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Fundamentals of Achieving Security

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Probability Theory Success, Failure, (In) Dependence, Distributions ... Theory. Shannon, Bell Labs, 1949. Mathematical Theory of Communication. Communication ... – PowerPoint PPT presentation

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Title: Fundamentals of Achieving Security


1
Fundamentals of Achieving Security
  • Karthik, MSyNC Lab

2
Goals of Security Mechanisms
  • Privacy Secrecy of data
  • Encryption
  • Authentication Validity of entities involved
  • Signatures, Passwords
  • Integrity Validity of data
  • Hash, CRC
  • Non-Repudiation Establishing source of data
  • Undeniable Signatures

3
Mathematical Ideas
  • Various fields of mathematics are used
  • Probability Theory Success, Failure, (In)
    Dependence, Distributions
  • Information Theory Entropy or Randomness, Ways to
    measure it,
  • Complexity Theory Algorithms, Running time,
    Complexity classes,
  • Number Theory Integers, Primes, Factoring,
  • Abstract Algebra Groups, Fields, Rings,

4
Shannons Theory
  • Shannon, Bell Labs, 1949
  • Mathematical Theory of Communication
  • Communication Theory of Secrecy Systems
  • Unconditional Security
  • If security is guaranteed even with unbounded
    resources
  • Provable Security
  • Prove security to some well studied problem that
    is considered difficult (NP complete).
  • Computational Security
  • The best known attack requires N operations where
    N is very large

5
Shannons Theory Contd
  • Perfect Secrecy
  • Prefect Secrecy is achieved if
  • i.e. if the probability of plaintext x is the
    same as its a posteriori probability given
    cipher text y
  • Key Equivocation
  • Measure of the information about the key revealed
    by the cipher text
  • Unicity Distance
  • Gives the amount of cipher text needed to reveal
    the key, for a language with redundancy D, the
    unicity distance U is

6
Basic Operations in Ciphers
  • Substitution
  • Substitute one plain text symbol with an unique
    cipher text letter
  • S-box, Non-Linear Codes
  • Permutation
  • Rearrange the plain text symbols
  • Permutation Functions, MDS Codes
  • Product Cryptosystems
  • Use Substitution and Permutation one after
    another
  • Fiestel Network, All Modern Ciphers

7
Avalanche Effect
  • This term was first coined by Fiestel to describe
    the result of substitution and permutation on the
    input plain text
  • As the plain text is processed by the cipher the
    each layer amplifies the pattern of 1s, the
    result is an unpredictable AVALANCHE that results
    in an average of half 0s and half 1s in the
    output
  • This makes the output of the cipher appear random
    and hides the distribution of the plain text and
    the Key in relation to the cipher text.

8
Effect of Compression
  • Compression reduces the redundancy
  • This makes the distribution of the plain texts in
    the source more even. Thus reducing the
    information leaked in each cipher text block is
    reduced.
  • Compression increases H(P) this make guessing the
    key more difficult

9
Any New Ideas ?
  • Which source coding techniques can be useful in
    providing security

10
Use of Channel Coding In Cryptography
  • Channel Coding has been used in several different
    scenarios to provide security
  • Examples
  • Encryption
  • McEliese Cipher
  • Secret Error Control Coding
  • Signing
  • Ximmei Scheme
  • Authentication
  • Aumann and Rabin Scheme

11
Reason for using Channel Codes
  • Usually both security and channel coding is
    needed by applications
  • Wireless applications
  • Channel codes may be good building blocks of
    ciphers
  • Would reduce hardware costs
  • Some similar applications already exist
  • MACS and ECC both detect errors

12
Usage of Channel Codes in Security machanizms
  • Difficulty in decoding a General Block Code
  • The problem of decoding an arbitrary code is
    considered to be NP hard. This property is used
    as follows
  • Select a good linear code
  • Keep the generator polynomial of the code secret
  • Encode the message to be sent
  • In McEliese System

13
Other Techniques
  • Burst Error Correction Codes
  • Use in Authentication
  • Signing

Problems In using Channel Codes
  • Adds redundancy
  • Codes vary according to the medium used
  • Simple combinations are not secure

14
Use of Codes in Current Ciphers
  • Non-linear Codes as S-boxes
  • S-boxes are a very important part of modern block
    and stream ciphers.
  • Provide non-linearity and help defend against
    differential and linear cryptanalysis.
  • Properties needed are Non-linearity, resilience
    and auto-correlation

15
MDS Codes in Mix-Column of AES
  • The Mix-Column operation of AES (rijndael) has
    been designed based on MDS codes.
  • The security is measured using a term called
    branch number. This is the measure of active
    bytes after each round.

16
Ideas on Applying Channel codes ?
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