According to C99, Section The C Standard, 6.2.5, "Types":paragraph 11 [ISO/IEC 9899:2024], states

A computation involving unsigned operands can never produce an 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 typearithmetic for the unsigned type is performed modulo 2^N .

This behavior is more informally referred to as 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:

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. Make sure you Programmers should understand integer conversion rules before trying to implement secure arithmetic operations. (see See INT02-C. Understand integer conversion rules.).

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

• as an array index
• in Integer operands of any pointer arithmetic
• as a length or size of an object
• as the bound of an array (for example, a loop counter)
• , including array indexing
• The assignment expression for the declaration of a variable length array
• The postfix expression preceding square brackets [] or the expression in square brackets [] of a subscripted designation of an element of an array object
• Function arguments of type size_t or rsize_t (for example, as 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 regular integer types. As a result, wrapping of atomic unsigned integers is identical to regular unsigned integers and should also be prevented or detected.

Addition

Addition is between two operands of arithmetic type or between a pointer to an object type and an integer type. This rule applies only 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 ARR38ARR30-C. Do not add or subtract an integer to a pointer if the resulting value does not refer to a valid array elementform or use out-of-bounds pointers or array subscripts.)

for rules about adding a pointer to an integer). Incrementing is equivalent to adding one1.

Noncompliant Code Example

This noncompliant code example may can result in an unsigned integer wrap during the addition of the unsigned operands ui1 and ui2 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 ui1ui_a, ui2, sum;

sumunsigned int ui_b) {
  unsigned int usum = ui1ui_a + ui2;
ui_b;
  /* ... */
}

Compliant Solution (Precondition Test)

This compliant solution tests the suspect addition operation 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 ui1, ui2, sum;

ui_a, unsigned int ui_b) {
  unsigned int usum;
  if (UINT_MAX - ui1ui_a < ui2ui_b) {
    /* handleHandle error condition*/
  } else {
    usum = ui_a + ui_b;
  }
  /* ... */
}
sum = ui1 + ui2;

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 */
  }
  /* ... */
}

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. This rule applies only to subtraction between two operands of arithmetic 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 ARR38and ARR30-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 form or use out-of-bounds pointers or array subscripts for information about pointer subtraction.)

Decrementing is equivalent to subtracting one1.

Noncompliant Code Example

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

void func(
unsigned int ui1, ui2, result;

result = ui1 - ui2;

Compliant Solution

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

void func(
unsigned int ui1, ui2, result;

if (ui1 < ui2ui_a, unsigned int ui_b) {
  unsigned int udiff;
  if (ui_a < ui_b){
    /* handleHandle 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 = ui1ui_a - ui2;
ui_b;
  if (udiff > ui_a) {
    /* Handle error */
  }
  /* ... */
}

Multiplication

Multiplication is between two operands of arithmetic type.

Noncompliant Code Example

Wiki MarkupThe 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 {{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|AA. C References#VU551436]\]. The {{signed int}} operand is converted to {{unsigned int}} prior to the multiplication operation (see [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 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)) {
  /* handleHandle error condition */
}
pen->vertices = malloc(
  pen->num_vertices * sizeof(cairo_pen_vertex_t)
);

...

Exceptions

INT30-C-EX1:

...

Left Shift Operator

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

Noncompliant Code Example

This noncompliant 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.

INT30-C-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)
• 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 no larger than the type precision; for example, UINT_MAX >> x is valid as long as 0 <=  x < 32 (assuming that the precision of unsigned int is 32 bits)

INT30-C-EX3. The left-shift operator takes two operands of integer type. Unsigned left shift << can exhibit modulo behavior (wrapping).  This exception is provided because of common usage, because this behavior is usually expected by the programmer, and because the behavior is well defined. For examples of usage of the left-shift operator, see INT34-C. Do not shift an expression by a negative number of bits or by greater than or equal to the number of bits that exist in the operand.

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 the CERT C Rule Pack can 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|BB. Definitions#exploit], described at \[[Wojtczuk 08|AA. C References#Wojtczuk 08]\], documents a vulnerability and exploit arising from a buffer overflow (caused by unsigned integer wrapping).

References

\[[Dowd 06|AA. C References#Dowd 06]\] Chapter 6, "C Language Issues" (Arithmetic Boundary Conditions, pp. 211-223)
\[[ISO/IEC 9899:1999|AA. C References#ISO/IEC 9899-1999]\] Section 6.2.5, "Types," Section 6.5, "Expressions," and Section 7.10, "Sizes of integer types {{<limits.h>}}"
\[[ISO/IEC PDTR 24772|AA. C References#ISO/IEC PDTR 24772]\] "XYY Wrap-around Error"
\[[Seacord 05|AA. C References#Seacord 05]\] Chapter 5, "Integers"
\[[Viega 05|AA. C References#Viega 05]\] Section 5.2.7, "Integer overflow"
\[[VU#551436|AA. C References#VU551436]\]
\[[Warren 02|AA. C References#Warren 02]\] Chapter 2, "Basics"
\[[Wojtczuk 08|AA. C References#Wojtczuk 08]\]

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 those 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).

Don Bailey [Bailey 2014] describes an unsigned integer wrap vulnerability in the LZO compression algorithm, which can be exploited in some implementations.

CVE-2014-4377 describes a vulnerability in iOS 7.1 resulting from a multiplication operation that wraps, producing an insufficiently small value to pass to a memory allocation routine, which is subsequently overflowed.

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

Related Guidelines

Key here (explains table format and definitions)

CERT-CWE Mapping Notes

Key here for mapping notes

CWE-131 and INT30-C

• Intersection( INT30-C, MEM35-C) = Ø

• Intersection( CWE-131, INT30-C) =

• Calculating a buffer size such that the calculation wraps. This can happen, for example, when using malloc() or operator new[] to allocate an array, multiplying the array item size with the array dimension. An untrusted dimension could cause wrapping, resulting in a too-small buffer being allocated, and subsequently overflowed when the array is initialized.

• CWE-131 – INT30-C =

• Incorrect calculation of a buffer size that does not involve wrapping. This includes off-by-one errors, for example.

INT30-C – CWE-131 =

• Integer wrapping where the result is not used to allocate memory.

CWE-680 and INT30-C

Intersection( CWE-680, INT30-C) =

• Unsigned integer overflows that lead to buffer overflows

CWE-680 - INT30-C =

• Signed integer overflows that lead to buffer overflows

INT30-C – CWE-680 =

• Unsigned integer overflows that do not lead to buffer overflows

CWE-191 and INT30-C

Union( CWE-190, CWE-191) = Union( INT30-C, INT32-C) Intersection( INT30-C, INT32-C) == Ø

Intersection(CWE-191, INT30-C) =

• Underflow of unsigned integer operation

CWE-191 – INT30-C =

• Underflow of signed integer operation

INT30-C – CWE-191 =

• Overflow of unsigned integer operation

Bibliography

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