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Subclause The C Standard, 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:

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The following sections examine specific operations that are susceptible to unsigned integer wrap. When operating on small integer types (smaller with less precision 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, especially if they are used in any of the following ways:

• integer Integer operands of any pointer arithmetic, including array indexing
• the The assignment expression for the declaration of a variable length array
• the The postfix expression preceding square brackets [] or the expression in square brackets [] of a subscripted designation of an element of an array object;
• function Function arguments of type size_t or rsize_t (for example, an argument to a memory allocation function)
• in In security-critical code

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

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Addition is between two operands of arithmetic type or between a pointer to an object type and an integer type. This rule only applies to addition between two operands of arithmetic type . See (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).

Incrementing is equivalent to adding 1.

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This noncompliant code example may can 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.

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#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;
  }
  /* ... */
}

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

  /* ... */
}

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Subtraction is between two operands of arithmetic type, two pointers to qualified or unqualified versions of compatible object types, or a pointer to an object type and an integer type. This rule only applies to subtraction between two operands of arithmetic type .  See (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.

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This noncompliant code example may can 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.

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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;
  }
  /* ... */
}

...

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

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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 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)
);

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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)
);

INT30-EX1.: Unsigned integers can exhibit modulo behavior (wrapping) when 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 or remainder by 0, of course)
• Subtracting any variable from its type's maximum; for example, any unsigned int may safely be subtracted from UINT_MAX
• Multiplying any variable by 1
• Division or remainder, as long as the divisor is nonzero
• Right-shifting any type maximum by any number smaller no larger than the type sizeprecision; for instanceexample, UINT_MAX >> x is valid as long as 0 <=  x < 32 (assuming that the size precision of unsigned int is 32 bits)

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

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Bibliography

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