Cryptography Basics

Cryptography Basics

Objectives

Explain general cryptography concepts Explain basic hashing concepts. Basic encryption concepts. Explain and implement protocols Explain core concepts of public key cryptography

Cryptography

Cryptography – science of encrypting information. “scrambles” data so only authorized parties can

“unscramble” and read data using two methodsCan substitute – change one letter with a different letterCan transpose – scramble the order of letters, without actually

changing one for another. The best cryptosystems both substitute and transpose.

Basic Idea

Cryptographic Terminology

Cryptography - a method of storing and transmitting data in a form only intended for authorized parties to read or process.

Cryptanalysis - science of studying, breaking, and reverse engineering algorithms and keys.

Encryption – the method of transforming data (plaintext) into an unreadable format.

Plain text – the format (usually readable) of data before being encrypted

Cipher text – the “Scrambled” format of data after being encrypted


Decryption – the method of turning cipher text back into plain text

Encryption algorithm – a set or rules or procedures that dictates how to encrypt and decrypt data. Also called an encryption “cipher”

Key – (crypto variable) a values used in the encryption process to encrypt and decrypt


Key space – the range of possible values used to construct keys example:

if a key can be 4 digits (0-9) key space = 10,000 (0000 – 9999)if it can be 6 digitskey space = 1,000,000 (000,000 – 999,999)

Key Clustering – Instance when two different keys generate the same cipher text from the same plaintext

Work factor – estimated time and resources to break a cryptosystem

Cryptography History

Romans used a shift cipher called a “CEASAR” cipher. Shift Ciphers simply shift characters in an alphabet.

ROT13 / shift cipher - http://www.rot13.com

Transposition Cipher

Jumbles up the ordering of characters in a message. The Spartans of Greece used a form of this called the “Scytale” Cipher.

Transposition Cipher

Scytale

Steganography

Hiding one message in another “Meet the mini me that ate later.” “Meet me later.”

Vigenere Cipher

The Vigenère cipher is named for Blaise de Vigenère, although Giovan Battista Bellaso had invented the cipher earlier. Vigenère did invent a stronger autokey cipher.

Vigenère cipher is a method of encrypting alphabetic text by using a series of different Caesar ciphers based on the letters of a keyword. It is a simple form of polyalphabetic substitution.

This cipher is well known because while it is easy to understand and implement, it often appears to beginners to be unbreakable.

Vigenere Table (tabula recta)

Vigenere Cipher

For example, suppose that the plaintext to be encrypted is: ATTACKATDAWN

The person sending the message chooses a keyword and repeats it until it matches the length of the plaintext, for example, the keyword "LEMON": LEMONLEMONLE

The first letter of the plaintext, A, is enciphered using the alphabet in row L, which is the first letter of the key. This is done by looking at the letter in row L and column A of the Vigenère square, namely L. The rest of the plaintext is enciphered in a similar fashion.

Plaintext: ATTACKATDAWN Key: LEMONLEMONLE Ciphertext: LXFOPVEFRNHR

Encryption Modes – Block

Take the message and break it up into fixed sized blocks, encrypt each block using the given key.

Block (ECB encryption)

Block Encryption Problems

Solving Block Encryption Problems

Often with block encryption, we include a value in addition to the key that changes for each block, so we don’t get repetitive cipher text blocks. This is called Cipher Block Chaining (see next slide)

Initialization Vectors are used with the first block in CBC

Cipher Block Chaining

XORing

XORing is a Boolean mathematical “function” which creates an output bit based on two input bits. It outputs a 1 IF and ONLY if one bit of input is 1 and the other is a 0.

INPUT1 INPUT 2 XOR OUTPUT---------------------------------------------------------------------------

0 0 = 00 1 = 11 0 = 11 1 = 0

Stream Encryption

The “key” is used as a key stream generator, which creates a series of bits each are is mathematically combined with the bit stream of plaintext to produce cipher text. This is done for small pieces of information, or information not in blocks.

Keyboard input Morse code Any input that arrives one bit or byte at a time

Stream Encryption

Plain Text Bit Keystream Bit Output Bit0 11 11 00 11 XOR 1 = 0

Cipher text = 0

Stream Encryption

Plain Text Bit Keystream Bit Output Bit

0 11 11 00 XOR 1 = 1

Cipher text = 0 1

Stream Encryption


0 11 11 XOR 0 = 1

Cipher text = 0 1 1

Stream Encryption


0 11 XOR 1 = 0

Cipher text = 0 1 1 0

Stream Encryption


0 XOR 1 = 1

Cipher text = 0 1 1 0 1

One Time Pad

1011 – plain text 0101 – pad ------ XOR 1110 – cipher text In a one time pad you use a different key/pad each time

you send a message

One Time Pad

A “perfect cryptosystem” Unbreakable if implemented properly The key is a series of bits (0 and 1) The plain text is converted to bits The message is XORed with the pad/key to generated the

cipher text (more)

One Time Pad considerations

The pad must be used only one time The pad must be shared by both sides. The pad must be as long as the message The pad must be securely distributed The pad must be used up of truly random values

Symmetric Encryption

Idea same key is used to BOTH encrypt and decrypt data!

Symmetric Encryption

Called Symmetric or “Private Key encryption” Must securely distribute keys to both parties.

Chicken in the egg situation with networks Anyone with the key can either encrypt or decrypt Very Fast to encrypt or decrypt Key Management is the big issue

Key Management

n: number of parties who want to securely communicate

# keys = (n*(n-1)) / 2 5 = (5*4)/2 = 10 keys 10 = (10*9)/2 = 45 keys 100 = (100*99)/2 = 4950 keys 1000 = (1000*999)/2 = 499500

keys

Symmetric Algorithms – DES

Data Encryption Standard Developed from at NIST request for an encryption standard Chosen algorithm was called “Lucifer” from IBM Block Cipher Fixed sized blocks of 64 bits Key size 64 bits, effective size is 56 bits 16 rounds of substitution and transposition DES is no longer considered strong enough, can be broken

easily with distributed computing.

Triple DES

Nothing but DES 3 times 3DES – EEE3 3DES – EDE3 3DES – EEE2 3DES – EDE2

Since it’s 3 x DES, 48 rounds of substitution and transposition.

AES

Developed as a replacement to DES Actual algorithm is called “Rinjdael” Block cipher 128 bit blocks Key sizes of 128,192, 256 Rounds depend on key size

9: for 128 keys 11: for 192 keys 13: for 256 bit keys

RC5

Block cipher Block size 32, 64, 128 Key Size up to 2048 bits Rounds up to 255, minimum of 12 recommended

RC6

Block cipher based on RC5 Same attributes as RC5 Developed to be a AES candidate Faster that RC5

RC4

Stream cipher – what was that again? Was proprietary, but released on Internet in 1994, “ARC4”

is the “open version of RC4” Key length 8 – 2048 bits Used in SSL and WEP communication

Blowfish

Block cipher 64 bit blocks Keys 32 - 448 bits 16 rounds is the “full version” Free algorithm

IDEA

International Data Encryption Algorithm Proposed AES candidate Block cipher 64 bit blocks 128 bit keys Not free, Patent expires soon though Used in PGP

Symmetric

That’s Symmetric Encryption Understand the concept (shared keys) Understand it’s strengths (fast for bulk encryption and

decryption) Understand it’s weaknesses (key management, non-

repudiation) Understand the different algorithm “properties” on the

slides.

Enter Non-Repudiation

Non-Repudiation – being able to definitively prove someone said or wrote something.

Proves they actually sent a message Proves the message was not altered

How do we provide non-repudiation? We’ll see soon after we talk about hashes, and asymmetric encryption.

Asymmetric Encryption

Use 2 keys, public key to encrypt a message, private key can decrypt


Called Public key encryption Requires 2 related keys Public key – given to anyone Private key – kept secret Public key is used to encrypt message Private key is used to decrypt message Private key is used to sign messages Public key is used to validate signed messages


Key exchange is simple! Asymmetric Encryption is SLOW, not suitable for

encrypting large amounts of data What is a problem with Asymmetric Encryption and key

exchange? (MiM) Can be used to “digitally sign” a message (in a few slides) Provides integrity Provides non-repudiation Can anyone see a use to Asymmetric encryption already?*

(very important)

Diffie-Hellman

The original Asymmetric algorithm Used with SSL, VPNs, ssh Used ONLY for key exchange Generates session keys for secure SYMETRIC encryption

communications

Asymmetric Algorithms – RSA

Can be 100 times slower than DES Can be used for encryption, key exchange and digital

signatures Security based on difficulty of factoring large numbers. Was patented, has expired

El-Gamal

Encryption or digital signatures Free Can be used for encryption, key exchange and digital

signatures Slow Based on / extended Diffie-Hellman

ECC - Elliptic Curve Cryptography

Encryption, key exchange or digital signatures Security based on analyzing elliptic curves in finite fields Does not require much computing overhead as such used

in devices with low resources (PDAs, Cell phones etc)*

Asymmetric Overview

Uses 2 keys, one for encryption, one for decryption This mitigates the key management, key distribution

problem (kind of…) Is VERY slow (orders of magnitude slower) Can provide integrity and proof of sender (non-repudiation) Often used in a hybrid system (along with private key

encryption) Encrypt symmetric keys using asymmetric algorithms Actually do large scale encryption with these asymmetric

keys!

Hashing - Băm

Hashing is similar to encryption… but different. Hashing is a one way operation. Take input message Put through hashing function Retrieve fixed length value (hash digest)

Hashing

Try for yourself at http://www.fileformat.info/tool/hash.htm

Hashes

Once hashed, no way to get back the original message

Hash digests are fixed, so multiple messages theoretically could produce the same hash digest (collision)

Hashes

Hashing can provide integrity (assuming no MiM (next slide))

Hashes can be combined with a private key to provide protection against MiM attacks (visualization in a few slides next slide)

The more bits in the digest, generally the more secure (less change for collision…generally)

One Example of a hash that you are probably familiar with is called a “CRC”

Normal use of Hash

Hash MiM attack (phase 1)

Hash MiM attack (phase 2)

HMAC

Hash-based Message Authentication Code

HMAC

function hmac (key, message) if (length(key) > blocksize) then key = hash(key) // keys longer than blocksize are shortened end if if (length(key) < blocksize) then key = key zeroes(blocksize - length(key)) // keys ∥shorter than blocksize are zero-padded end if o_key_pad = [0x5c * blocksize] key // Where blocksize ⊕is that of the underlying hash function i_key_pad = [0x36 * blocksize] key // Where is exclusive ⊕ ⊕or (XOR) return hash(o_key_pad hash(i_key_pad message)) // ∥ ∥Where is concatenation∥end function

Hash algorithms – SHA

Secure Hash Algorithm Designed/Published by NIST and NSA Designed for use in the DSS Modeled after MD4 SHA-1 (SHA-160) – 160 bit digest

512 bit blocks SHA-256 – 256 bit digest



1024 bit blocks

MD2

Developed by Ronald Rivest (of RC and RSA fame) Optimized to run on 8 bit computers 128 bit digest 128 bit blocks

MD4

Optimized for 32 bit computers 128 bit digest Collisions can be found in under 1 minute on a PC ;(

MD5

Similar to MD4, but more secure Slower and more secure 128 bit digest 512 bit blocks Was part of the NTLM authentication protocol Collisions in 8 hours on a PC Moving away from, to SHA

Hash overview

Know what a hash is Concept Fixed length digest What is a hash used for Know what a collision is Know it’s susceptible to MiM Know what HMAC is, and what it tries to accomplish

Be familiar with MDx, and SHA-x Understand that SHA is considered the best algorithm

Digital Signatures

Digital Signing

Digital Signing

Generally when I digital sign something.. I don’t encrypt the whole message. Instead Run message through hash algorithm, generated message

digest Sign the “message digest” Send both the original message and the encrypted message

digest

Digital Signing

Provides Integrity Non repudiation NOT confidentiality

Digital Signing

Documents

Cryptography Basics