Cryptography (continued)

Enabling Alice and Bob to Communicate Securely

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Alice

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Kerckhoff’s Principle

• Bob needs two things to decrypt the ciphertext – the decryption algorithm and the key

• The security of the encryption method depends only on the secret of the key, not on the security of the algorithm(s)– Algorithms are hard to change whereas key are not– Protects the longevity of the algorithm– If the cryptographic systems is built for multiple (millions

of) users everyone uses the same algorithm but different keys

• Public algorithms are amenable to more robust testing

• Moral – Don’t trust proprietary crypto systems

Four Issues

• Confidentiality• Authentication• Integrity• Non-repudiation

Confidentiality

• Assures that encrypted files can only be decrypted by those who hold the secret key

• What’s missing?– Who is on the other end of the line?– Has the file you received been

tampered with?

Authentication

• Who is on the other end?• Challenge response

1) Pick a random number2) Challenge the computer sending you a

message to encrypt it using the secret key

3) If successful, authentication has occurred

• Note re. the randomness of random numbers

Integrity

• Also known as message authentication and digital fingerprinting

• Message Authentication Codes (MACs)– Use a hashing algorithm– Use one way compression so for example

a 50MB document produces a 8B MAC– Avalanche effect

Non-repudiation

• Assurance that a sender cannot deny a file was sent

• Not possible with a shared secret key

Some Attacks

• Ciphertext only• Known plaintext• Chosen plaintext• Chosen ciphertext• Birthday and Meet in the Middle

attacks

Block Ciphers

• An encryption function for fixed sized blocks (today 128 bits). Blocks are split into words, usually 32 bits

• Common key sizes – 128 and 256 bits• Algorithms consist of multiple rounds

of operations on words, e.g. Boolean operations AND, XOR, NOT

Block Cipher Examples

• DES – 64 bit block size, 56 bit key• AES – NIST RFP from Crypto

community. Winner was Rijndael• Twofish – AES finalist• Serpent – AES finalist• All support 128, 192, and 156 bit

keys. Larger than 128 bits is necessary to avoid collision attacks.

Hashing

• A hash uses a secret key and an algorithm to create a new value from a message of a fixed size. Also known as a message digest.

• Should be a one way function. • Should have collision resistance.

Hashing Example

• Example – key = 194, plain text = 45678, Multiply 45678 by 194 = 8861532, Reverse the number = 2351688, Take the 5 most significant digits = 23516

• Send the hash (23516) along with the message (45678)

Secret Key Exchange

• Distribution and escrow• Vulnerability of a trusted 3rd party

Public Exchange of Secret Keys

• Exchange a file of (key, serial #) pairs1) Pick one2) Send serial number3) Use associated key to encrypt and decrypt

• Encrypt the file using a single key and a known algorithm

1) Decrypt the file2) Pick a pair3) Send serial #4) Use associated key to encrypt and decrypt

Public Exchange of Secret Keys (cont.)

• Encrypt each pair in the file separately

1) Pick a pair and decrypt it2) Send the serial #3) Use the associated key to encrypt

and decrypt

Asymmetric Ciphers (e.g. Diffie-Hellman)

• Keys for encryption and decryption are different, but related

• A key made publicly is shared• How does it work?

Public Key Encryption Math

• Inverse operations• Inverse numbers• Circle analogy• Modular arithmetic• Primes and relative primes

PK Math

1) Pick p and q that are relatively prime

2) n = p*q 3) Find d and e where d*e = (p-1)(q-

1)+1 4) The receiver makes n and e public 5) Encryption me mod n = c 6) Decryption cd mod n = m

PK Example

1) p = 17, q = 5, n = 852) d * e = (17 – 1)(5 – 1) + 1 = 65, d

= 13, e = 53) Encrypt the letter x, x = 24

PGP

• Developed by Phil Zimmerman• Used RSA patented algorithms to

produce freeware strong encryption

• Copied widely around the world• MIT published PGP code and made

it available on their websites

Steganography

• Steganography means hidden writing

• Hiding a message in an image• Ancient technique

Steganography

• Steganography - hiding a message in an image or a sound file

• Every image is made of pixels• There often is one byte per pixel for each

color: red, green, and blue• One bit in each byte is the least

significant—changing it will be indistinguishable to the human eye

Uses of Steganography

• Al-Qaida• Digital Watermarking

• Using steganography to hide identifying information in a document

• To prove copyright ownership

• To identify different copies of a document

Replay Attacks

• Replay Attacks– Retransmit an intercepted message– Message is encrypted so that replay

attacker cannot read it

• Why Replay Attacks– Repetition might work—for instance,

replaying an encrypted username and password might result in access to a poorly designed system

Replay Attacks

• Preventing Replay Attacks

– Insert a time stamp in messages and accept messages only if they are very recent

– Insert a sequence number in each message

– Insert a nonce (random number selected for the occasion) in a request message; only accept a reply message with the same nonce. Other party does not accept a request message with a previous nonce