Introduction to Cryptography and its Basic Fundamentals
- 1. Computer Security Communications, Networking & Security Cryptography
- 2. • Well established needs for secure communication – War time communication – Business transactions – Illicit Love Affairs • Requirements of secure communication 1. Secrecy – Only intended receiver understands the message 2. Authentication – Sender and receiver need to confirm each others identity 3. Message Integrity – Ensure that their communication has not been altered, either maliciously or by accident during transmission Secure Communication Needs and Requirements
- 3. • Cryptography is the science of secret, or hidden writing • It has two main Components: 1. Encryption – Practice of hiding messages so that they can not be read by anyone other than the intended recipient 2. Authentication & Integrity – Ensuring that users of data/resources are the persons they claim to be and that a message has not been surreptitiously altered Cryptography Basics
- 4. • Cipher is a method for encrypting messages • Encryption algorithms are standardized & published • The key which is an input to the algorithm is secret – Key is a string of numbers or characters – If same key is used for encryption & decryption the algorithm is called symmetric – If different keys are used for encryption & decryption the algorithm is called asymmetric Encryption Cipher Plain Text Encryption Algorithm Key A Key B Cipher Text Plain Text Decryption Algorithm
- 5. • Algorithms in which the key for encryption and decryption are the same are Symmetric – Example: Caesar Cipher • Types: 1. Block Ciphers – Encrypt data one block at a time (typically 64 bits, or 128 bits) – Used for a single message 2. Stream Ciphers – Encrypt data one bit or one byte at a time – Used if data is a constant stream of information Encryption Symmetric Algorithms
- 6. • Strength of algorithm is determined by the size of the key – The longer the key the more difficult it is to crack • Key length is expressed in bits – Typical key sizes vary between 48 bits and 448 bits • Set of possible keys for a cipher is called key space – For 40-bit key there are 240 possible keys – For 128-bit key there are 2128 possible keys – Each additional bit added to the key length doubles the security • To crack the key the hacker has to use brute-force (i.e. try all the possible keys till a key that works is found) – Super Computer can crack a 56-bit key in 24 hours – It will take 272 times longer to crack a 128-bit key (Longer than the age of the universe) Symmetric Encryption Key Strength
- 7. • Caesar Cipher is a method in which each letter in the alphabet is rotated by three letters as shown Substitution Ciphers Caesar Cipher 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 • Let us try to encrypt the message – Attack at Dawn Assignment: Each student will exchange a secret message with his/her closest neighbor about some other person in the class and the neighbor will decipher it.
- 8. Substitution Ciphers Caesar Cipher Encryption Plain Text Message: Attack at Dawn Cipher Text Message: Dwwdfn Dw Gdyq Cipher: Caesar Cipher Algorithm Key (3) Decryption Plain Text Message: Attack at Dawn Cipher Text Message: Dwwdfn Dw Gdyq Cipher: Caesar Cipher Algorithm Key (3) How many different keys are possible?
- 9. • Any letter can be substituted for any other letter – Each letter has to have a unique substitute • There are 26! pairing of letters (~1026) • Brute Force approach would be too time consuming – Statistical Analysis would make it feasible to crack the key Substitution Cipher Monoalphabetic Cipher 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 M N B V C X Z A S D F G H J K L P O I U Y T R E W Q Encrypted Message: Nkn, s gktc wky. mgsbc Message: Bob, I love you. Alice Cipher: Monoalphabetic Cipher Key
- 10. • Developed by Blaise de Vigenere – Also called Vigenere cipher • Uses a sequence of monoalpabetic ciphers in tandem – e.g. C1, C2, C2, C1, C2 • Example Substitution Cipher Polyalphabetic Caesar Cipher Encrypted Message: Gnu, n etox dhz. tenvj Message: Bob, I love you. Alice Cipher: Monoalphabetic Cipher Key Plain Text 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 C1(k=6) F G H I J K L M N O P Q R S T U V W X Y Z A B C D E C2(k=20) T U V W X Y Z A B C D E F G H I J K L M N O P Q R S
- 11. • Obtain a key to for the algorithm and then shift the alphabets – For instance if the key is word we will shift all the letters by four and remove the letters w, o, r, & d from the encryption • We have to ensure that the mapping is one-to-one – no single letter in plain text can map to two different letters in cipher text – no single letter in cipher text can map to two different letters in plain text Substitution Cipher Using a key to shift alphabet Encrypted Message: ?? Message: Bob, I love you. Alice Cipher: WORD Plain Text 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 C1(k=6) W O R D A B C E F G H I J K L M N P Q S T U V X Y Z
- 12. • This involves rearrangement of characters on the plain text into columns • The following example shows how letters are transformed – If the letters are not exact multiples of the transposition size there may be a few short letters in the last column which can be padded with an infrequent letter such as x or z Transposition Cipher Columnar Transposition T H I S I S A M E S S A G E T O S H O W H O W A C O L U M N A R T R A N S P O S I T I O N W O R K S T S S O H O A N I W H A A S O L R S T O I M G H W U T P I R S E E O A M R O O K I S T W C N A S N S Plain Text Cipher Text
- 13. • The amount of secrecy needed should determine the amount of labor appropriate for the encryption and decryption. • The set of keys and the enciphering algorithm should be free from complexity. • The implementation of the process should be as simple as possible. • Errors in ciphering should not propagate and cause corruption of further information in the message. • The size of the enciphered text should be no larger than the text of the original message. Ciphers Shannon’s Characteristics of “Good” Ciphers
- 14. • It is based on sound mathematics. – Good cryptographic algorithms are are derived from solid principles. • It has been analyzed by competent experts and found to be sound. – Since it is hard for the writer to envisage all possible attacks on the algorithm • It has stood the “test of time.” – Over time people continue to review both mathematical foundations of an algorithm and the way it builds upon those foundations. – The flaws in most algorithms are discovered soon after their release. Encryption Systems Properties of Trustworthy Systems
- 15. • Cryptanalysis is the process of breaking an encryption code – Tedious and difficult process • Several techniques can be used to deduce the algorithm – Attempt to recognize patterns in encrypted messages, to be able to break subsequent ones by applying a straightforward decryption algorithm – Attempt to infer some meaning without even breaking the encryption, such as noticing an unusual frequency of communication or determining something by whether the communication was short or long – Attempt to deduce the key, in order to break subsequent messages easily – Attempt to find weaknesses in the implementation or environment of use of encryption – Attempt to find general weaknesses in an encryption algorithm, without necessarily having intercepted any messages Cryptanalysis Techniques
- 16. • Goal of DES is to completely scramble the data and key so that every bit of cipher text depends on every bit of data and ever bit of key • DES is a block Cipher Algorithm – Encodes plaintext in 64 bit chunks – One parity bit for each of the 8 bytes thus it reduces to 56 bits • It is the most used algorithm – Standard approved by US National Bureau of Standards for Commercial and nonclassified US government use in 1993 Data Encryption Standard (DES) Basics
- 17. • DES run in reverse to decrypt • Cracking DES – 1997: 140 days – 1999: 14 hours • TripleDES uses DES 3 times in tandem – Output from 1 DES is input to next DES Data Encryption Standard (DES) Basics 64-bit input L1 R1 F(L1, R1, K1) L2 R2 L3 R3 L17 R17 56-bit key 48-bit k1 48-bit k2 48-bit k3 48-bit k16 F(L2, R2, K2) F(L16, R16, K16)
- 18. Encryption Algorithm Summary Algorithm Type Key Size Features DES Block Cipher 56 bits Most Common, Not strong enough TripleDES Block Cipher 168 bits (112 effective) Modification of DES, Adequate Security Blowfish Block Cipher Variable (Up to 448 bits) Excellent Security AES Block Cipher Variable (128, 192, or 256 bits) Replacement for DES, Excellent Security RC4 Stream Cipher Variable (40 or 128 bits) Fast Stream Cipher, Used in most SSL implementations
- 19. • Any exposure to the secret key compromises secrecy of ciphertext • A key needs to be delivered to the recipient of the coded message for it to be deciphered – Potential for eavesdropping attack during transmission of key Symmetric Encryption Limitations
- 20. • Uses a pair of keys for encryption – Public key for encryption – Private key for decryption • Messages encoded using public key can only be decoded by the private key – Secret transmission of key for decryption is not required – Every entity can generate a key pair and release its public key Asymmetric Encryption Basics Plain Text Cipher Public Key Private Key Cipher Text Plain Text Cipher
- 21. • Two most popular algorithms are RSA & El Gamal – RSA • Developed by Ron Rivest, Adi Shamir, Len Adelman • Both public and private key are interchangable • Variable Key Size (512, 1024, or 2048 buts) • Most popular public key algorithm – El Gamal • Developed by Taher ElGamal • Variable key size (512 or 1024 bits) • Less common than RSA, used in protocols like PGP Asymmetric Encryption Types
- 22. • Choose two large prime numbers p & q • Compute n=pq and z=(p-1)(q-1) • Choose number e, less than n, which has no common factor (other than 1) with z • Find number d, such that ed – 1 is exactly divisible by z • Keys are generated using n, d, e – Public key is (n,e) – Private key is (n, d) • Encryption: c = me mod n – m is plain text – c is cipher text • Decryption: m = cd mod n • Public key is shared and the private key is hidden Asymmetric Encryption RSA
- 23. • P=5 & q=7 • n=5*7=35 and z=(4)*(6) = 24 • e = 5 • d = 29 , (29x5 –1) is exactly divisible by 24 • Keys generated are – Public key: (35,5) – Private key is (35, 29) • Encrypt the word love using (c = me mod n) – Assume that the alphabets are between 1 & 26 Asymmetric Encryption RSA Plain Text Numeric Representation me Cipher Text (c = me mod n) l 12 248832 17 o 15 759375 15 v 22 5153632 22 e 5 3125 10
- 24. • Decrypt the word love using (m = cd mod n) – n = 35, c=29 Asymmetric Encryption RSA Cipher Text cd (m = me mod n) Plain Text 17 481968572106750915091411825223072000 17 l 15 12783403948858939111232757568359400 15 o 22 852643319086537701956194499721110000000 22 v 10 100000000000000000000000000000 10 e
- 25. • Efficiency is lower than Symmetric Algorithms – A 1024-bit asymmetric key is equivalent to 128-bit symmetric key • Potential for man-in-the middle attack • It is problematic to get the key pair generated for the encryption Asymmetric Encryption Weaknesses
- 26. • Hacker could generate a key pair, give the public key away and tell everybody, that it belongs to somebody else. Now, everyone believing it will use this key for encryption, resulting in the hacker being able to read the messages. If he encrypts the messages again with the public key of the real recipient, he will not be recognized easily. Asymmetric Encryption Man-in-the-middle Attack Bob Attacker David Bob’s Message + Public key Cipher David’s Public Key Trudeau (Middle-man) Trudeau’s Message + public key Cipher Trudeau’s Public Key Bob’s Encrypted Message Trudeau’s Encrypted Message David’s Message + public key Cipher Trudeau’s Encrypted Message Bob’s Public Key Trudeau’s New Message + public key Cipher Trudeau’s Encrypted Message David’s Public Key
- 27. • Used to improve efficiency – Symmetric key is used for encrypting data – Asymmetric key is used for encrypting the symmetric key Asymmetric Encryption Session-Key Encryption Plain Text Cipher (DES) Session Key Recipient’s Public Key Cipher Text Encrypted Key Cipher (RSA) Send to Recipient
- 28. • Pretty Good Privacy (PGP) – Used to encrypt e-mail using session key encryption – Combines RSA, TripleDES, and other algorithms • Secure/Multipurpose Internet Mail Extension (S/MIME) – Newer algorithm for securing e-mail – Backed by Microsoft, RSA, AOL • Secure Socket Layer(SSL) and Transport Layer Socket(TLS) – Used for securing TCP/IP Traffic – Mainly designed for web use – Can be used for any kind of internet traffic Asymmetric Encryption Encryption Protocols
- 29. • Key agreement is a method to create secret key by exchanging only public keys. • Example – Bob sends Alice his public key – Alice sends Bob her public key – Bob uses Alice’s public key and his private key to generate a session key – Alice uses Bob’s public key and her private key to generate a session key – Using a key agreement algorithm both will generate same key – Bob and Alice do not need to transfer any key Asymmetric Encryption Key Agreement Cipher (DES) Session Key Cipher (DES) Bob’s Public Key Alice’s Public Key Bob’s Private Key Alice’s Private Key Alice and Bob Generate Same Session Key!
- 30. Asymmetric Encryption Key Diffie-Hellman Mathematical Analysis Bob & Alice agree on non-secret prime p and value a Generate Secret Random Number x Compute Public Key ax mod p Compute Session Key (ay)x mod p Generate Secret Random Number y Compute Public Key ay mod p Compute Session Key (ax)y mod p Bob Alice Identical Secret Key Bob & Alice exchange public keys
- 31. • Diffie-Hellman is the first key agreement algorithm – Invented by Whitfield Diffie & Martin Hellman – Provided ability for messages to be exchanged securely without having to have shared some secret information previously – Inception of public key cryptography which allowed keys to be exchanged in the open • No exchange of secret keys – Man-in-the middle attack avoided Asymmetric Encryption Key Agreement con’t.
- 32. • Authentication is the process of validating the identity of a user or the integrity of a piece of data. • There are three technologies that provide authentication – Message Digests / Message Authentication Codes – Digital Signatures – Public Key Infrastructure • There are two types of user authentication: – Identity presented by a remote or application participating in a session – Sender’s identity is presented along with a message. Authentication Basics
- 33. • A message digest is a fingerprint for a document • Purpose of the message digest is to provide proof that data has not altered • Process of generating a message digest from data is called hashing • Hash functions are one way functions with following properties – Infeasible to reverse the function – Infeasible to construct two messages which hash to same digest • Commonly used hash algorithms are – MD5 – 128 bit hashing algorithm by Ron Rivest of RSA – SHA & SHA-1 – 162 bit hashing algorithm developed by NIST Authentication Message Digests Message Message Digest Algorithm Digest
- 34. • A message digest created with a key • Creates security by requiring a secret key to be possesses by both parties in order to retrieve the message Message Authentication Codes Basics Message Message Digest Algorithm Digest Secret Key
- 35. • Password is secret character string only known to user and server • Message Digests commonly used for password authentication • Stored hash of the password is a lesser risk – Hacker can not reverse the hash except by brute force attack • Problems with password based authentication – Attacker learns password by social engineering – Attacker cracks password by brute-force and/or guesswork – Eavesdrops password if it is communicated unprotected over the network – Replays an encrypted password back to the authentication server Password Authentication Basics
- 36. • Set of rules that governs the communication of data related to authentication between the server and the user • Techniques used to build a protocol are – Transformed password • Password transformed using one way function before transmission • Prevents eavesdropping but not replay – Challenge-response • Server sends a random value (challenge) to the client along with the authentication request. This must be included in the response • Protects against replay – Time Stamp • The authentication from the client to server must have time-stamp embedded • Server checks if the time is reasonable • Protects against replay • Depends on synchronization of clocks on computers – One-time password • New password obtained by passing user-password through one-way function n times which keeps incrementing • Protects against replay as well as eavesdropping Authentication Protocols Basics
- 37. • Kerberos is an authentication service that uses symmetric key encryption and a key distribution center. • Kerberos Authentication server contains symmetric keys of all users and also contains information on which user has access privilege to which services on the network Authentication Protocols Kerberos
- 38. • Personal Tokens are hardware devices that generate unique strings that are usually used in conjunction with passwords for authentication • Different types of tokens exist – Storage Token: A secret value that is stored on a token and is available after the token has been unlocked using a PIN – Synchronous one-time password generator: Generate a new password periodically (e.g. each minute) based on time and a secret code stored in the token – Challenge-response: Token computes a number based on a challenge value sent by the server – Digital Signature Token: Contains the digital signature private key and computes a computes a digital signature on a supplied data value • A variety of different physical forms of tokens exist – e.g. hand-held devices, Smart Cards, PCMCIA cards, USB tokens Authentication Personal Tokens
- 39. • Uses certain biological characteristics for authentication – Biometric reader measures physiological indicia and compares them to specified values – It is not capable of securing information over the network • Different techniques exist – Fingerprint Recognition – Voice Recognition – Handwriting Recognition – Face Recognition – Retinal Scan – Hand Geometry Recognition Authentication Biometrics
- 40. • Probability of two irises producing exactly the same code: 1 in 10 to the 78th power • Independent variables (degrees of freedom) extracted: 266 • IrisCode record size: 512 bytes • Operating systems compatibility: DOS and Windows (NT/95) • Average identification speed (database of 100,000 IrisCode records): one to two seconds Authentication Iris Recognition The scanning process takes advantage of the natural patterns in people's irises, digitizing them for identification purposes Facts
- 41. • A digital signature is a data item which accompanies or is logically associated with a digitally encoded message. • It has two goals – A guarantee of the source of the data – Proof that the data has not been tampered with Authentication Digital Signatures Message Sent to Receiver Digest Algorithm Digital Signature Sent to Receiver Message Digest Sender’s Private Key Sender’s Public Key Message Digest Signature Algorithm Signature Algorithm Digest Algorithm Message Digest Sender Receiver Same?
- 42. • A digital certificate is a signed statement by a trusted party that another party’s public key belongs to them. – This allows one certificate authority to be authorized by a different authority (root CA) • Top level certificate must be self signed • Any one can start a certificate authority – Name recognition is key to some one recognizing a certificate authority – Verisign is industry standard certificate authority Authentication Digital Cerftificates Identity Information Certificate Authority’s Private Key Sender’s Public Key Signature Algorithm Certificate
- 43. • Chaining is the practice of signing a certificate with another private key that has a certificate for its public key – Similar to the passport having the seal of the government • It is essentially a person’s public key & some identifying information signed by an authority’s private key verifying the person’s identity • The authorities public key can be used to decipher the certificate • The trusted party is called the certificate authority Authentication Cerftificates Chaining Certificate Authority’s Private Key Signature Algorithm New Certificate Certificate
- 44. • Practice of analyzing and breaking cryptography • Resistance to crypt analysis is directly proportional to the key size – With each extra byte strength of key doubles • Cracking Pseudo Random Number Generators – A lot of the encryption algorithms use PRNGs to generate keys which can also be cracked leading to cracking of algorithms • Variety of methods for safe guarding keys (Key Management) – Encryption & computer access protection – Smart Cards Cryptanalysis Basics