Security

1
Security Cryptography
2
Protection vs Security

• The protection mechanisms (ACLs, etc) discussed
  earlier assist us in preventing unauthorized
  access and use of computer resources
• what happens if an intruder bypasses the
  protection mechanisms?
• Cryptography can be used so that an intruder is
  unable to understand or use information obtained
  without authorization

3
Cryptography Terminology

• Plaintext (or cleartext)
• is the intelligible message
• Ciphertext
• is the unintelligible message
• Encryption and decryption
• Are the processes to convert between plaintext
  and ciphertext
• Key
• Is the parameter used in an encryption/decryption
  algorithm

4
Cryptography Terminology

• Cryptosystem
• A system for encryption/decryption of information
• Symmetric cryptosystem
• use the same key for both encryption and
  decryption
• Asymmetric cryptosystem
• use the different keys for encryption and
  decryption
• Cryptology
• the designing breaking of cryptosystems
• Cryptography
• the practice of using cryptosystems for
  confidentiallity of information
• Cryptoanalysis
• the breaking cryptosystems

5
Basic Structure of a Cryptosystem
Eve
Plaintext M
Side Information
Break
Bob
Alice
Plaintext M
Plaintext M
Encrypt
Decrypt
Ciphertext C
Encryption Key Ke
Decryption Key Kd
6
Basic Attacks to Cryptosystems

• Cryptosystem attacks are classified based on the
  amount of side information available to an
  intruder
• Attack classification
• ciphertext-only
• intruder only has access to the ciphertext
• known-plaintext
• intruder has access to the ciphertext and
  considerable amount of plaintext
• chosen-plaintext
• intruder has access to a chosen plaintext and its
  corresponding ciphertext

7
Design Principles for Cryptosystems

• Shannons principles
• Diffusion principle
• spread the correlations and dependencies among
  key and words over the text as much as possible
  in order to maximize the length of plaintext
  needed to break the system
• Confusion principle
• change a piece of information so that ciphertext
  has no obvious relationship with plaintext
• Computational Intractability principle
• every algorithm for determining a key needed to
  break cryptosystem is believed to require
  exhaustive search of a very large search space

8
A Taxonomy of Cryptosystems

• Conventional systems
• Modern systems
• private key systems
• public key systems

9
Conventional Cryptosystems

• Conventional cryptosystems are based on
  substitution ciphers
• Caesars cipher
• E(M) (M k) modulo 26
• where M is a letter and k3 is the key
• Simple substitution cipher
• E(M) KeyM
• where Key is an arbitrary permutation of a single
  alphabet
• Vigenere cipher
• choose N simple substitution ciphers and encrypt
  the jth letter using the (j mod N) substitution
  cipher
• One-time pad
• encrypt by Xoring message with a key, whose size
  equals the size of the message

10
DES

• The Data Encryption Standard (DES) is a modern
  private-key cryptosystem
• It is a block cipher that uses two basic
  operations
• permutation,
• and substitution
• It breaks a message in 64-bit blocks and
  encrypts/decrypts each block individually
• It uses a 56-bit secret key, which is expanded to
  64-bits using parity bits

11
DES

• Has three stages
• plaintext block undergoes an initial permutation
  IP
• permuted block undergoes for 16 times a complex
  transformation
• A block at the ith iteration is broken into two
  32-bit blocks Li Ri
• transformed block undergoes the inverse IP of
  the permutation IP at the 1st stage
• DES transformation in the ith iteration,
  i1,2,,16
• K i Phi(Key, i) 48-bit key of ith iteration
• L i Ri-1
• R i L i xor F (Ri-1 , K i )

12
DES

• Function F does the following
• expands R i into a 48-bits quantity E(R i) by
  permuting and duplicating some bits of R
• Xors E(R i) with K i and partitions the result
  into eight 6-bit blocks Q1, Q2,,Q8
• passes each Q j 6-bit block through a separate
  6-to-4 bit substitution box
• concatenates all transformed 4-bit Q j blocks and
  then permutes them

13
DES

• Decryption is done by executing the three stages
  in reverse order and each time using the inverse
  function/operation
• permute cipher text using IP
• undo the 16 transformations, for i16,15,,1,
  using the same keys K1, K2, , K16
• R i-1 R i
• L i-1 R i xor f ( L i , K i )
• permute transformed ciphertext with IP
• For added security, block chaining can be used
• each plaintext block is Xored with the ciphertext
  of the previous plaintext block
• triple encryption (DES does not form a group)
• Rijdael new private key standard

14
Public-Key Cryptosystems

• Private key cryptosystems requires a secure
  mechanism for distributing the private keys to
  communicating parties
• Diffie and Hellman proposed public key
  cryptosystems
• public key systems make the encryption key
  publicly available and keep the decryption key
  secret
• public key systems are based on the computational
  intractability principle (using problems such as
  factoring primes, discrete logarithm, knapsack,
  etc)

15
Public Key Cryptosystems

• public key systems satisfy the following
• DSK(EPK(M)) M for every message M
• The encryption and decryption functions E and D
  are computationally efficient
• Knowledge of E, D, and PK (public key) does not
  compromise SK (secret key)
• DPK(ESK(M)) M for every message M, if message
  singing/verification is desired

16
Trapdoor One-Way Functions

• One-way functions F
• F is invertible and easy to compute
• inverting F is computationally intractable, ie
  given y finding x such that yF(x) is believed to
  be computationally infeasible
• Trapdoor one-way functions F
• yF(x) can be solved efficiently provided some
  secret information for F is available
• Diffie and Hellman suggested that one way to
  implement public key systems is to use trapdoor
  one-way functions

17
Number Theory Background

• GCD Recursion Theorem the Extended Euclids
  algorithm

18
Number Theory Background

• Eulers phi function, Eulers and Fermats
  Theorems

19
Number Theory Background

• The Chinese Remainder Theorem
• Origins
• Sun-Tsu, circa 100 A.D. considered the problem of
  finding those integers x that leave remainders 2,
  3, and 2 when divided by 3, 5, and 7 respectively
  (which are of the form x23105k).
• Its essence

20
Number Theory Background

• A corollary of the Chinese Remainder Theorem
  states that

21
RSA

• Rivest, Shamir, and Adleman introduced the RSA
  public-key cryptosystem based on Diffie and
  Hellman
• RSA works as follows

22
RSA

• RSAs encryption function is
• EPK(M) Me mod n
• where PK(e,n)
• RSAs decryption function is
• DSK(M) Md mod n
• where SK(d,n)
• these two encryption/decryption functions satisfy
• DSK(EPK(M)) M
• DPK(ESK(M)) M
• can be computed efficiently given PK or SK
• knowledge of PK does not compromise SK

23
RSA

• Correctness of RSA is based on
• Fermats theorem and on the Chinese Remainder
  Theorem
• Example values for RSA
• choose p5 and q11
• set n55 and N40
• choose d23
• compute e7 using the extended Euclid algorithm
• encrypt M8 to 2 using repeated squaring

24
RSA

• A more realistic example set of values for RSA
• (courtesy of Prof. Stephens)
• n 2419753086 4197530864 2125371358 0246913580
  2471460971 7
• p 1555555555 5555555555 560261
• q 1555555555 5555555555 560497
• e 512896171
• d 1955459782 2571725357 3495557871 3933814929
  3601459917 1
• sqrt(n) approximately 1555555555 5555555555
  560378
• number of positive integers lt n that are relative
  prime to n is equal to phi(n)
• phi(n) 2419753086 4197530864 2125340246
  9135802469 1360348896 0

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Authentication

• Objective
• verify the identity of communicating entities
• Authentication services
• interactive communication (synchronous)
• one-way communication (asynchronous)
• signed communication (verifiable conversation by
  third party)
• Potential threats
• altering messages
• replaying old messages
• denial of service
• interference with ongoing communication
• impersonation

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Interactive Communication Protocols

• Require an authoritative Authentication Server
  (AS) for securely distributing conversation keys
• Each user registers its secret key with the AS,
  which is shared only between the AS and the user,
  and their public key if any
• Requirements use case
• Alice wants to communicate with Bob so that
• the message is intelligible to Bob, but not Eve
• it should be evident that the message was sent by
  Alice, and that is not a replay of an older
  message from Alice

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Interactive Communication with Private Key Systems

• Alice wants to converse with Bob
• Denning-Saccos modification to handle
  compromised conversation keys
• A message is not a reply attack if
  LocalClock-TltLocalClocks disrepancy from ASs
  clock plus the estimated maximum network delay

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Interactive Communication with Public Key Systems

• Alice wants to communicate with Bob

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One-Way Communication with Private Key Systems

• Alice wants to email message M to Bob
• Bob should be able to authenticate integrity of
  Alices message even if Alice is not currently
  available
• Eve should not be able to impersonate Alice

Protocol is succeptible to playback attacks
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One-Way Communication with Public Key Systems

• Alice wants to email message M to Bob

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Digital Signatures

• Must satisfy the following
• a user can not forge signatures
• sender of signed message can not deny the
  validity of his signature
• receipient can not modify the signature of a
  signed message

32
Digital Signatures using Private Key Systems

• Alice wants to sign a message to be sent to Bob

33
Digital Signatures using Public Key Systems

• Alice wants to sign a message to be sent to Bob

34
Kerberos

• An authentication system for an open network
  computing environment where users machines are
  under their complete control and can not be
  trusted to identify users to network services
• Consists of
• Client (C)
• Kerberos Server (K)
• Ticket Granting Server (TGS)
• Server (S)
• User (U)

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Kerberos Phase I Getting the Initial Ticket

• User provides the Client machine his/her identity
  
• Client sends to Kerberos server K the msg
• Kerberos server K
• Client upon receipt of msg

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Kerberos, Phase II Getting a Server Ticket

• User/Client wants to use a network service S
• Ticket Granting Server TGS
• Client upon receiving msg from TGS

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Kerberos, Phase III Requesting a Service

• Client requests service from server S
• Service server S upon receipt of the msg