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Cryptography Basics

IT443 – Network Security AdministrationInstructor: Bo Sheng

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Outline• Basic concepts in cryptography system• Secret key cryptography• Public key cryptography• Hash functions

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Encryption/Decryption

• Plaintext: a message in its original form• Ciphertext: a message in the transformed, unrecognized form• Encryption: the process that transforms a plaintext into a ciphertext• Decryption: the process that transforms a ciphertext to the

corresponding plaintext• Key: the value used to control encryption/decryption.

plaintextencryption

ciphertextdecryption

plaintext

key key

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Cryptanalysis• “code breaking”, “attacking the cipher”

• Difficulty depends on– sophistication of the cipher– amount of information available to the code

breaker

• Any cipher can be broken by exhaustive trials, but rarely practical

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Caesar Cipher• Replace each letter with the one 3 letters

later in the alphabet– ex.: plaintext CAT ciphertext FDW

A B C D E F G H I J K …

A B C D E F G H I J K …

plaintextalphabet

ciphertextalphabet

Trivial to break

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Mono-Alphabetic Ciphers• Generalized substitution cipher: an arbitrary (but

fixed) mapping of one letter to another– 26! ( 4.0*1026 288) possibilities

A B C D E F G H I J K …

A B C D E F G H I J K …plaintextalphabet

ciphertextalphabet

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Attacking Mono-Alphabetic Ciphers• Broken by statistical analysis of letter, word, and phrase

frequencies of the language• Frequency of single letters in English language, taken

from a large corpus of text:

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Ciphertext Only Attacks• Ex.: attacker can intercept encrypted

communications, nothing else

• Breaking the cipher: analyze patterns in the ciphertext– provides clues about the encryption

method/key

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Known Plaintext Attacks• Ex.: attacker intercepts encrypted text, but

also has access to some of the corresponding plaintext (definite advantage)

• Makes some codes (e.g., mono-alphabetic ciphers) very easy to break

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Chosen Plaintext Attacks• Ex.: attacker can choose any plaintext

desired, and intercept the corresponding ciphertext

• Allows targeted code breaking (choose exactly the messages that will reveal the most about the cipher)

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The “Weakest Link” in Security• Cryptography is rarely the weakest link• Weaker links

– Implementation of cipher– Distribution or protection of keys– … …

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Secret Keys vs Secret Algorithms• Security by obscurity

– We can achieve better security if we keep the algorithms secret

– Hard to keep secret if used widely– Reverse engineering, social engineering

• Publish the algorithms– Security of the algorithms depends on the secrecy of the

keys– Less unknown vulnerability if all the smart (good) people

in the world are examine the algorithms

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Outline• Basic concepts in cryptography system• Secret key cryptography• Public key cryptography• Hash functions

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Secret Key Cryptography

• Same key is used for encryption and decryption• Also known as

– Symmetric cryptography– Conventional cryptography

plaintextencryption

ciphertextdecryption

plaintext

key keySame key

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Secret Key Cryptography• Stream cipher• Block cipher

– Converts one input plaintext block of fixed size k bits to an output ciphertext block of k bits

– DES, IDEA, AES, …– AES

• Selected from an open competition, organized by NSA• Joan Daemen and Vincent Rijmen (Belgium)• Block size=128 bits, Key Size= 128/192/256 bits

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Key Size• Keys should be selected from a large potential

set, to prevent brute force attacks• Secret key sizes

– 40 bits were considered adequate in 70’s– 56 bits used by DES were adequate in the 80’s– 128 bits are adequate for now

• If computers increase in power by 40% per year, need roughly 5 more key bits per decade to stay “sufficiently” hard to break

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Public Key Cryptography

• A public/private key pair is used– Public key can be publicly known– Private key is kept secret by the owner of the key

• Much slower than secret key cryptography• Also known as asymmetric cryptography• Another mode: digital signature

plaintextencryption

ciphertextdecryption

plaintext

Public key Private key

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Public Key Cryptography

• Digital signature– Only the party with the private key can create a digital signature.– The digital signature is verifiable by anyone who knows the public key.– The signer cannot deny that he/she has done so.

plaintextSign

ciphertextVerify

plaintext

Private key Public key

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Public Key Cryptography• It must be computationally

– easy to generate a public / private key pair– hard to determine the private key, given the public key

• It must be computationally – easy to encrypt using the public key– easy to decrypt using the private key– hard to recover the plaintext message from just the

ciphertext and the public key

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Symmetric vs Asymmetric • Symmetric algorithms are much faster

– In the order of a 1000 times faster

• Symmetric algorithms require a shared secret– Impractical if the communicating entities don’t have another

secure channel

• Both algorithms are combined to provide practical and efficient secure communication– E.g., establish a secret session key using asymmetric crypto and

use symmetric crypto for encrypting the traffic

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Outline• Basic concepts in cryptography system• Secret key cryptography• Public key cryptography• Hash functions

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Hash Function

• Also known as– Message digest– One-way transformation– One-way function– Hash

• Length of H(m) much shorter than length of m• Usually fixed lengths: 128 or 160 bits

Message of arbitrary length

Hash A fixed-length short message

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Properties of Hash• Consider a hash function H

– Performance: Easy to compute H(m)

– One-way property: Given H(m) but not m, it’s computationally infeasible to find m

– Weak collision resistance (free): Given H(m), it’s computationally infeasible to find m’ such that H(m’) = H(m).

– Strong collision resistance (free): Computationally infeasible to find m1, m2 such that H(m1) = H(m2)

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Hash Applications• File / Message integrity

– Check if a downloaded file is corrupted– Detect if a file has been changed by someone

after it was stored– Compute a hash H(F) of file F

– openssl dgst -md5 filename

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Hash Applications• Password verification

– Password cannot be stored in plaintext– In a hashed format– Linux: /etc/passwd, /etc/shadow

– cat /etc/shadow

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Hash Applications• User authentication

– Alice wants to authenticate herself to Bob– Assuming they already share a secret key K

Alice Bob

time

“I’m Alice”

RcomputesY=H(R|K)

Yverifies thatY=H(R|K)

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Modern Hash Functions• MD5 (128 bits)

– Previous versions (i.e., MD2, MD4) have weaknesses.– Broken; collisions published in August 2004– Too weak to be used for serious applications

• SHA (Secure Hash Algorithm)– Weaknesses were found

• SHA-1 (160 bits)– Broken, but not yet cracked – Collisions in 269 hash operations, much less than the brute-force attack

of 280 operations– Results were circulated in February 2005, and published in CRYPTO

’05 in August 2005• SHA-256, SHA-384, …

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Birthday Attack• What is the smallest group size k such that

– The probability that at least two people in the group have the same birthday is greater than 0.5?

– 23• Implication for hash function H of length m

– With probability at least 0.5– If we hash about 2m/2 random inputs, – Two messages will have the same hash image– m=64, 1ns per hash

• Brute force (264): 1013 seconds over 300 thousand years• Birthday attack (232): 4 seconds

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Lab 1• Sample codes

– eecs.mit.edu’s IP is 18.62.1.6– Assume their subnetwork use 28-bit prefix

18. 62. 1. 00000110

– Scan 18.62.1.0 ~ 18.62.1.15– dig -x 18.62.1.0 +short– /home/shengbo/it443/scanip.sh– /home/shengbo/it443/scanip.pl

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Electronic Code Book (ECB)

E E E EKey

128

M1 M2 M3 M4

128 46 + padding

128

Plaintext

C1 C2 C3 C4

128 128 128128

Ciphertext

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Cipher Block Chaining (CBC)

InitializationVector

E E E EKey

C1 C2 C3 C4

128 128 128128

M1 M2 M3 M4

128 128 46 + padding

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