Cryptography basics
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This document provides an overview of cryptography and several encryption techniques throughout history. It begins with an introduction to terminology used in cryptography. Traditional cryptography techniques are then discussed, including transposition ciphers, Playfair ciphers, and the Vigenere cipher. The document also provides examples of how to implement each of these traditional ciphers. Finally, it discusses modern cryptography and provides a detailed explanation of how the RSA algorithm works, including how to generate public/private key pairs and how the encryption and decryption processes are performed.
Cryptography basics
- 1. 1Solutions www.domain.com Workshop #1 Inroduction to RSA Cryptography Cb_salah_salah@esi.dz
- 6. 6Solutions www.domain.comCb_salah_salah@esi.dz History of cryptography Transposition Cipher It is another type of cipher where the order of the alphabets in the plaintext is rearranged to create the ciphertext. The actual plaintext alphabets are not replaced. Playfair Cipher In this scheme, pairs of letters are encrypted, instead of single letters as in the case of simple substitution cipher The Vigenere code It uses a text string (say, a word) as a key, which is then used for doing a number of shifts on the plaintext . The code of CAESAR It is a mono-alphabetic cipher wherein each letter of the plaintext is substituted by another letter to form the ciphertex
- 7. 7Solutions www.domain.com Exemple:Caesar1 DLWFE TNT DYLVP UP GZFD OTD WP XZE AZFC ALDDPC WP RCZD NSTPY OF QLXPFI NPDLC DTTZTSLNYPLA offset is 15 SALUT ICI SNAKE JE VOUS DIS LE MOT POUR PASSER LE GROS CHIEN DU FAMEUX CESAR SIIOIHACNEAP
- 8. 8Solutions www.domain.com Exemple: Vigenere2 The sender and the receiver decide on a key. Say ‘point’ is the key. Numeric representation of this key is ‘16 15 9 14 20’. The sender wants to encrypt the message, say ‘attack from south east’. He will arrange plaintext and numeric key as follows: a t t a c k f r o m s o u t h e a s t 16 15 9 14 20 16 15 9 14 20 16 15 9 14 20 16 15 9 14 The Cipher text will be as follows Q I C O W A U A C G I D D H B U P B H
- 9. 9Solutions www.domain.com Exemple: Playfair Cipher3 T U O R I A L S B C D E F G H K M N P Q V W X Y Z HI DE MO NE YZ T U O R I A L S B C D E F G H K M N P Q V W X Y Z T U O R I A L S B C D E F G H K M N P Q V W X Y Z T U O R I A L S B C D E F G H K M N P Q V W X Y Z The sender and the receiver deicide on a particular key, say ‘tuorials’ Let us say we want to encrypt the message “hide money”. It will be written as: Using these rules, the result of the encryption of ‘hide money’ with the key of ‘tuorials’ would be: QC EF NU MF ZV
- 10. 10Solutions www.domain.com Exemple: Transposition Cipher3 The plaintext is “golden statue is in eleventh cave” and the secret random key chosen is “five”. We arrange this text horizontally in table with number of column equal to key value. The resulting text is shown below. G O L D E N S T A T U E I S I N E L E V E N T H C A V E The ciphertext is obtained by reading column vertically downward from first to last column. The ciphertext is ‘gnuneaoseenvltiltedasehetivc’.
- 11. 11Solutions www.domain.com Modern cryptography:Case od study RSA
- 12. 12Solutions www.domain.com • Basicly used in e-commerce but it is also used in bleu cardes and some softwares like opnessh(secure communication using ssh protocol) • Was first created by Ron Rivest, Adi Shamir et LenAdleman, en 1977 ) Cb_salah_salah@esi.dz Asymmetric cryptography : RSA
- 13. 13Solutions www.domain.comCb_salah_salah@esi.dz RSA: How Does it Work? World of cryptography A single key used for encryption and decryption Called private key Ex: Ceasar Two keys are used One for encryption, known by every one, called public key. The other one for decryption, known only by the receiver, called private key . Ex :RSA Symmetric cryptography Asymmetric cryptography
- 14. 14Solutions www.domain.comCb_salah_salah@esi.dz RSA: How Does it Work?
- 15. 15Solutions www.domain.comCb_salah_salah@esi.dz RSA: How to create public and private key? Public Key: (N,C) • P ,Q: two prime number • N=P×Q • M=(P−1)×(Q−1 • C :coprime number with M Private Key: (N,U) • Need to calcualte U • Theory of Etienne Bézout: to prove that two numbers a and b are coprime if only existed two number u and v that for a×u+b×v=1 ( u and v are integers) • It existed u v for that for C×u+M×v=1
- 16. 16Solutions www.domain.comCb_salah_salah@esi.dz RSA: How to find U?
- 17. 17Solutions www.domain.comCb_salah_salah@esi.dz RSA: Secure keys N is the product of P & Q and it is public We construct our keys only by P Q Decomposition of any number into prime factors is unique So it is not thar secure!!!
- 18. 18Solutions www.domain.comCb_salah_salah@esi.dz RSA: Real keys exemple N = 31074182404900437213507500358885679300373460228427275457201619488232064405 18081504556346829671723286782437916272838033415471073108501919548529007337 724822783525742386454014691736602477652346609 P = 16347336458092538484431338838650908598417836700330 92312181110852389333100104508151212118167511579 Q = 1900871281664822113126851573935413975471896789968 515493666638539088027103802104498957191261465571 80 processors Opteron 2.2GHz for 5 months to find P and Q
- 19. 19Solutions www.domain.comCb_salah_salah@esi.dz RSA: Encryption process? Alice wants to send to Bob : « Bonjour ! » Step2 B⇔66⇒66^7 o⇔111⇒111^7 n⇔110⇒110^7 j⇔106⇒106^7 o⇔111⇒111^7 u⇔117⇒117^7 r⇔114⇒114^7 (espace)⇔32⇒32^7 !⇔33⇒33^7 Step1 B⇔66 o⇔111 n⇔110 j⇔106 o⇔111 u⇔117 r⇔114 (espace)⇔32 !⇔33 Step3 (66^7)mod(5141)=386 (111^7)mod(5141)=1858 (110^7)mod(5141)=2127 (106^7)mod(5141)=2809 (111^7)mod(5141)=1858 (117^7)mod(5141)=1774 (114^7)mod(5141)=737 (32^7)mod(5141)=3675 (33^7)mod(5141)=244 "Bonjour !" becomes "386 1858 2127 2809 1858 1774 737 3675 244"
- 20. 20Solutions www.domain.comCb_salah_salah@esi.dz RSA: Decryption process? Bob receives from Alice this message : « 386 737 970 204 1858 » Step2 (386^4279)mod(5141)=66 (737^4279)mod(5141)=114 (970^4279)mod(5141)=97 (204^4279)mod(5141)=118 (1858^4279)mod(5141)=111 Step1 386⇒386^4279 737⇒737^4279 970⇒970^4279 204⇒204^4279 1858⇒1858^4279 Step3 66⇔B 114⇔r 97⇔a 118⇔v 111⇔o
- 21. 21Solutions www.domain.com THANK YOU FOR YOUR ATTENTION!