Security

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Security CryptoLandscape overview
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What is Cryptography?

• It all started with
• Encryption / Decryption

- plaintext
attack at midnight
- ciphertext
buubdl bu njeojhiu
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Encryption / Decryption (cont.)
ciphertext msg
decoder
(ciphertext in - plaintext out)
encoder
(plaintext in - ciphertext out)
cmb-cmb
eavesdropper
(should understand nothing about the msg)
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Other scenarios/tools

• Key exchange
• Authentication
• public
• private
• Signatures
• Hashing
• Certificates, PKI

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Key exchange

• Alice and Bob want to establish a shared secret
  (key) when other people (eavesdroppers) are
  listening

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Authentication
M
Alice sends a msg to Bob, who wants to be sure
the msg is really from Alice
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Signatures
(M, SigM)
SAlice
SigM Sign(M, SAlice )
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Authentication public

• checks
• contracts
• love letters ???

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Public Key Signatures
PAlice

• Public Key
• Secret Key

Verify(M, SigM, PAlice )
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Authentication private
SAlice
Message Authentication Code (MAC) Sign(M, SAlice
)Hash(M, SAlice )
Verify(M, SigM, SAlice ) Check SigM
Sign(M, SAlice )
MAC Shared Secret Sig Symmetric Sig
(SignVerify)
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Hashing
Hash
y
x1
collision
x2

• Crypto Hash
• collisions may exist, but
• are hard to find
• Given y hard to find x, s.t. Hash(x)y

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Another setting
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Applications

• Military applications
• Love letters
• Banking transactions
• Television Broadcasts
• Internet

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Real Life e-thieves

• E-thieves (pirates/hackers)
• Recreational (do it for fun - e-hooligans)
• Professionals
• Defense
• Cost time aspects
• Periodic renewals
• Multiple defense lines
• Obscurity vs. security (or security by obscurity)
• Recovery from security breaches

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No Ultimate solution!

• we are at an on-going electronic warfare with
  e-thieves

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Encryption/Decryption -more details

• Outline
• Block vs. Stream ciphers
• Symmetrical vs. Asymmetrical (public key)
• Tool Pseudo-Random Number Generators
• Complexity (what is hard?)
• Public Key Crypto
• Diffie-Hellman
• Rabins encryption
• RSA

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Block vs. Stream Ciphers

• Cipher Encoder or Encryption/Decryption scheme
• Stream cipher encodes/decodes char by char
• Block cipher encodes/decodes block by block
• Stream cipher Block cipher with block size of 1
  char (state)

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Symmetric Asymmetric schemes

• Symmetric
• decryption as easy as encryption (and vice versa)
• i.e. if you can encrypt then you can decrypt
• (and vice versa)
• (DES is a symmetric block cipher)
• Asymmetric
• may not be able to decrypt even if can encrypt
• (and vice versa)
• e.g. RSA

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Symmetric cipher - example

• Caesar's cipher
• the letters of the alphabet are shifted ()
• e.g. a is replaced with b, b with c,
  etc.
• so msg attack at midnight is encrypted as
  buubdl bu njeojhiu
• () the shift can be by one (as in the example)
  or more
• encryption and decryption are equally easy (too
  easy, in fact)

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One-time pad

• For each character of the future msg indicate the
  shift

pad
?
msg (plain)
ciphertext (encrypted msg)
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One-time random pad (cont.)

• Symmetric
• Pad is selected at random
• Perfectly secure, but...
• One time only
• so sending the pad is just as hard as sending
  the msg

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Pseudo-random pad

• Pseudo-random bit string (PRBS) generator
• PRBS Hard to guess a bit (after seeing many
  others)

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Complexity what is hard?

• measure hardness in terms of size of input
• easy polynomial hard exponential
• Easy problems
• Finding max of n numbers - O(n)
• Sorting n elements - O(n lg n)
• Hard problems
• Factoring N (n bits long) -
• current best (?)

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Other hard problems

• Let Np?q, where p,q are large primes
• Square root mod N
• given x,N find y mod N, i.e. y2x mod N
• (equivalent to factoring N)
• Discrete log
• given b,N and x, find y
• How hard are these problems really?
• One-way functions easy to compute hard to invert
• Trap-door a secret making inverting a owf easy

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Public-Key Crypto

• Key exchange - Diffie-Hellman
• PK Encryption - Rabin, RSA
• e-Signatures - Rabin, RSA ElGamal (a la
  DH) DSA Fiat-Shamir

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Diffie-Hellman key exchange
p, g
Alice
Bob
a
b
mb? gbmod p
ma? gamod p
ma
mb
mbamod p
mabmod p
gabmod p
shared secret key!
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Rabins scheme

• to encrypt msg m simply square it mod N
• if p,q (such that p?qN) are known, then
  decryption (finding m given x) is easy
• (using Chinese Reminder Theorem)

mod N
ciphertext
plaintext
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RSA

• Let Np?q, and find e,d such that
• Encryption
• Decryption

plaintext
ciphertext
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Public Key Cryptography

• Encryption and Decryption are different
• i.e. use different keys (asymmetric)
• RSA
• Public N,e (needed to encrypt)
• Private d (needed to decrypt,
• can be computed from p,q)
• Rabins
• Public N
• Private p,q

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Identification, Authentication, Signature schemes

• Signature sSI(m) of a msg m
• only I can sign, i.e. compute s, from I and m
• given s,I, and m, everyone can verify that
  sSI(m)
• Message Authentication
• like Signature, but only the receiver of the msg
  is required to be able to verify it
• Identification
• only I can prove that he is I

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Identification, Authentication, Signature schemes
(cont.)

• Signature can be used for Authentication
• Signature and Authentication can be used for
  Identification
• use interaction
• two players
• Prover P - e.g. user, who wants to prove that he
  is I
• Verifier V - e.g. wants to verify that P is
  really I

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Identification (cont.)

• must consider all the scenarios
• both P and V are honest
• both P and V are dishonest
• V is honest but P is dishonest
• P is honest, but V is dishonest
• note an eavesdropper (observer) should learn
  little from witnessing the P-V dialog
• usual password scheme - bad!

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Fiat-Shamir Identification scheme(simplified)

• Let Np?q, where p,q are large primes
• using p,q, compute s, such that s2 I 1 (mod N)
• public (P,V have) N (and I)
• private (only I has) s
• also, production center has p,q

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Fiat-Shamir (cont.)
P (user)
V (e.g., system)
N, I, s
N
pick random r set xr2 mod N
I,x
query 0 1
check r2x mod N (rs)2Ix mod N
r r?s modN
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Fiat-Shamir (cont.)

• Proof (of P knowing s)
• after k rounds the probability of mistake (i.e. P
  cheating without being caught) is (1/2)k
• Zero-Knowledge
• if query is known in advance
• for query0, select r, and xr2 mod N
• for query1, select z, and xz2I mod N
• (z pretends to be rs mod N)

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Security of Fiat-Shamir

• Relies on
• hardness of factoring
• an algorithm cracking Fiat-Shamir yields an
  algorithm for factoring N
• randomness
• of r for Zero-Knowledge
• of query - to prevent P from cheating

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Summary

• We are in a continuous chess game against
  e-thieves
• Cryptography provides a wide array of ideas and
  tools
• Customization of these tools is needed
• Multiple lines of defense are important (i.e.
  cannot rely on any single tool)