Introduction to Cryptography

1. Introduction to Cryptography

2. Cryptography • Cryptography • Original meaning: the art of secret writing • Send information in a way that prevents others from reading it • Other services: • Integrity checking • Authentication • Process data into unintelligible form, reversible, without data loss

3. Encryption/Decryption plaintext encryption decryption ciphertext plaintext • Plaintext: a message in its original form • Ciphertext: a message in the transformed, unrecognized form • Encryption: the process for producing ciphertext from plaintext • Decryption: the reverse of encryption • Key: a secret value used to control encryption/decryption

4. Computationally Difficult • Cryptographic algorithms need to be reasonably efficient • Cryptographic algorithms are not impossible to break with the key • e.g. try all the keys – brute-force cryptanalysis • Time can be saved by spending money on more computers. • A scheme can be made more secure by making the key longer • Increase the length of the key by one bit • The good guy’s job just a little bit harder • The bad guy’s job up to twice as hard.

5. To Publish or Not to Publish • Not to publish the algorithms • We can achieve better security if we keep the algorithm secret • Hard to keep secret if widely used • Reverse Engineering • Publish the algorithms • Security of the algorithms depend on the secrecy of the keys • Less unknown vulnerabilities if all the smart (good) people examine the algorithm • Common practice • Commercial: published • Military: kept secret

6. Some Trivial Cipher • Caesar cipher: • Substitution cipher • Replace each letter with the one 3 letters later • A -> D, O -> R • Caption Midnight Secret Decoder rings • Pick a secret n between 1 and 25 • Shift variable by n: HAL -> IBM if n is 1 • Monoalphabetic cipher • Arbitrary mapping of one letter to another • 26!, approximately 4 x 1026 • Statistical analysis of letter frequencies

7. Cryptanalysis: Break an Encryption Scheme • Ciphertext only • Analyze only with the ciphertext • Exhaustive search until “recognizable plaintext” • Need enough ciphertext • Known Plaintext • <plaintext, ciphertext> is obtained • Great for monoalphabetic cipher • Chosen Plaintext: • Choose plaintext, get the ciphertext • Useful if limited set of messages

8. Types of Cryptographic functions • Secret Key Cryptography • One key • Public Key Cryptography • Two keys: public, private • Hash function • No key

9. Secret Key Cryptography plaintext encryption decryption ciphertext plaintext key same key key • Same key is used for both encryption and decryption • Symmetric cryptography • Conventional cryptography • Ciphertext is about the same length as the plaintext • Examples: DES, IDEA, AES…

10. Secret Key Cryptography cont’d • Transmitting over an insecure channel • Challenge: how to share the key? • Secure storage on insecure media • Strong Authentication: prove knowledge of a secret without revealing it • Send challenge r, and verify the returned encrypted{r} • Challenge should be chosen from a large pool • Integrity Check: a fixed-length cryptographic checksum for a message • Send MIC (Message Integrity Code) along with the message

11. Public Key Cryptography encryption decryption ciphertext plaintext plaintext public key private key • Invented/published in 1975 • Each individual has two keys: • Private key is kept secret • Public key is publicly known • Much slower than secret key cryptography • Also known as • Asymmetric cryptography

12. Public Key Cryptography cont’d plaintext signing verification Signed message plaintext private key public key • Digital Signature • Only the party with the private key can generate a digital signature • Verification of the signature only requires the knowledge of the public key • The signer cannot deny he/she has done so.

13. Applications of Public Key Cryptography • Security uses of public key cryptography • Known public key cryptography is orders of magnitude slower than the best known secret key cryptographic algo. • Transmitting over an Insecure Channel Alice Bob Encrypt mA using eB Decrypt to mA using dB Decrypt to mB using dA Encrypt mB using eA • Secure Storage on Insecure Media • Because of performance issues, you can randomly generate a secret key, encrypt the data with that secret key, and encrypt the secret key with the public key • Using public key of a trusted person

14. Applications of Public Key Cryptography • Authentication • No need to store secrets, only public keys. • Alice wants to verify Bob’s identity Alice Bob Encrypt rusing eb Decrypt to rusing db r • Secret key cryptography: need to share secret key for every person to communicate with

15. Case Study: Applications of Public Key Cryptography in SSH2 • Assume that bsun@galaxy1.cs.lamar.edu tries to log into mensa.cs.lamar.edu as bsun: • Run “ssh-keygen” at galaxy1.cs.lamar.edu • Copy the generated public key in id_rsa.pub to ./ssh/authorized_keys in mensa.cs.lamar.edu • id_rsa (at galaxy1.cs.lamar.edu) holds the generated private key

16. Applications of Public Key Cryptography • Digital Signatures • Authorship: Prove who generate the information • Integrity: the information has not been modified • Non-repudiation: cannot do with secret key cryptography

17. Hash Algorithms • Message digests, one-way transformations Message of arbitrary length A fixed-length short message Hash h • Easy to compute h(m) • Given h(m), no easy way to find m • Computationally infeasible to find m1 and m2, so that h(m1) = h(m2)

18. Applications of Hash Algorithms • Password hashing • Store the hash of the password • Message integrity • Keyed Hash • Alice and Bob agree on a secret key k • Alice computes h(m|k) and sends it with m • Does not require encryption • Message Fingerprint • For a large data structure: save the message digest of the data on the tamper-proof backing store. • Digital Signature Efficiency • Compute a message digest and sign it • Public key algorithms are processor-intensive