulnerability in the Mozilla Scalable Vector Graphics (SVG) viewer 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 size_t prior to the multiplication operation so that the multiplication takes place between two size_t integers, which are unsigned. (See INT02-C. 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 operands of the multiplication 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 takes two operands of integer type. For examples of usage of the left-shift operator, see INT34-C. Do not shift a negative number of bits or more bits than exist in the operand.

Atomic Integers

The C Standard defines arithmetic on atomic integer types as read-modify-write operations with the same representation as nonatomic integer types. As a result, wrapping of atomic unsigned integers is identical to nonatomic unsigned integers and should also be prevented or detected.

This section includes an example only for the addition of atomic integer types. For other operations, you can use tests similar to the precondition tests for nonatomic integer types.

Noncompliant Code Example

This noncompliant code example using atomic integers can result in unsigned integer overflow wrapping:

#include <stdatomic.h>
 
atomic_uint i;

void func(unsigned int a) {
  atomic_init(&i, 42); 
  atomic_fetch_add(&i, a);
  /* ... */
}

This compliant solution performs a postcondition test to ensure that the result of the unsigned addition operation to i is not less than the operand a. However, this code contains a race condition where i can be modified after the addition, but prior to the atomic load. This solution is only compliant if i is guaranteed to only be access by a single thread. See CON08-C. Do not assume that a group of calls to independently atomic methods is atomic for more information.

#include <stdatomic.h>
 
atomic_uint i;

void func(unsigned int a) {
  atomic_fetch_add(&i, a);
  if (atomic_load(&i) < a) {
    /* Handle error condition */
  }
  /* ... */
}

INT30-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.

INT30-EX2. Checks for wraparound can be omitted when it can be determined at compile time that wraparound will not occur. As such, the following operations on unsigned integers require no validation:

• Operations on two compile-time constants
• Operations on a variable and 0 (except division by 0, of course)
• Subtracting any variable from its type's maximum; for instance, any unsigned int may safely be subtracted from UINT_MAX
• Multiplying any variable by 1
• Division, as long as the divisor is nonzero
• Right-shifting any type maximum by any number smaller than the type size; for instance, UINT_MAX >> x is valid as long as 0 <=  x < 32 (assuming that the size of unsigned int is 32 bits)
• Left-shifting 1 by any number smaller than the type size

Risk Assessment

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

Automated Detection

Related Vulnerabilities

CVE-2009-1385 results from a violation of this rule. The value performs an unchecked subtraction on the length of a buffer and then adds that many bytes of data to another buffer [xorl 2009]. This can cause a buffer overflow, which allows an attacker to execute arbitrary code.

A Linux kernel vmsplice exploit, described by Rafal Wojtczuk [Wojtczuk 2008], documents a vulnerability and exploit arising from a buffer overflow (caused by unsigned integer wrapping).

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

Related Guidelines

Bibliography