According to Sun's Secure Coding Guidelines [[SCG 2007]]

The (Java) language is type-safe, and the runtime provides automatic memory management and range-checking on arrays. These features also make Java programs immune to the stack-smashing and buffer overflow attacks possible in the C and C++ programming languages, and that have been described as the single most pernicious problem in computer security today.

While this statement is true, arithmetic operations in the Java platform require as much caution as in C and C++. Integer operations can result in overflow because Java does not provide any indication of overflow conditions and silently wraps. While integer overflows in vulnerable C and C++ programs may result in execution of arbitrary code, in Java, wrapped values typically result in incorrect computations and unanticipated outcomes.

According to the Java Language Specification Section 4.2.2 "Integer Operations"

The built-in integer operators do not indicate overflow or underflow in any way. Integer operators can throw a NullPointerException if unboxing conversion of a null reference is required. Other than that, the only integer operators that can throw an exception are the integer divide operator / and the integer remainder operator %, which throw an ArithmeticException if the right-hand operand is zero, and the increment and decrement operators ++ and -- which can throw an OutOfMemoryError if boxing conversion is required and there is not sufficient memory available to perform the conversion.

The integral types in Java are byte, short, int, and long, whose values are 8-bit, 16-bit, 32-bit and 64-bit signed two’s-complement integers, respectively, and char, whose values are 16-bit unsigned integers representing UTF-16 code units.

According to the Java Language Specification Section 4.2.1 "Integral Types and Values," the values of the integral types are integers in the following ranges:

• For byte, from –128 to 127, inclusive
• For short, from –32,768 to 32,767, inclusive
• For int, from –2,147,483,648 to 2,147,483,647, inclusive
• For long, from –9,223,372,036,854,775,808 to 9,223,372,036,854,775,807, inclusive
• For char, from \u0000 to \uffff inclusive, that is, from 0 to 65,535

The table below shows the integer overflow behavior of the integral operators.

Failure to account for integer overflow has resulted in failures of real systems, for instance, when implementing the compareTo() method. The meaning of the return value of the compareTo() method is defined only in terms of its sign and whether it is zero; the magnitude of the return value is irrelevant. Consequently, an apparent — but incorrect — optimization would be to subtract the operands and return the result. For operands of opposite sign, this can result in integer overflow; consequently violating the compareTo() contract [[Bloch 2008, item 12]].

Overview of Compliant Techniques

The three main techniques for detecting unintended integer overflow are:

• Pre-condition testing of the inputs. Check the inputs to each arithmetic operator to ensure that overflow cannot occur. Throw an ArithmeticException when the operation would overflow if it were performed, otherwise perform the operation. We call this technique "Pre-condition the inputs" hereafter, for convenience.
• Use a larger type and downcast. Cast the inputs to the next larger primitive integer type and perform the arithmetic in the larger size. Check each intermediate result for overflow of the original smaller type; throw an ArithmeticException if the range check fails. Note that the range check must be performed after each arithmetic operation. Downcast the final result to the original smaller type before assigning to the result variable. This approach cannot be use for type long, because long is already the largest primitive integer type.
• Use BigInteger. Convert the inputs into objects of type BigInteger and perform all arithmetic using BigInteger methods. Throw an ArithmeticException if the final result is outside the range of the original smaller type, otherwise convert back to the intended result type.

The "Pre-condition the inputs" technique requires different pre-condition for each arithmetic operation. This can be somewhat more difficult to understand than either of the other two approaches.

The "Use a larger type and downcast" technique is the preferred approach for the cases to which it applies. The checks it requires are simpler than those of the previous technique; it is substantially more efficient than using BigInteger.

The "Use BigInteger" technique is conceptually the simplest of the three techniques. However, it requires use of method calls for each operation in place of primitive arithmetic operators; this may obscure the intended meaning of the code. This technique will execute more slowly and will use more memory than either of the other techniques; performance degradation may be substantial.

Noncompliant Code Example

Either arithmetic operation in this noncompliant code example could produce a result that overflows the range representable by type int. When overflow occurs, the result will be incorrect.

public int multAccum(int oldAcc, int newVal, int scale) {
  // May result in overflow 
  return oldAcc + (newVal * scale);
}

Compliant Solution (Pre-condition the inputs)

The code example below shows the necessary pre-conditioning checks required for each arithmetic operation on arguments of type int. The checks for the other integral types are analogous.

static final preAdd(int left, int right) throws ArithmeticException {
   if (right > 0 ? left > Integer.MAX_VALUE - right : left < Integer.MIN_VALUE - right) {
    throw new ArithmeticException("Integer overflow");
  }
}

static final preSubtract(int left, int right) throws ArithmeticException {
  if (right > 0 ? left < Integer.MIN_VALUE + right : left > Integer.MAX_VALUE + right) {
    throw new ArithmeticException("Integer overflow");
  }
}

static final preMultiply(int left, int right) throws ArithmeticException {
  if (right>0 ? left > Integer.MAX_VALUE/right || left < Integer.MIN_VALUE/right :
       (right<-1 ? left > Integer.MIN_VALUE/right || left < Integer.MAX_VALUE/right :
         right == -1 && left == Integer.MIN_VALUE) ) {
    throw new ArithmeticException("Integer overflow");
  }
}

static final preDivide(int left, int right) throws ArithmeticException {
  if ((left == Integer.MIN_VALUE) && (right == -1)) {
    throw new ArithmeticException("Integer overflow");
  }
}

static final preAbs(int a) throws ArithmeticException {
  if (a == Integer.MIN_VALUE) {
    throw new ArithmeticException("Integer overflow");
  }
}

static final preNegate(int a) throws ArithmeticException {
  if (a == Integer.MIN_VALUE) {
    throw new ArithmeticException("Integer overflow");
  }
}

Note that although these pre-conditioning checks are correct, more efficient code may well be possible. Further, the checks can be simplified when the original type was char. Because the range of type char includes only positive values, all comparisons with negative values may be omitted.

public int multAccum(int oldAcc, int newVal, int scale) throws ArithmeticException {
  preMultiply(newVal, Scale);
  final int temp = newVal * scale;
  preAdd(oldAcc, temp);
  return oldAcc + temp;
}

Compliant Solution (Use a Larger Type and Downcast)

For all integral types other than long, the next larger integral type can represent the result of any single integral operation. For example, operations on values of type int, can be safely performed using type long. Therefore, we can perform an operation using the larger type and range-check before down casting to the original type. Note, however, that this guarantee holds only for a one arithmetic operation; larger expressions without per-operation bounds checks may overflow the larger type.

This approach cannot be applied for type long because long is the largest primitive integral type. Use the "Use BigInteger" technique when the original variables are of type long.

This compliant solution shows the implementation of a method for checking whether a long value falls within the representable range of they int. The implementations of range checks for the smaller primitive integer types are exactly analogous.

public long intRangeCheck(long value) throws ArithmeticOverflow {
  if ((value < Integer.MIN_VALUE) || (value > Integer.MAX_VALUE)) {
    throw new ArithmeticException("Integer overflow");
  }
  return value;
}

public int multAccum(int oldAcc, int newVal, int scale) throws ArithmeticException {
  final long res = 
    intRangeCheck(((long) oldAcc) + intRangeCheck((long) newVal * (long) scale));
  return (int) res; // safe down-cast
}

Compliant Solution (Use BigInteger)

Type BigInteger is the standard arbitrary-precision integer type provided by the Java standard libraries. The arithmetic operations implemented as methods of this type cannot themselves overflow; instead, they produce the numerically correct result. As a consequence, compliant code performs only a single range check — just before converting the final result to the original smaller type. This property provides conceptual simplicity. An unfortunate consequence of this technique is that compliant code must be written using method calls in place of primitive arithmetic operators; this may obscure the intent of the code.

Note that operations on objects of type BigInteger may be significantly less efficient than operations on the original primitive integer type. Whether this loss of efficiency is important will depend on the context in which the code is used.

private static final BigInteger bigMaxInt = BigInteger.valueOf(Integer.MAX_VALUE);
private static final BigInteger bigMinInt = BigInteger.valueOf(Integer.MIN_VALUE);

public BigInteger intRangeCheck(BigInteger val) throws ArithmeticException {
  if (val.compareTo(bigMaxInt) == 1 ||
          val.compareTo(bigMinInt) == -1) {
    throw new ArithmeticException("Integer overflow");
  }
  return val;
}

public int multAccum(int oldAcc, int newVal, int scale) throws ArithmeticException { 
  BigInteger product =
    BigInteger.valueOf(newVal).multiply(BigInteger.valueOf(scale));
  BigInteger res = intRangeCheck(BigInteger.valueOf(oldAcc).add(product));
  return res.intValue(); // safe conversion
}

AtomicInteger

Operations on objects of type AtomicInteger suffer from the same overflow issues as do the other integer types. The solutions are generally similar to those shown above; however, concurrency issues add additional complications. First, avoid possible issues with time-of-check-time-of-use (see VNA02-J. Ensure that compound operations on shared variables are atomic for more information). Secondly, use of an AtomicInteger creates happens-before relationships between the various threads that access it. Consequently, changes to the number or order of accesses may alter the execution of the overall program. In such cases you must either choose to accept the altered execution or carefully craft the implementation of your compliant technique to preserve the exact number and order of accesses to the AtomicInteger.

Noncompliant Code Example

This noncompliant code example uses an AtomicInteger which is part of the concurrency utilities. The concurrency utilities lack integer overflow checks.

class InventoryManager {
  private final AtomicInteger itemsInInventory = new AtomicInteger(100);

  //...
  public final void returnItem() {
    itemsInInventory++;
  }
} 

Consequently, itemsInInventory may wrap around to Integer.MIN_VALUE after the increment operation.

Compliant Solution

This compliant solution uses the get() and compareAndSet() methods provided by AtomicInteger to guarantee successful manipulation of the shared value of itemsInInventory. Note that:

1. The number and order of accesses to itemsInInventory remains unchanged from the noncompliant code example.
2. All operations on the value of itemsInInventory are performed on a temporary local copy of its value.
3. The overflow check in this example is performed in open code, rather than encapsulated in a method call. This is an acceptable alternative implementation. The choice of method call vs. open code should be made according to your organization's standards and needs.

class InventoryManager {
  private final AtomicInteger itemsInInventory = new AtomicInteger(100);

  public final void returnItem() {
    while (true) {
      int old = itemsInInventory.get();
      if (old == Integer.MAX_VALUE) {
        throw new ArithmeticException("Integer overflow");
      }
      int next = old + 1; // Increment
      if (itemsInInventory.compareAndSet(old, next)) {
        break;
      }
    } // end while
  } // end removeItem()
}

The arguments to the compareAndSet() method are the expected value of the variable when the method is invoked and the intended new value. The variable's value will be updated if and only if the current value and the expected value are equal [[API 2006]] class AtomicInteger. Refer to guideline VNA02-J. Ensure that compound operations on shared variables are atomic for more details.

Exceptions

INT00-EX1: Depending on circumstances, integer overflow may be benign. For instance, the Object.hashcode() method may return all representable values of type int; further, many algorithms for computing hashcodes intentionally allow overflow to occur.

INT00-EX2: The added complexity and cost of programmer-written overflow checks may exceed their value for all but the most-critical code. In such cases, consider the alternative of treating integral values as though they are tainted data, using appropriate range checks as the notional "sanitizing" code. These range checks should ensure that incoming values cannot cause integer overflow. Note that sound determination of allowable ranges may require deep understanding of the details of the code protected by the range checks; correct determination of the allowable ranges may be extremely difficult.

Risk Assessment

Failure to perform appropriate range checking can lead to integer overflows, which may cause unexpected program control flow or unanticipated program behavior.

Automated Detection

Automated detection of integer operations that may potentially overflow is straightforward. Automatic determination of which potential overflows are true errors and which are intended by the programmer is infeasible. Heuristic warnings may be helpful.

Related Vulnerabilities

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

Other Languages

This guideline appears in the C Secure Coding Standard as INT32-C. Ensure that operations on signed integers do not result in overflow.

This guideline appears in the C++ Secure Coding Standard as INT32-CPP. Ensure that operations on signed integers do not result in overflow.

Bibliography

[[API 2006]] class AtomicInteger
[[Bloch 2005]] Puzzle 27: Shifty i's[[SCG 2007]] Introduction
[[JLS 2003]] 4.2.2 Integer Operations and 15.22 Bitwise and Logical Operators
[[MITRE 2009]] CWE ID 682 "Incorrect Calculation", CWE ID 190 "Integer Overflow or Wraparound", CWE ID 191 "Integer Underflow (Wrap or Wraparound)"
[[Seacord 2005]] Chapter 5. Integers
[[Tutorials 2008]] Primitive Data Types

06. Integers (INT)      06. Integers (INT)      INT01-J. Check ranges before casting integers to narrower types