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:
Operator 
Wrap 

Operator 
Wrap 

Operator 
Wrap 

Operator 
Wrap 

yes 

yes 

<< 
yes 

< 
no 

yes 

yes 

>> 
no 

> 
no 

yes 

/= 
no 

& 
no 

>= 
no 

/ 
no 

%= 
no 

 
no 

<= 
no 
% 
no 

yes 

^ 
no 

== 
no 

++ 
yes 

>>= 
no 

~ 
no 

!= 
no 
 
yes 

&= 
no 

! 
no 

&& 
no 
= 
no 

= 
no 

un + 
no 

 
no 
yes 

^= 
no 

un  
yes 

?: 
no 
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 welldefined.
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. Make sure you understand integer conversion rules before trying to implement secure arithmetic operations. (See recommendation INT02C. Understand integer conversion rules.)
Integer values must not be allowed to wrap if they are used in any of the following ways:
Addition is between two operands of arithmetic type or between a pointer to an object type and an integer type. (See rules ARR37C. Do not add or subtract an integer to a pointer to a nonarray object and ARR38C. Do not add or subtract an integer to a pointer if the resulting value does not refer to a valid array element for information about adding a pointer to an integer.) Incrementing is equivalent to adding one.
This noncompliant code example 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 can lead to an exploitable vulnerability.
unsigned int ui1, ui2, usum; /* Initialize ui1 and ui2 */ usum = ui1 + ui2; 
This compliant solution performs a precondition test of the operands of the addition to guarantee there is no possibility of unsigned wrap.
unsigned int ui1, ui2, usum; /* Initialize ui1 and ui2 */ if (UINT_MAX  ui1 < ui2) { /* handle error condition */ } else { usum = ui1 + ui2; } 
This compliant solution performs a postcondition test to ensure that the result of the unsigned addition operation usum
is not less than either of the operands.
unsigned int ui1, ui2, usum; /* Initialize ui1 and ui2 */ usum = ui1 + ui2; if (usum < ui1  usum < ui2) { /* handle error condition */ } 
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 rules ARR36C. Do not subtract or compare two pointers that do not refer to the same array, ARR37C. Do not add or subtract an integer to a pointer to a nonarray object, and ARR38C. Do not add or subtract an integer to a pointer if the resulting value does not refer to a valid array element for information about pointer subtraction. Decrementing is equivalent to subtracting one.
This noncompliant code example 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, udiff; /* Initialize ui1 and ui2 */ udiff = ui1  ui2; 
This compliant solution performs a precondition test of the unsigned operands of the subtraction operation to guarantee there is no possibility of unsigned wrap.
unsigned int ui1, ui2, udiff; /* Initialize ui1 and ui2 */ if (ui1 < ui2){ /* handle error condition */ } else { udiff = ui1  ui2; } 
This compliant solution performs a postcondition test that the result of the unsigned subtraction operation udiff
is not greater than the minuend.
unsigned int ui1, ui2, udiff ; /* Initialize ui1 and ui2 */ udiff = ui1  ui2; if (udiff > ui1) { /* handle error condition */ } 
Multiplication is between two operands of arithmetic type.
The Mozilla Scalable Vector Graphics (SVG) viewer contains a heap buffer overflow 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)}} \[[VU#551436AA. Bibliography#VU551436]\]. 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 recommendation [INT02C. 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.
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) ); 
INT30EX1. 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.
INT32EX2. Checks for wraparound can be omitted when it can be determined at compiletime that wraparound will not occur. As such, the following operations on unsigned integers require no validation:
unsigned int
may safely be subtracted from UINT_MAX
.UINT_MAX >> x
is valid as long as x < sizeof(unsigned int)
.Integer wrap can lead to buffer overflows and the execution of arbitrary code by an attacker.
Rule 
Severity 
Likelihood 
Remediation Cost 
Priority 
Level 

INT30C 
high 
likely 
high 
P9 
L2 
Tool 
Version 
Checker 
Description 











[CVE20091385http://web.nvd.nist.gov/view/vuln/detail?vulnId=CVE20091385] 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 \[[xorl 2009http://xorl.wordpress.com/2009/06/10/cve20091385linuxkernele1000integerunderflow/]\]. This can cause a buffer overflow, which allows an attacker to execute arbitrary code. 
A Linux kernel vmsplice [exploitBB. Definitions#exploit], described at \[[Wojtczuk 2008AA. Bibliography#Wojtczuk 08]\], 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.
CERT C++ Secure Coding Standard: INT30CPP. Ensure that unsigned integer operations do not wrap
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 TR 24772 "XYY Wraparound Error"
MITRE CWE: CWE190, "Integer Overflow (Wrap or Wraparound)"
\[[Dowd 2006AA. Bibliography#Dowd 06]\] Chapter 6, "C Language Issues" (Arithmetic Boundary Conditions, pp. 211223) \[[Seacord 2005AA. Bibliography#Seacord 05]\] Chapter 5, "Integers" \[[Viega 2005AA. Bibliography#Viega 05]\] Section 5.2.7, "Integer overflow" \[[VU#551436AA. Bibliography#VU551436]\] \[[Warren 2002AA. Bibliography#Warren 02]\] Chapter 2, "Basics" \[[Wojtczuk 2008AA. Bibliography#Wojtczuk 08]\] \[[xorl 2009AA. Bibliography#xorl 2009]\] ["CVE20091385: Linux kernel E1000 Integer Underflow"http://xorl.wordpress.com/2009/06/10/cve20091385linuxkernele1000integerunderflow/] 