The C Standard, 6.2.5, paragraph 9 [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:
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 
 No 
 No 
Yes 
 No 
 Yes 
 No 
The following sections examine specific operations that are susceptible to unsigned integer wrap. 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. Programmers should understand integer conversion rules before trying to implement secure arithmetic operations. (See INT02C. Understand integer conversion rules.)
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
orrsize_t
(for example, an argument to a memory allocation function)  In securitycritical code
The C Standard defines arithmetic on atomic integer types as readmodifywrite 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 ARR37C. Do not add or subtract an integer to a pointer to a nonarray object and ARR30C. Do not form or use outofbounds 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 a pointer to an object type and an integer type. This rule applies only to subtraction between two operands of arithmetic type. (See 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 ARR30C. Do not form or use outofbounds 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 200701 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 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.
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
INT30CEX1: 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.
INT30CEX2: 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 compiletime 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 fromUINT_MAX
 Multiplying any variable by 1
 Division or remainder, as long as the divisor is nonzero
 Rightshifting any type maximum by any number no larger than the type precision; for example,
UINT_MAX >> x
is valid as long as0 <= x < 32
(assuming that the precision ofunsigned int
is 32 bits)
INT30CEX3. The leftshift 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 leftshift operator, see INT34C. 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.
Rule  Severity  Likelihood  Remediation Cost  Priority  Level 

INT30C  High  Likely  High  P9  L2 
Automated Detection
Tool  Version  Checker  Description 

Astrée  17.04i  integeroverflow  Fully checked 
CodeSonar  5.0p0  ALLOC.SIZE.ADDOFLOW  Addition overflow of allocation size 
Compass/ROSE  Can detect violations of this rule by ensuring that operations are checked for overflow before being performed (Be mindful of exception INT30EX2 because it excuses many operations from requiring validation, including all the operations that would validate a potentially dangerous operation. For instance, adding two  
Coverity  2017.07  INTEGER_OVERFLOW  Implemented 
Klocwork  2018  NUM.OVERFLOW CWARN.NOEFFECT.OUTOFRANGE  
LDRA tool suite  9.7.1  493 S, 494 S  Partially implemented 
Parasoft C/C++test  10.4  CERT_CINT30a  Avoid integer overflows 
Polyspace Bug Finder  R2018a  Unsigned integer overflow  Overflow from operation between unsigned integers 
PRQA QAC  9.3  2910 (C)  Partially implemented 
PRQA QAC++  4.1  2910, 2911, 2912, 2913  
PVSStudio  6.23  V658  
RuleChecker  17.04i  integeroverflow  Fully checked 
Related Vulnerabilities
CVE20091385 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.
CVE20144377 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)
Taxonomy  Taxonomy item  Relationship 

CERT C  INT02C. Understand integer conversion rules  Prior to 20180112: CERT: Unspecified Relationship 
CERT C  ARR30C. Do not form or use outofbounds pointers or array subscripts  Prior to 20180112: CERT: Unspecified Relationship 
CERT C  ARR36C. Do not subtract or compare two pointers that do not refer to the same array  Prior to 20180112: CERT: Unspecified Relationship 
CERT C  ARR37C. Do not add or subtract an integer to a pointer to a nonarray object  Prior to 20180112: CERT: Unspecified Relationship 
CERT C  CON08C. Do not assume that a group of calls to independently atomic methods is atomic  Prior to 20180112: CERT: Unspecified Relationship 
ISO/IEC TR 24772:2013  Arithmetic WrapAround Error [FIF]  Prior to 20180112: CERT: Unspecified Relationship 
CWE 2.11  CWE190, Integer Overflow or Wraparound  20161202: CERT: Rule subset of CWE 
CWE 2.11  CWE131  20170516: CERT: Partial overlap 
CWE 2.11  CWE191  20170518: CERT: Partial overlap 
CWE 2.11  CWE680  20170518: CERT: Partial overlap 
CERTCWE Mapping Notes
Key here for mapping notes
CWE131 and INT30C
 Intersection( INT30C, MEM35C) = Ø
 Intersection( CWE131, INT30C) =
 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 toosmall buffer being allocated, and subsequently overflowed when the array is initialized.
 CWE131 – INT30C =
 Incorrect calculation of a buffer size that does not involve wrapping. This includes offbyone errors, for example.
INT30C – CWE131 =
 Integer wrapping where the result is not used to allocate memory.
CWE680 and INT30C
Intersection( CWE680, INT30C) =
 Unsigned integer overflows that lead to buffer overflows
CWE680  INT30C =
 Signed integer overflows that lead to buffer overflows
INT30C – CWE680 =
 Unsigned integer overflows that do not lead to buffer overflows
CWE191 and INT30C
Union( CWE190, CWE191) = Union( INT30C, INT32C) Intersection( INT30C, INT32C) == Ø
Intersection(CWE191, INT30C) =
 Underflow of unsigned integer operation
CWE191 – INT30C =
 Underflow of signed integer operation
INT30C – CWE191 =
 Overflow of unsigned integer operation
Bibliography
[Bailey 2014]  Raising Lazarus  The 20 Year Old Bug that Went to Mars 
[Dowd 2006]  Chapter 6, "C Language Issues" ("Arithmetic Boundary Conditions," pp. 211–223) 
[ISO/IEC 9899:2011]  Subclause 6.2.5, "Types" 
[Seacord 2013b]  Chapter 5, "Integer Security" 
[Viega 2005]  Section 5.2.7, "Integer Overflow" 
[VU#551436]  
[Warren 2002]  Chapter 2, "Basics" 
[Wojtczuk 2008]  
[xorl 2009]  "CVE20091385: Linux Kernel E1000 Integer Underflow" 
16 Comments
David Svoboda
Enforcing this rule is possible, but I'm a little hesitant to recommend it, because of how disruptive it would be (just how much addition, etc. would need to be protected).
To enforce addition, one need merely check that any 'a + b' expr is preceded by a (max  b > a) expr. Subtraction, etc. are similar. There are probably many exceptions.
Hm...building a Rose checker would be a useful exercise mainly because it will help us learn the exceptions to this rule. I suspect there are many more than we realize.
Alex Volkovitsky
Unary

can cause wrappingAlso, so can division/modulo by a negative number ...
David Svoboda
All true, but those are technically signed int operations. So the 'surprise' behavior occurs in converting signed to unsigned & back.
Alex Volkovitsky
In that case, we should probably either not list them in the table, or mark them as capable of producing wrapping
Alex Volkovitsky
as far as automatic detection, this is a subset of INT35C. Evaluate integer expressions in a larger size before comparing or assigning to that size
Martin Sebor
The second sentence under the heading Noncompliant Code Example in the Multiplication section states:
I don't believe that is completely accurate. In a multiplication expression involving operands of types
signed int
andsize_t
, thesigned int
operand is converted tosize_t
. The type ofsize_t
may be the same as eitherunsigned int
orunsigned long
in ILP32 but is the same asunsigned long
in LP64 wheresizeof(int) < sizeof(long)
.The vulnerability in the example is unrelated to the signedness of the type of the first operand but rather to the possibility of arithmetic overflow of the product of the two operands after the usual arithmetic conversions. The same vulnerability exists when both operands are of an unsigned integer type.
David Svoboda
I
s/unsigned int/size_t/
in the paragraph. I believe overflow is possible on a 32 or 64bit architecture (though for 64bits, the sizeof() operation would have to return a really big size.) While the conversion occurs, it is not that important, as overflow is still possible, and easy on ILP32 if an attacker can specifynum_vertices
.Andrew Browne
I think there is a mistake in the Subtraction Compliant Solution (Postcondition Test)
The second condition in the if statement should not be there.
Eg:
ui1 = 10, ui2 = 2
udiff = 8
It is still valid with 8 > 2.
It looks like this was a copy paste mistake from the addition's compliant postcondition test.
Robert Seacord
nice catch, thanks!
Andrew Browne
Also the description just above that code.
Robert Seacord
thanks, that should be fixed now too.
Neil Schellenberger
I think that there's a minor thinko in the example given in the second to last item in INT32EX2:
" .... For instance,
UINT_MAX >> x
is valid as long asx < sizeof(unsigned int)"
The comparison should be to the number of bits, not the sizeof. Rather than faff around with CHAR_BITS or INT_BITS, which will probably only serve to obscure the main point, it might be best to just drop the example.
David Svoboda
Fixed, thanks!
Neil Schellenberger
The CS for Atomic Integers is somewhat misleading since it assumes that no writes have occurred between the atomic_fetch_add() and the subsequent atomic_load(). Given that the primary use case of atomics is environments where precisely that sort of thing can occur, safer (for selected values of "safer") might be something like (totally untested):
A very minor nitpick: the variable naming in both the NCE and the CE appears to be wrong, as the (signed) type for ui_a doesn't seem to match the name (assuming ui_a is supposed to be a mnemonic for "an unsigned integer called a")
John Benito
Neil, as far as I am know the names are not meant to be mnemonic. I changed them from ui1 to ui_a, just to rid them of the 'l' (ell) and '1' (one) confusion factor.
Robert Seacord (Manager)
So the multiplication example in this rule does not parallel the multiplication example in INT32C. For this rule, we use a real world example but we provide only the portable solution and not the "store the product in twice as many bits solution". Consequently, this rule does not require the UWIDTH() macro, which actually works with unsigned numbers right now. Right now my feeling is that these two rules should be a little more parallel, and maybe we should include a twice the bits solution here, or remove it from INT32C.