ComputerSecurity-2.pptx this is for srudents

Computer security

1. Computer Security-2 Dr.R.Nagulan Cryptography

2. Basic Terminology Cryptology: Cryptology is the research and study of encryption and decryption; it includes both cryptography and cryptanalysis . Cryptography: is the science of secret writing with the goal of hiding the meaning of a message. it refers to the practice of using encryption to conceal text. Cryptographer Cryptanalysis : is the science and sometimes art of breaking cryptosystems. Importance: without people who try to break our crypto methods, we will never know whether they are really secure or not Cryptanalyst

3. Cryptography Cryptography seems closely linked to modern electronic communication. However, cryptography is a rather old business (Julius Caesar – Rome - 100 B.C) Symmetric Cryptography: Two parties have an encryption and decryption method for which they share a secret key. All cryptography from ancient times until 1976 was exclusively based on symmetric methods. Symmetric ciphers are still in widespread use, especially for data encryption and integrity check of messages Asymmetric Cryptography: In 1976 an entirely different type of cipher was introduced by Whitfield Diffie , Martin Hellman and Ralph Merkle . In public-key cryptography, a user possesses a secret key as in symmetric cryptography but also a public key.

4. Symmetric Cryptography symmetric-key, secret-key, private-key and single-key schemes or algorithms. if Alice and Bob represent two offices of a car manufacturer, and they are transmitting documents containing the business strategy for the introduction of new car models in the next few years, these documents should not get into the hands of their competitors. Symmetric cryptography offers a powerful solution.

5. Terminology and Background Consider the steps involved in sending messages from a sender, S (Alice), to a recipient, R (Bob) S send a message (x) to R via T , T then becomes the transmission medium. an outsider, opponent O (Oscar) , wants to access the message (to read, change, or even destroy it), we call O an interceptor or intruder. Any time after S transmits it via T, the message is vulnerable to exploitation.

6. O might try to access the message in any of the following ways: Interruption. Block it, by preventing its reaching R, thereby affecting the availability of the message. Intercept it, by reading or listening to the message, thereby affecting the confidentiality of the message. Modify it, by seizing the message and changing it in some way, affecting the message's integrity.

7. Encryption is the process of using an algorithm to transform information to make it unreadable for unauthorized users. The original form of a message is known as plaintext (x), and the encrypted form is called ciphertext (y). The process of creating a ciphertext from a plaintext is called encryption . The process of turning a ciphertext back into a plaintext is called decryption. The verbs encipher and decipher are synonymous with the verbs encrypt and decrypt. A system for encryption and decryption is called a cryptosystem.

8. The system needs a secure channel for distribution of the key k between Alice and Bob. In any case, the key has only to be transmitted once between Alice and Bob and can then be used for securing many subsequent communications. Both the encryption and the decryption algorithms are publicly known. The only thing that should be kept secret in a sound cryptosystem is the key .

9. Encryption/Decryption Algorithm : A mathematical procedure or rules for performing encryption/decryption on data. Alice encrypts her message x using a symmetric algorithm, yielding the ciphertext y. Bob receives the ciphertext y and decrypts the message. We denote a plaintext message x as a sequence of individual characters x =<x 1 ,x 2 ,x 3 ,…, x n >. Similarly, ciphertext is written as y =<y 1 ,y 2 ,…. y m >. For instance, the plaintext message "I want cookies" can be denoted as the message string (<I, , w,a,n,t , , c,o,o,k,i,e,s >) It can be transformed into ciphertext < b,d,f,g,h,a,s,f,g,e >, and the encryption algorithm tells us how the transformation is done. If we have a strong encryption algorithm, the ciphertext will look like random bits to Oscar and will contain no information whatsoever that is useful to him.

10. C = E(P) and P = D(C) y=e(x, k) or y= e k (x) x= d(y, k) or x= d k (y) Where x is the plaintext, y represents the ciphertext, e is the encryption rule and d is the decryption rule, What we seek is a cryptosystem for which x= d k ( e k (x)) In other words, we want to be able to convert the message to protect it from an intruder , but we also want to be able to get the original message back.

11. Cryptosystem A cryptosystem is a five- tuple ( X,Y,K,E,D ), where the following are satisfied: X is a finite set of possible plaintexts . Y is a finite set of possible ciphertexts . K , the key space , is a finite set of possible keys  k  K ,  E K  E (encryption rule),  D K  D (decryption rule). Each E K : X  Y and D K : Y  X are functions such that  x  X , D K ( E K ( x )) = x .

12. Cryptanalysis Cryptanalysis Goals 1. knows cipher text only recovering the plain text x from the cipher text y . deduce the key k, to break subsequent messages easily. recognize patterns in cipher text, to be able to break subsequent ones. infer some meaning without even breaking the encryption, such as noticing an unusual frequency of communication or determining the communication was short or long. Knows one or more plaintext & cipher text pairs Deduce the Key

13. An encryption algorithm is breakable when given enough time and data, an analyst can determine the algorithm/key. consider a 25-character message that is expressed in just uppercase letters. A given cipher scheme may have 26 25 (approximately 10 35 ) possible decipherments (Substitution ciphers), so the task is to select the right one out of the 26 25 If your computer could perform on the order of 10 10 operations per second, finding this decipherment would require on the order of 10 16 seconds, or roughly 10 11 years. In this case, although we know that theoretically we could generate the solution, determining the deciphering algorithm by examining all possibilities can be ignored as infeasible with current technology. Breakable Encryption

14. Brute-force attack/Exhaustive Search

15. Brute-force attack/Exhaustive Search The attacker tries every possible key on a piece of ciphertext until an intelligible translation into plaintext is obtained. On average, half of all possible keys must be tried to achieve success.

16. In practice, a brute-force attack can be more complicated because incorrect keys can give false positive results. It is important to note that a brute-force attack against symmetric ciphers is always possible in principle. If testing all the keys on many modern computers takes too much time, i.e., several decades, the cipher is computationally secure against a brute-force attack. Brute-force attack/Exhaustive Search

17. Number Sets Irrational numbers  ( I ): Real numbers that are not rational. Natural numbers  (N ): The counting numbers {1, 2, 3, ...} are commonly called natural numbers. Real numbers  (R ): Numbers that can represent a distance along a line.

18. Modulo Real World Example Consider the hours on a clock. If you keep adding one hour, you obtain: Even though we keep adding one hour, we never leave the set. Divides : a divides b means there exists an integer n such that b= na If  a divides  b ,  a  is a factor of  b , or in other words,  b  is divisible by  a . For instance,  3  divides 15  because  15=3⋅5 ,  3  is a factor of  15 .

19. Modular Arithmetic If b= q* a+r a,b,q,r are integers, a≠0 and 0≤r<|a| then b mod a =r Examples 17 mod 5 = 2 7 mod 11 = 7 20 mod 3 = 2 11 mod 11 = 0 -3 mod 11 = 8 -1 mod 11 = 10 25 mod 5 = 0 -11 mod 11 = 0

20. Properties of Modular Arithmetic If ( a mod n ) =r1 ( b mod n ) = r2 Then ( a+b ) mod n = ( r1+r2 ) mod n If ( a mod n ) =r1 ( b mod n ) = r2 Then (a-b) mod n = ( r1-r2 ) mod n

21. Examples 11 mod 8 = 3 ; 15 mod 8 = 7 => 26 mod 8 = 10 mod 8=2 -6 mod 26 =20 3 mod 26 =3 => -3 mod 26 =23 mod 26=23

22. Modulo Inverse where  a −1  is the  modular multiplicative inverse  of  a   modulo   m . I.e., it satisfies the equation. 1= a a −1 mod m Example 1 = 3.9 mod 26 2= 5.21 mod 26 Multiplicative inverses modulo 26: 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, and 25, whose inverses are 1, 9, 21, 15, 3, 19, 7, 23, 11, 5, 17, and 25, respectively. The numbers which have no inverse modulo 26 are 0, 2, 4, 6, 8, 10, 12, 13, 14, 16, 18, 20, 22, and 24.