The C Standard, 6.2.5, paragraph 11 [ISO/IEC 9899:2024], states

A computation involving unsigned operands can never produce an overflow, because arithmetic for the unsigned type is performed modulo 2^N .

This behavior is more informally called unsigned integer wrapping. Unsigned integer operations can wrap

Integer values used in any of the the following ways must be guaranteed correct:

• 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)
• in security-critical code

Most integer operations can result in overflow if the resulting value cannot be represented by the underlying representation of the integer. The following table indicates which operators can result in overflowwrapping:

The following sections examine specific operations that are susceptible to unsigned integer overflow. The specific tests that are required to guarantee that the operation does not result in an integer overflow depend on the signedness of the integer types. When operating on small types (smaller than int), integer conversion rules applywrap. When operating on integer types 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 understand implicit Programmers should understand integer conversion rules before trying to implement secure arithmetic operations. (see See INT02-AC. Understand integer conversion rules.). AnchorAdditionAddition

Addition

Addition is between two operands of arithmetic type or between a pointer to an object type and an integer type. Incrementing is equivalent to adding one.

Non-Compliant Code Example (Unsigned)

This code may result in an unsigned integer overflow 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 (Unsigned)

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

unsigned int ui1, ui2, sum;

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

Non-Compliant Code Example (Signed)

This code may result in a signed integer overflow during the addition of the signed operands si1 and si2. If this behavior is unanticipated, it could lead to an exploitable vulnerability.

int si1, si2, sum;

sum = si1 + si2;

Compliant Solution (Two's Complement Signed)

This compliant solution tests the addition operation to ensure no overflow occurs, assuming two's complement representation.

signed int si1, si2, sum;

if ( ((si1^si2) | (((si1^(~(si1^si2) & (1 << (sizeof(int)*CHAR_BIT-1))))+si2)^si2)) >= 0) {
   /* handle error condition */
}

sum = si1 + si2;

Compliant Solution (General Signed)

This compliant solution tests the suspect addition operation to ensure no overflow occurs regardless of representation.

signed int si1, si2, sum;

if (((si1>0) && (si2>0) && (si1 > (INT_MAX-si2))) ||
    ((si1<0) && (si2<0) && (si1 < (INT_MIN-si2)))) {
   /* handle error condition */
}

sum = si1 + si2;

This solution is more readable but contains branches and consequently may be less efficient than the solution that is specific to two's complement representation.

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

• Integer operands of any pointer arithmetic, 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, an argument to a memory allocation function)
• 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 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.

Noncompliant Code Example

This noncompliant code example 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.

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 */
  } 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 */
  }
  /* ... */
}

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. Decrementing is equivalent to subtracting one.

Non-Compliant Code Example (Unsigned)

This code may result in an unsigned integer overflow 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 (Unsigned)

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

unsigned int ui1, ui2, result;

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

result = ui1 - ui2;

Non-Compliant Code Example (Signed)

This code can result in a signed integer overflow during the subtraction of the signed operands si1 and si2. If this behavior is unanticipated, 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.

signed int si1, si2, result;

result = si1 - si2;

Compliant Solution (Two's Complement Signed)

This compliant solution tests the suspect subtraction operation to guarantee there is no possibility of signed overflow, presuming two's complement representation.

signed int si1, si2, result;

if (((si1^si2) & (((si1 ^ ((si1^si2) & (1 << (sizeof(int)*CHAR_BIT-1))))-si2)^si2)) < 0) {
  /* handle error condition */
}
result = si1 - si2;

...

Multiplication

Multiplication is between two operands of arithmetic type.

Non-Compliant Code Example (Signed)

This non-compliant code example can result in a signed integer overflow during the multiplication of the signed operands si1 and si2. If this behavior is unanticipated, 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.

signed int si1, si2, result;

result = si1 * si2;

Compliant Solution (Signed)

This compliant solution guarantees there is no possibility of signed overflow.

signed int si1, si2, result;

signed long long tmp = (signed long long)si1 * (signed long long)si2;

/*
 * If the product cannot be represented as a 32-bit integer, handle as an error condition
 */
if ( (tmp > INT_MAX) || (tmp < INT_MIN) ) {
  /* handle error condition */
}
result = (int)tmp;

The preceding code is compliant only on systems where long long is at least twice the size of int. On systems where this relationship does not exist, the following compliant solution may be used to ensure signed overflow does not occur.

signed int si1, si2, result;

if (si1 > 0){  /* si1 is positive */
  if (si2 > 0) {  /* si1 and si2 are positive */
    if (si1 > (INT_MAX / si2)) {
      /* handle error condition */
    }
  } /* end if si1 and si2 are positive */
  else { /* si1 positive, si2 non-positive */
    if (si2 < (INT_MIN / si1)) {
        /* handle error condition */
    }
  } /* si1 positive, si2 non-positive */
} /* end if si1 is positive */
else { /* si1 is non-positive */
  if (si2 > 0) { /* si1 is non-positive, si2 is positive */
    if (si1 < (INT_MIN / si2)) {
      /* handle error condition */
    }
  } /* end if si1 is non-positive, si2 is positive */
  else { /* si1 and si2 are non-positive */
    if ( (si1 != 0) && (si2 < (INT_MAX / si1))) {
      /* handle error condition */
    }
  } /* end if si1 and si2 are non-positive */
} /* end if si1 is non-positive */

result = si1 * si2;

Non-Compliant Code Example (Unsigned)

The Mozilla Scalable Vector Graphics (SVG) viewer contains a heap buffer overflow vulnerability resulting from an unsigned integer overflow 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 [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 overflow can result in allocating memory of insufficient size.

Compliant Solution (Unsigned)

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

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));

...

Division

Division is between two operands of arithmetic type. Overflow can occur during twos-complement signed integer division when the dividend is equal to the minimum (negative) value for the signed integer type and the divisor is equal to -1. Both signed and unsigned division operations are also susceptible to divide-by-zero errors (see INT33-C. Ensure that division and modulo operations do not result in divide-by-zero errors).

Non-Compliant Code Example (Signed)

This code can result in a signed integer overflow during the division of the signed operands sl1 and sl2 or in a divide-by-zero error. The IA-32 architecture, for example, requires that both conditions result in a fault, which could easily result in a denial-of-service attack.

signed long sl1, sl2, result;

result = sl1 / sl2;

Compliant Solution (Signed)

This compliant solution guarantees there is no possibility of signed overflow or divide-by-zero errors.

signed long sl1, sl2, result;

if ( (sl2 == 0) || ( (sl1 == LONG_MIN) && (sl2 == -1) ) ) {
  /* handle error condition */
}
result = sl1 / sl2;

...

Modulo

The modulo operator provides the remainder when two operands of integer type are divided.

Non-Compliant Code Example (Signed)

This code can result in a divide-by-zero or an overflow error during the modulo operation on the signed operands sl1 and sl2. Overflow can occur during a modulo operation when the dividend is equal to the minimum (negative) value for the signed integer type and the divisor is equal to -1.

signed long sl1, sl2, result;

result = sl1 % sl2;

Compliant Solution (Signed)

This compliant solution tests the suspect modulo operation to guarantee there is no possibility of a divide-by-zero error or an overflow error.

signed long sl1, sl2, result;

if ( (sl2 == 0 ) || ( (sl1 == LONG_MIN) && (sl2 == -1) ) ) {
  /* handle error condition */
}
result = sl1 % sl2;

...

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 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 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.

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 */
  } 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 */
  }
  /* ... */
}

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 */
}
pen->vertices = malloc(
  pen->num_vertices * sizeof(cairo_pen_vertex_t)
);

Exceptions

INT30-C-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-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

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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Unary Negation

The unary negation operator takes an operand of arithmetic type. Overflow can occur during twos-complement unary negation when the operand is equal to the minimum (negative) value for the signed integer type.

Non-Compliant Code Example

This non-compliant code example can result in a signed integer overflow during the unary negation of the signed operand si1. If this behavior is unanticipated, 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.

signed int si1, result;

result = -si1;

Compliant Solution

This compliant solution tests the suspect negation operation to guarantee there is no possibility of signed overflow.

signed int si1, result;

if (si1 == INT_MIN) {
  /* handle error condition */
}
result = -si1;

...

Left Shift Operator

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

Non-Compliant Code Example (Unsigned)

This code can result in an unsigned overflow during the shift operation of the unsigned operands ui1 and ui2. If this behavior is unanticipated, 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, uresult;

uresult = ui1 << ui2;

Compliant Solution (Unsigned)

This compliant solution tests the suspect shift operation to guarantee there is no possibility of unsigned overflow. This solution must also be compliant with INT36-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 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 overflow 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 http://www.avertlabs.com/research/blog/index.php/2008/02/13/analyzing-the-linux-kernel-vmsplice-exploit/,
documents a vulnerability and exploit arising directly out of integer overflow.

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 6.5, "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"

INT15-A. Take care when converting from pointer to integer or integer to pointer      04. Integers (INT)       Image Modified