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The following sections examine specific operations that are susceptible to 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 apply. 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 conversion rules before trying to implement secure arithmetic operations.

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

The following code can result in an unsigned integer overflow during the addition 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, sum;

sum = ui1 + ui2;

Compliant Solution

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

unsigned int ui1, ui2, sum;

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

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

The following 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

The following compliant solution tests the suspect subtraction operation to guarantee there is no possibility of signed overflow.

signed int si1, si2, result;

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

Multiplication

Multiplication is between two operands of arithmetic type.

Non-Compliant Code Example

The following code 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

The following compliant solution tests the suspect multiplication operation to guarantee there is no possibility of signed overflow.

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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;

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.

Non-Compliant Code Example

The following 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. 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 long sl1, sl2, result;

result = sl1 / sl2;

Compliant Solution

The following compliant solution tests the suspect division operation to guarantee 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;

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

The following code 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

The following 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

The following 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, result;

result = ui1 << ui2;

Compliant Solution

The following compliant solution tests the suspect shift operation to guarantee there is no possibility of unsigned overflow.

unsigned int ui1, ui2, result;

if ( (ui2 < 0) || (ui2 >= sizeof(int)*8) ) {
  /* handle error condition */
}
result = ui1 << ui2;

Right Shift Operator

The shift operator is between two operands of integer type.

Non-Compliant Code Example

The following 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, result;

result = ui1 >> ui2;

Compliant Solution

The following compliant solution tests the suspect shift operation to guarantee there is no possibility of unsigned overflow.

unsigned int ui1, ui2, result;

if ( (ui2 < 0) || (ui2 >= sizeof(int)*8) ) {
  /* handle error condition */
}
result = ui1 >> ui2;

Exceptions

Unsigned integers can be allowed to exhibit modulo behavior if and only if

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If the integer exhibiting modulo behavior contributes to the value of an integer not marked as exhibiting modulo behavior, the resulting integer must obey this rule.

Consequences

Integer overflow can lead to buffer overflows and the execution of arbitrary code by an attacker.

References

• ISO/IEC 9899-1999 Section 6.5 Expressions, Section 7.10 Sizes of integer types <limits.h>
• Seacord 05 Chapter 5 Integers
• Warren 02 Chapter 2 Basics