lecture 12 - integerself.cs.pub.ro/cns/res/lectures/lecture-12.pdf · cse dep, acs, upb lecture 12,...

Lecture 12Integers

Computer and Network Security19th of December 2016

Computer Science and Engineering Department

CSE Dep, ACS, UPB Lecture 12, Integers 1/40

Outline

Data Types

Representation

Conversions

Operations

Issues

Rules and Recommendations

Conclusion


Integers

I numbers

I non-floating point

I positive, negative or zero


Integer Use

I actual numbers and integers values and . . .

I array index

I length/size of an object

I pointer arithmetic

I loop counter, array bound

I argument to a memory allocation function


Data Types

I char

I short

I int

I long

I long long

I pointer


Size of Data Types. Data Models

CERT C Programming Language Secure Coding Standard, pg. 118


To Bear in Mind

I representation of data types

I bounds (minimum, maximum)

I signedness

I conversion

I pointers and integers


Outline

Data Types

Representation

Conversions

Operations

Issues


Conclusion


Positive Integers

I always the same

I first bit is 0 for signed integers and the rest is the value

I the actual value is stored for unsigned integers

I representation differs for (signed) negative integers


Signed-magnitude for Negative Integers

I direct representation

I first bit is 1

I the rest of the bits are the actual value

I issue: difficult hardware implementation


1’s Complement for Negative Integers

I first bit is 1

I the rest of the bits are complemented (reversed)

I the circuitry is simpler

I issue: two values for zero (positive and negative zero)


2’s Complement for Negative Integers

I first bit is 1

I the rest of the bits are complemented and added one

I a single (positive) representation for zero


Signed/Unsigned Representation and Ranges

I we use 2’s complement

I consider N bits width representation

I 2N possible values

I for unsigned integers range is (0. . . 2N − 1)

I for signed integers, range is (−2N−1 . . . 2N−1 − 1)


Outline

Data Types

Representation

Conversions

Operations

Issues


Conclusion


Promotions

I integers smaller than int are promoted to int when performingoperations

I done to avoid overflows

I char c1, c2; c1 = c1 + c2;


Types and Ranks

I type: signed or unsigned

I ranks: long long > long > int > short > char

I convert to the larger rank


Unsigned to Unsigned

I safe from shorter range to larger range

I truncation if converting from larger range to shorter range


Unsigned to Signed

I same rank

I high-order bit is signed bit

I sign may change


Signed to Signed

I sign-extension is convert to larger rank

I preserve lower part in case of conversion to a smaller rank


Signed to Unsigned

I value unchanged if signed integer is positive

I truncation if unsigned rank is smaller

I sign-extension if larger unsigned rank

I in case of negative integers, a large positive integers isobtained


Signed/Unsigned Characters

I char may be signed char on unsigned char

I when storing negative signed char in an integer, the result is alarge negative number

I if value above 127 (0x7F) use unsigned char


In a Nutshell


Outline

Data Types

Representation

Conversions

Operations

Issues


Conclusion


Addition

I integer and integer

I pointer and integer

I may result in overflow

I arithmetic conversion


Subtraction

I integer and integer

I pointer and integer

I may result in negative overflow


Multiplication

I prone to overflow even for small operands

I good idea to allocate twice the storage for the product


Division

I division by zero

I division of minimum signed integer value divided by -1


Modulo

I similar to division, since division is involved

I careful at negative remainders


Shifting

I careful when shifting signed negative integers

I integer promotion must be taken into consideration


Outline

Data Types

Representation

Conversions

Operations

Issues


Conclusion


Truncation

I convert to a smaller integer type

I the initial value is outside range

I high order bits are lost in case of converting from larger toshorter


Overflow

I may be signed on usigned

I go beyond maximum value or below minimum value


Sign Error

I convert unsigned to signedI if “bit sign” in integer is set it results in a negative number

I convert signed to unsignedI negative numbers result in large positive numbers


Negative Indices

I negative arrays index

I value outside bounds


Outline

Data Types

Representation

Conversions

Operations

Issues


Conclusion


Recommendations

I INT00-C to INT18-C on “04. Integers (INT)” in CERT CSecure Coding Standard


Rules

I INT30-C to INT36-C on “04. Integers (INT)” in CERT CSecure Coding Standard


Outline

Data Types

Representation

Conversions

Operations

Issues


Conclusion


Keywords

I integer

I type

I long long, long, int, short,char

I signed, unsigned

I bounds/range

I 2’s complement

I conversion

I promotion

I rank

I addition

I subtraction

I multiplication

I division

I modulo

I truncation

I overflow

I sign error

I negative index


References

I CERT C Secure Coding Standard – 04. Integers (INT) –https://www.securecoding.cert.org/confluence/

pages/viewpage.action?pageId=270

I Secure Coding in C and C++ ClassI Module 3. Integers

I Secure Coding in C and C++I Chapter 5. Integer Security


https://www.securecoding.cert.org/confluence/pages/viewpage.action?pageId=270

https://www.securecoding.cert.org/confluence/pages/viewpage.action?pageId=270

lecture 12 - integerself.cs.pub.ro/cns/res/lectures/lecture-12.pdf · cse dep, acs, upb lecture 12,...

Documents