Introduction to Cryptography

Introduction to Cryptography

Outline • Function of Cryptography • Crash Course in Cryptography • Public Key Infrastructure (PKI) • Example: SSL

Cryptography • Cryptography is the science or study of secret writing (cipher texts). • Cryptanalysis is the science or study of breaking cipher texts • Cryptology is the study of cryptography and cryptanalysis

Uses of Cryptography? • Private communications • What else? • Electronic Information Has Unique Characteristics • Can be given away and still kept • Can be stolen and not missed • Can be owned and no one can tell • Can be distributed instantly to almost everyone • Cannot tell if it is “real” or not

BOB For Sale: $500 ALICE Examples of Threats • Bob wants to buy Alice’s car. • He agrees to pay her $500 and transfer it to her bank account via their online bank.

BOB BANK Transfer $50 from Bob’s account 1234 to Alice’s account 5678 Transfer $500 from Bob’s account 1234 to Alice’s account 5678 Simple Transmission error?

BOB BANK Transfer $500 from Bob’s account 1234 to Alice’s account 5678 Transfer $50000 from Bob’s account 1234 to Hal’s account 5666 “Man in the Middle” “Session Hijack”

Transfer $500 from Bob’s account 1234 to Alice’s account 5678 ALICE BOB BANK Transfer $500 from Bob’s account 1234 to Alice’s account 5678 REPLAY ATTACK Transfer $500 from Bob’s account 1234 to Alice’s account 5678 Transfer $500 from Bob’s account 1234 to Alice’s account 5678 Transfer $500 from Bob’s account 1234 to Alice’s account 5678 Transfer $500 from Bob’s account 1234 to Alice’s account 5678 Transfer $500 from Bob’s account 1234 to Alice’s account 5678 Transfer $500 from Bob’s account 1234 to Alice’s account 5678 Transfer $500 from Bob’s account 1234 to Alice’s account 5678 Transfer $500 from Bob’s account 1234 to Alice’s account 5678 Transfer $500 from Bob’s account 1234 to Alice’s account 5678 Transfer $500 from Bob’s account 1234 to Alice’s account 5678 Transfer $500 from Bob’s account 1234 to Alice’s account 5678

BOB BOB BANK LATER….. I didn’t authorize that transaction!!! Transfer $500 from Bob’s account 1234 to Alice’s account 5678 Bob repudiates the transaction.

Functions of Cryptography • Integrity : Has the data changed since it was sent? • Confidentiality : Can we keep an eavesdropper from learning our message? • Authentication : Can we identify the source of the data? • Non-Repudiation : Can we prove to a third party the source of the data? • Access Control : Can we control who accesses data?

Tools • Hash Functions • Encryption • (Symmetric vs. Asymmetric) • Keyed Hash (MAC) • Key Exchange • Digital Signatures

Hash Functions • h should be chosen so that it is • Easy to compute h(x) • Given y=h(x) it is computationally infeasible to find x (pre-image resistant) • It is computationally infeasible to find x, x’ such that h(x)=h(x’) (collision resistant) • Common Hash functions in cryptography: • SHA-1 • MD5 h maps strings of arbitrary lengths to a fixed length string: h(1101010000…….11001000111) = 100110011101

BANK Problem: Still subject to man in middle (Hacker can Hash) Hash Functions • Hash Functions can be used for message integrity (M’,h(M)’) (M,h(M)) Bank checks that h(M’)=h(M)’ (eliminates transmission errors)

Hashing with Authentication: Message Authentication Codes (MACs) • MACs are also known as keyed hashes. • The sender and receiver share a key that is hashed with the message: • MAC = Hash(M,Key) • A MAC can give integrity and authentication

BANK Hacker cannot change message because the MAC won’t verify! MAC (M,h(M,K)) (M’,h(M,K)’) Bank checks that h(M’,K)=h(M,K)’

Encryption/Decryption • An encryption algorithm takes plaintext and transforms it into ciphertext. • The corresponding decryption algorithm transforms the ciphertext back into the original plaintext. • Cryptographic keys are used in both transformations: • There are two types of encryption/decryption algorithms – symmetric (key1=key2) and asymmetric (key1  key2) E(key1,plaintext)=ciphertext D(key2,ciphertext)=plaintext

Encryption (symmetric) Encryption/ Decryption Algorithm Plaintext Ciphertext Private Key Shared With Trusted Channel Encryption/ Decryption Algorithm Ciphertext Plaintext

Encryption Decryption Example of Symmetric Key Cipher Key = Key1=Key2 = random string of zeros and ones Plaintext = 110010101000110101 Key = 111000111000111000 If key is as long as PT (& only used once): “one time pad”

Keys are the Key • Cryptography moves the information to be protected from the message to be sent into the key for the cryptosystem • The key must be protected!!! • How easy is it for a cryptanalyst to break the cipher - I.e., find the key?

What size key is secure enough? NumberHow long would it take to count to this number from 0 - one count per second? _______________________________________________ 1=100 = 20 1 second 1,000=103~ 210 17 minutes 1,000,000=106 ~ 220 12 days 1,000,000,000=109 ~ 230 32 years 1,000,000,000,000=1012 ~ 240 32,000 years* 1,000,000,000,000,000=1015 ~ 250 32 million years** 1,000,000,000,000,000,000=1018 ~ 260 32 billion years*** * Longer than there has been civilization on earth ** Longer than there have been humans on earth *** More than the age of the Universe Mass of earth: ~6*1027 ~ 6*290 grams Nevertheless, your symmetric key size should be at least 80 bits!! (280)

BOB BANK E(Key,Message)=101011101011000101 D(Key,110111101011110011) = kdsaojriewj???? Encryption can give integrity, confidentiality, and authentication. May need to be combined with a keyed MAC. 110111101011110011

BOB BOB E(Message)=CT=101011101011000101 I did not send that message!!! Prove he did! BANK D(CT)=Transfer Money. Non-repudiation?

New Directions • In 1976, Diffie and Hellman came out with a groundbreaking paper called: “New Directions in Cryptography” • Introduced the idea of asymmetric cryptography based on hard mathematical problems

The key must be K!!! MessageA MessageB Public Key Exchange ???????

Public Key (Asymmetric) Cryptography • Asymmetric algorithms are based on key pairs, a public key and a private key. • The keys are mathematically related such that one key performs an operation on data that only the other key can undo. • Knowledge of the public key reveals nothing about the private key

Public Key Cryptography Public Key: Anyone can use the public key to send a secret to the owner. Private key: Only the private key can unlock the secret. The private key cannot be deduced from the public key.

Public Key Cryptography for Encryption Encryption/ Decryption Algorithm Plaintext Ciphertext Public Key of Receiver Encryption/ Decryption Algorithm Ciphertext Plaintext Private Key of Receiver

Public Key Cryptography - Digital Signatures • Besides being used for encryption and key exchange, public key systems can be used to provide “digital signatures” • The decryption algorithm is used to provide a signature (only the owner of the private key can decrypt or “sign”) • The encryption algorithm is used to “verify” the signature (since this key can be public anyone can verify)

Message + Signature algorithm SigM,k Private key Digital Signatures • Digital Signatures can be used in a way similar to usual signatures. • Only the person with the private key can produce • the signature.

Message Validity Verifying Digital Signatures Message + SigM,k + Verification algorithm Public key • Anyone can verify that the signature is valid.

BOB Digital Signatures • Benefits: • Data authentication: The signature is unique not only to the person who owns the key, but also to the message associated to it. • Non-repudiation: The signer cannot deny signing the message.

Are we done? No. • Obviously we are not done. We still have a lot of work to do: • Proving systems/components are secure • Developing specialized solutions • Integrating crypto into the real world • Etc., etc. etc…

A partial solution: PKI • As a means of addressing these problems, the general idea of a Public Key Infrastructure was born. • PKI is essentially a way to “publish” public key values in a way that is almost (but not really) analogous to a telephone book.

How Does PKI Work? • PKI helps us by providing two things: • Certification: The binding of a public key to something (person, place or thing…) • Validation: The ability to check if such a binding is a valid one.

On-Line Validation • We could just ask the issuing CA if the certificate we are looking at is still good. This is a lot like credit card approval. • PRO: • Immediate notification of certificate revocation. • CON: • Do we really want to ask about every certificate? • Can the CA handle the onslaught of queries?

How Much Protection Do We Really Get? • What is stopping amazon.com from getting a certificate and spoofing the amazon.com web site? • If they have a valid certificate, we might never notice.

What about the little guy? • PKI isn’t really set up to support individuals well. • Less stringent identity verification means less trust in the certificate. • There are 11 Gilbert Bacas in Albuquerque alone. • How well can you protect your personal key?

Public Key Cryptography for Encryption Encryption/ Decryption Algorithm Plaintext Ciphertext Public Key of Receiver Certification Authority or Trusted Channel Encryption/ Decryption Algorithm Ciphertext Plaintext Private Key of Receiver

Example • SSL/TLS

BOB SSL/TLS The Bank

Hi, I’m the Bank Prove it. Here’s my certificate. O.K., here’s a symmetric key encrypted with your public key Encrypted Session SSL (Simplified) The Bank Verify Cert.

The Bank

THANKING YOU

Introduction to Cryptography