Simple Overview Caesar and RSA Encryption_by_Tarek_Gaber
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The document outlines a lecture on network security focusing on symmetric and asymmetric encryption techniques, specifically the Caesar cipher and RSA algorithm. It explains the mechanics of the Caesar cipher, its vulnerabilities, and provides a detailed overview of the RSA algorithm, including key generation, encryption, and decryption processes. Additionally, it includes examples and a homework assignment to apply the techniques learned in the lecture.
Simple Overview Caesar and RSA Encryption_by_Tarek_Gaber
- 1. Introduction to Network Security Lecture 2: Caesar and RSA Location:E.T.S. de Ingenierias Informatica y de Telecomunicacion Universidad de Granada 18071, Granada (SPAIN), 24-28 April 2017 Dr. Tarek Gaber Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt tmgaber@gmail.com
- 2. Lecture Objectives To learn Caesar encryption as an example of symmetric encryption techniques To learn RSA encryption as an example of asymmetric encryption techniques
- 3. Lecture Outlines What is Caesar Algorithm How does Caesar algorithm works What is RSA technique Simple numerical example of RSA
- 4. Caesar Cipher • The earliest known as substitution cipher by Julius Caesar • First attested use in military affairs • Replaces each letter by 3rd letter later • example: meet me after the toga party PHHW PH DIWHU WKH WRJD SDUWB http://www.xarg.org/tools/caesar- cipher/
- 5. What is a Caesar Cipher? • Caesar used to encrypt his messages using a very simple algorithm, which could be easily decrypted if you know the key. • He would take each letter of the alphabet and replace it with a letter a certain distance away from that letter. When he got to the end, he would wrap back around to the beginning. • Example with a shift of 3: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z D E F G H I J K L M N O P Q R S T U V W X Y Z A B C https://www.youtube.com/watch?v=fR8rVR72a6o
- 6. Caesar Wheel
- 7. Caesar Cipher • can define transformation as: a b c d e f g h i j k l m n o p q r s t u v w x y z D E F G H I J K L M N O P Q R S T U V W X Y Z A B C • mathematically give each letter a number a b c d e f g h i j k l m 0 1 2 3 4 5 6 7 8 9 10 11 12 n o p q r s t u v w x y Z 13 14 15 16 17 18 19 20 21 22 23 24 25 • then have Caesar cipher as: C = E(p) = (p + k) mod (26) p = D(C) = (C – k) mod (26)
- 8. MOD Function • MOD is short for modulus, which means ' the remainder left over after a value is divided by something' Examples: 27 mod 26... 27 / 26 is 1 R 1, so 27 mod 26 is 1 53 mod 26... 53 / 26 is 2 R 1 so 53 mod 26 is also 1 10 mod 3 is also 1 (since 10 / 3 = 3 R 1) 2 mod 2 = 0 5 mod 2 = 1 25 mod 26 = 25 50 mod 26 = 24 • if a = (b) mod c then a = (c*k + b) mod c (where k = 1,2,3.......) • So, if we have (-4 mod 3), we could write it as ( 3x2 -4) mod 3 =2
- 9. Caesar Algorithm • 1. Convert the characters to numbers 2. Pick a number to shift by 3. Add the number to each character 4. Mod each resulting number by 26 5. You message is now encrypted!
- 10. Cryptanalysis of Caesar Cipher • only have 26 possible ciphers – A maps to A,B,..Z • could simply try each in turn • a brute force search • given ciphertext, just try all shifts of letters • do need to recognize when have plaintext • eg. break ciphertext “ERE L ORYH BRX DOLFH“ (HOMEWORK)
- 11. The Problem with Caesar’s Cipher • It’s too easy to break! Let’s go back to our five letter alphabet. • Say you had the word DBCA, but didn’t know the key. It would be easy to make a list of all possible keys. If you expected the unencrypted text to be in English, you could easily figure out which word was right: • If you were using the full English alphabet, this would take longer, but for someone trying to find our your secret, it’s a small price to pay! Shift of 1 CABE Shift of 2 BEAD The clear winner! Shift of 3 ADEC Shift of 4 ECDB How dare you insult my cipher! Though, you have a good point…
- 12. RSA Algorithm • The RSA algorithm is named after Ron Rivest, Adi Shamir and Len Adleman, who invented it in 1977. • The RSA cryptosystem is the most widely-used public key cryptography algorithm in the world. It can be used to encrypt a message without the need to exchange a secret key separately. • The RSA algorithm can be used for both public key encryption and digital signatures. • Its security is based on the difficulty of factoring large integers.
- 13. Prime Number • A Prime Number can be divided evenly only by 1 or itself and it must be a whole number greater than 1. • Examples: – Is 8 a Prime Number? • No, because it can be divided evenly by 2 or 4 (2×4=8), as well as by 1 and 8. – Is 73 a Prime Number? • Yes, it can only be divided evenly by 1 and 73.
- 14. Prime and Co-prime Number • Two numbers are said to be Co-primes when they have only 1 as a common factor. • Example 1: Are numbers 6 and 25 Coprime ? Answer = Two given numbers are 6 and 25 Factors of 6 = 1, 2, 3, 6 and Factors of 25 = 1, 5, 25 On comparing the factors of numbers 6 and 25, you can see that both have only 1 as a common factor, So, 6 and 25 are Coprimes. • The Factors of a given number are those which divide a given number completely, without leaving any remainder. – Factors of a given number 12 are 1, 2, 3, 4, 6 & 12
- 15. RSA Key Generation Algorithm • Generate two large random primes, p and q, of approximately equal size such that their product n = pq is of the required bit length, e.g. 1024 bits. • Compute n = pq and (phi) φ = (p-1)(q-1). • Choose an integer e, 1 < e < phi, such that gcd(e, phi) = 1. Compute the secret exponent d, 1 < d < phi, such that ed ≡ 1 (mod phi). – ( e *d) / phi = ? with the remainder of 1, (1 mod phi equivalent to e*d mod phi). • The public key is (n, e) and the private key (p, q, d) or (n, d). • Keep all the values d, p, q and phi secret.
- 16. Summary of RSA • Key Generation – n = pq, where p and q are distinct primes. – phi, φ = (p-1)(q-1) – e < n such that gcd(e, phi)=1 – d = e-1 mod phi. • Encryption/Decryption – c = me mod n, 1<m<n. – m = cd mod n.
- 17. Homework (Caesar and RSA) • Using the Caesar algorithm, how you can get the key used to get the ciphertext “ERE L ORYH BRX DOLFH“ and what should be the plaintext of this ciphertext. • In the RSA numerical example given in the lecture, we have chosen e = 7, – change e to 11, – compute d, and – compute the public and private key pair – encrypt the message M =2 • Send it to tmgaber@gmai.com by 12:00 (PM) 27-4-2017
- 18. Thanks for your attention Questions, please