Insufficient Precision or Accuracy of a Real Number

The product processes a real number with an implementation in which the number's representation does not preserve required accuracy and precision in its fractional part, causing an incorrect result.

Abstraction

Base

Structure

Simple

Likelihood of Exploit

Medium

Understand the problem

What is the problem?

The product processes a real number with an implementation in which the number's representation does not preserve required accuracy and precision in its fractional part, causing an incorrect result.

Extended description

When a security decision or calculation requires highly precise, accurate numbers such as financial calculations or prices, then small variations in the number could be exploited by an attacker. There are multiple ways to store the fractional part of a real number in a computer. In all of these cases, there is a limit to the accuracy of recording a fraction. If the fraction can be represented in a fixed number of digits (binary or decimal), there might not be enough digits assigned to represent the number. In other cases the number cannot be represented in a fixed number of digits due to repeating in decimal or binary notation (e.g. 0.333333...) or due to a transcendental number such as Π or √2. Rounding of numbers can lead to situations where the computer results do not adequately match the result of sufficiently accurate math.

Root cause

How and when does the problem arise?

Lifecycle phase

Implementation

This weakness is introduced when the developer picks a method to represent a real number. The weakness may only be visible with very specific numeric inputs.

There are three major ways to store real numbers in computers. Each method is described along with the limitations of how they store their numbers. - Fixed: Some implementations use a fixed number of binary bits to represent both the integer and the fraction. In the demonstrative example about Muller's Recurrence, the fraction 108.0 - ((815.0 - 1500.0 / z) / y) cannot be represented in 8 binary digits. The numeric accuracy within languages such as PL/1, COBOL and Ada is expressed in decimal digits rather than binary digits. In SQL and most databases, the length of the integer and the fraction are specified by the programmer in decimal. In the language C, fixed reals are implemented according to ISO/IEC TR18037 - Floating: The number is stored in a version of scientific notation with a fixed length for the base and the significand. This allows flexibility for more accuracy when the integer portion is smaller. When dealing with large integers, the fractional accuracy is less. Languages such as PL/1, COBOL and Ada set the accuracy by decimal digit representation rather than using binary digits. Python also implements decimal floating-point numbers using the IEEE 754-2008 encoding method. - Ratio: The number is stored as the ratio of two integers. These integers also have their limits. These integers can be stored in a fixed number of bits or in a vector of digits. While the vector of digits method provides for very large integers, they cannot truly represent a repeating or transcendental number as those numbers do not ever have a fixed length.

Risk

What does successful exploitation lead to?

DoS: Crash, Exit, or Restart

Affected security scopes: Availability

This weakness will generally lead to undefined results and therefore crashes. In some implementations the program will halt if the weakness causes an overflow during a calculation.

Execute Unauthorized Code or Commands

Affected security scopes: Integrity

The results of the math are not as expected. This could cause issues where a value would not be properly calculated and provide an incorrect answer.

Read Application DataModify Application Data

Affected security scopes: Confidentiality, Availability, Access Control

This weakness can sometimes trigger buffer overflows which can be used to execute arbitrary code. This is usually outside the scope of a product's implicit security policy.

Defence

How is it prevented and fixed?

Implementation · Patching and Maintenance

Defence to apply across several lifecycle phases

Detail

The developer or maintainer can move to a more accurate representation of real numbers. In extreme cases, the programmer can move to representations such as ratios of BigInts which can represent real numbers to extremely fine precision. The programmer can also use the concept of an Unum real. The memory and CPU tradeoffs of this change must be examined. Since floating point reals are used in many products and many locations, they are implemented in hardware and most format changes will cause the calculations to be moved into software resulting in slower products.

Verification

How is it detected?

Automated Static Analysis

Automated static analysis, commonly referred to as Static Application Security Testing (SAST), can find some instances of this weakness by analyzing source code (or binary/compiled code) without having to execute it. Typically, this is done by building a model of data flow and control flow, then searching for potentially-vulnerable patterns that connect "sources" (origins of input) with "sinks" (destinations where the data interacts with external components, a lower layer such as the OS, etc.)