Security and Cryptography

1
Security and Cryptography

• Security all issues which make secure
  communication (information transmission, two
  (multiple) party interaction) over insecure
  channels.
• Cryptography the science and art of manipulating
  messages to make them secure.
• Classical cryptographic techniques.
• Along with the development of communication
  networks and their broad applications, network
  security is becoming a more serious problem.
• Thus, call for modern cryptography.

2
Network threats and attacks
Eavesdropping
Passive
Traffic analysis
Masquerading
Replay
Active
Modification
Denial of service
3
Security requirements for transmitting information

• Privacy or confidentiality the information
  should be readable only by the intended receiver.
  i.e., protect the information from eavesdropping.
  
• Integrity the receiver can confirm that a
  message has not been altered during transmission,
  i.e., protect the information from tampering.
• Authentication any party (sender or receiver)
  can verify that the other party is who he or she
  claims to be, i.e., validate the identity of the
  other party.
• Nonrepudiation the sender can not deny having
  sent a given message. i.e., if a transaction
  (e.g., a purchase) has occurred between two
  parties, the nonrepudiation service can prove
  that for any party, he/she really performed the
  transaction him/herself, not by any other person.

4
Approaches to implementing security
By encryption (and decryption)
Confidentiality
Sender encrypts the message using a key and
sends the encrypted message. Receiver decrypts
the encrypted message using the same key as the
senders key or a key derivable
from the senders key.
Integrity
By checksum or hash value/message digest.
Sender computes checksum/hash value/message
digest from the message and sends
the message along with the checksum/hash
value/message digest. Receiver re-computes
checksum/hash value/message digest from received
message and compares with the
transmitted checksum/hash value/message digest.
Both are transmitted
message
checksum
In some sense, it likes error-detection.
Problem the attacker, after intercepting the
message, modifies the message, computes
the checksum for modified message, and resends
them.
Solution keyed checksum/hash value/message
digest.
Message checksum are transmitted
key
message
checksum
5
Approaches to implementing security (cont.)
Authentication
Traditional user ID and password.
Modern cryptography based authentication. --Dig
ital signature.
Undeniable signature, i.e.,
Nonrepudiation
Digital signature verification protocol
disavowal protocol
6
Security requirements and their implementation
encryption (and decryption)
Confidentiality
Integrity
checksum or hash value/message digest or MAC.
Authentication
user ID and password or Digital signature.
Nonrepudiation
Undeniable signature
Availability
Intrusion detection and defense
Authorization
Access control
Accountability
Log, record, trace, system administration
Q how to defense Replay attack?
Timestamps and/or sequence numbers.
7
Classification of cryptosystems

• Secret key systems vs. public key systems
• Classical vs. modern
• Classical secret key systems
• Shift, Affine, Vigenere, Hill, Permutation
  (transposition) cipher, Stream cipher
• Modern
• Secret key systems
• DES, AES, PGM
• Public key systems
• RSA, ElGamal, Elliptic Curve

8
Shift cipher--example

• Suppose a plaintext word cryptography
• Change each letter by shifting the letter three
  position rightward
• The cipherword is FUBSWRJUDSKB

Question if given the above cipherword, how to
get original word?
Change each letter by shifting the letter three
position leftward.
This kind of cryptosystem is called Caesar
Cipher
9
Secret cryptosystem--DES

• Data Encryption Standard (DES)
• First version in 1975, developed by IBM.
• A type of iterated cipher.
• Plaintext block 64 bits, key 56 bits,
  ciphertext block64 bits.
• Steps
• Initial permutation (IP)
• 16 rounds of transformations
• Inverse permutation (IP-1)

10
Key management and exchange

• Key is the essential part in any cryptosystem,
  especially in secret key systems.
• How to distribute/exchange key/keys between two
  users/any pair of multiple users.
• Therefore key management and key exchange come
  into play.
• Also public key systems appeared.

11
Why public-key cryptography

• The two communicants in secret key system require
  the
• prior communication of key, using a
  secure channel.
• it is very difficult to achieve in
  practice. Unless the two
• communicants meet together, phone call,
  post mail, email
• etc., are not secure.

• Suppose there are n users and every pair of users
  want to
• communicate. In secret-key system, it is
  necessary that
• the total number of keys is n(n-1)/2. Very
  difficult to
• management and quite insecure.
• However, in public-key system, every user
  selects his/her
• own private key and public key, and
  publicizes the public
• key but keep the private key secret. Quite
  easy and very secure.

The main problem with public-key system is that
it is very slow.
12
Public-key cryptosystem

• Secret-key cryptosystem
• eK dK dK is the same as or derived from eK.
• Called symmetric-key cryptosystem.
• Problem how to distribute eK dK to Alice Bob
  securely.
• Public-key cryptosystem
• Computationally infeasible to compute dK from eK.
• Called asymmetric-key cryptosystem.
• eK is made public, called public key
• But dK is kept secret, called private key.

13
Public-key system how it works

• Everybody selects its own public key P and
  private key S, and publicizes P.
• Therefore Alice has (Pa , Sa), and Bob has (Pb ,
  Sb).
• Everybody knows Pa, Pb,
• Suppose Alice wants to send a message to Bob.
• Alice encrypts the message with Bobs public key
  Pb and sends out.
• (only) Bob can decrypt the message using his
  private key Sb. Nobody else can.

14
RSA cryptosystem

• Suppose np?q, where p and q are big primes.
• Select (find) a and b, such that a?b1 mod ?(n).
• K(n,p,q,a,b), publicize n,b, but keep p,q,a
  secret.
• For any x,y?Zn , define
• eK(x) xb mod n
• dK(y) ya mod n
• Of course, from n,b, it is very difficult to get
  a (as well as p,q,?(n)).

15
Two party key management

• By public key cryptosystems
• Alice selects a random value k as a key
• Alice encrypts the key k with Bobs public key
  and sends to Bob
• Bob decrypts the key using his private key
• Alice and Bob encrypt/decrypt messages using
  secret key systems such as DES with the key k.
• This is a typical combination of secret and
  public key systems.
• By Diffie-Hellman key agreement
• Based on Discrete Logarithm Problem

16
DLP (Discrete Logarithm Problem)

• Suppose p is an odd prime.
• Zp0,1,,p-1 is a finite field.
• Zp the set of integers which are relatively
  prime to p.
• a ? Zp gcd(a, p)11,,p-1
• it is a cyclic multiplicative group.
• g is a generator of Zp ,
• i.e. , Zp g 0 mod p, g 1mod p, , g p-2 mod
  p.
• DLP problem
• Given any a, compute bg a (mod p) is easy.
• given any b, find an a such that b g a (mod
  p) is difficult.
• Denoted as a log g b. Omit mod p for
  simplicity.

17
(Two-party) Diffie-Hellman (DH) key exchange
Suppose p and g are publicly known
? g a mod p)
(b ? g b mod p)
(a
g a
Bob
Alice
g b
K(ga) bg ab
K(gb) ag ab
Anyone else can compute g a g b g ab but
not g ab
18
cryptology

• Cryptology cryptography cryptanalysis.
• Cryptography devise cryptosystems.
• Cryptanalysis break cryptosystems.

19
Kerckhoff principle and attack levels

• Kerckhoff principle the cryptosystem is
  publicly known, but only the key is secret.
  Breaking a cryptosystem (i.e., cryptanalysis)
  means figuring out the key currently used.
• Attack levels
• Ciphertext-only the attacker possesses a string
  of ciphertext, y.
• Known plaintext the attacker possesses a string
  of plaintext, x, and the corresponding
  ciphertext, y.
• Chosen plaintext the attacker has obtained
  temporary access to the encryption machinery.
  Hence, he can choose a plaintext string, x, and
  construct the corresponding ciphertext string, y.
• Chosen ciphertext the attacker has obtained
  temporary access to the decryption machinery.
  Hence, he can choose a ciphertext string, y, and
  construct the corresponding plaintext string, x.

20
Internet security protocols

• The Internet has implemented a suite of security
  protocols combining secret-key, public-key,
  digital signature, message digest, etc.
• IPSec (IP security) i.e., IP layer / network
  layer
• SSL (Secure Socket Layer) TLS (Transport Layer
  Security) transport layer
• SSH (Secure Shell), SFTP, HTTPS, PGP (Pretty Good
  Privacy) application layer

21
IPSec key agreement
Crypto suites I support
Crypto suite I choose
ga mod p
Entity A
Entity B
gb mod p
gab mod pAlice, proof I am Alice
gab mod pBob, proof I am Bob
22
SSL position
Copied from http//developer.netscape.com/docs/man
uals/security/sslin/
23
SSL functionality

• Server authentication (by public certificate)
• Client authentication (Optional)
• Data encryption (by secret key system)
• Integrity protection by (MAC)

24
SSL handshake
I want to talk, ciphers I support, RC
Certificate (PS), cipher I choose, RS
Client
Server
SPS, keyed hash of handshake MSG
compute
compute
Kf(S,RC,RS)
keyed hash of handshake MSG
Kf(S,RC,RS)
Data protected by keys derived from K
There are total six keys, three keys (encryption
key, IV, integrity key) in each direction.