Key Management Network Systems Security

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Key Management Network Systems Security

• Mort Anvari

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Key Management

• Asymmetric encryption helps address key
  distribution problems
• Two aspects
• distribution of public keys
• use of public-key encryption to distribute secret
  keys

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Distribution of Public Keys

• Four alternatives of public key distribution
• Public announcement
• Publicly available directory
• Public-key authority
• Public-key certificates

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Public Announcement

• Users distribute public keys to recipients or
  broadcast to community at large
• E.g. append PGP keys to email messages or post to
  news groups or email list
• Major weakness is forgery
• anyone can create a key claiming to be someone
  else and broadcast it
• can masquerade as claimed user before forgery is
  discovered

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Publicly Available Directory

• Achieve greater security by registering keys with
  a public directory
• Directory must be trusted with properties
• contains name, public-key entries
• participants register securely with directory
• participants can replace key at any time
• directory is periodically published
• directory can be accessed electronically
• Still vulnerable to tampering or forgery

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Public-Key Authority

• Improve security by tightening control over
  distribution of keys from directory
• Has properties of directory
• Require users to know public key for the
  directory
• Users can interact with directory to obtain any
  desired public key securely
• require real-time access to directory when keys
  are needed

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Public-Key Authority
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Public-Key Certificates

• Certificates allow key exchange without real-time
  access to public-key authority
• A certificate binds identity to public key
• usually with other info such as period of
  validity, authorized rights, etc
• With all contents signed by a trusted Public-Key
  or Certificate Authority (CA)
• Can be verified by anyone who knows the CAs
  public key

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Public-Key Certificates
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Distribute Secret KeysUsing Asymmetric Encryption

• Can use previous methods to obtain public key of
  other party
• Although public key can be used for
  confidentiality or authentication, asymmetric
  encryption algorithms are too slow
• So usually want to use symmetric encryption to
  protect message contents
• Can use asymmetric encryption to set up a session
  key

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Simple Secret Key Distribution

• Proposed by Merkle in 1979
• A generates a new temporary public key pair
• A sends B the public key and As identity
• B generates a session key Ks and sends encrypted
  Ks (using As public key) to A
• A decrypts message to recover Ks and both use

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Problem with Simple Secret Key Distribution

• An adversary can intercept and impersonate both
  parties of protocol
• A generates a new temporary public key pair KUa,
  KRa and sends KUa IDa to B
• Adversary E intercepts this message and sends KUe
  IDa to B
• B generates a session key Ks and sends encrypted
  Ks (using Es public key)
• E intercepts message, recovers Ks and sends
  encrypted Ks (using As public key) to A
• A decrypts message to recover Ks and both A and B
  unaware of existence of E

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Distribute Secret KeysUsing Asymmetric Encryption

• if A and B have securely exchanged public-keys

?
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Problem with Previous Scenario

• Message (4) is not protected by N2
• An adversary can intercept message (4) and replay
  an old message or insert a fabricated message

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Order of Encryption Matters

• What can be wrong with the following protocol?
• A?B N
• B?A EKUaEKRbKsN
• An adversary sitting between A and B can get a
  copy of secret key Ks without being caught by A
  and B!

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Diffie-Hellman Key Exchange

• First public-key type scheme proposed
• By Diffie and Hellman in 1976 along with advent
  of public key concepts
• A practical method for public exchange of secret
  key
• Used in a number of commercial products

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Diffie-Hellman Key Exchange

• Use to set up a secret key that can be used for
  symmetric encryption
• cannot be used to exchange an arbitrary message
• Value of key depends on the participants (and
  their private and public key information)
• Based on exponentiation in a finite (Galois)
  field (modulo a prime or a polynomial) - easy
• Security relies on the difficulty of computing
  discrete logarithms (similar to factoring) hard

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Primitive Roots

• From Eulers theorem aø(n) mod n1
• Consider am mod n1, GCD(a,n)1
• must exist for m ø(n) but may be smaller
• once powers reach m, cycle will repeat
• If smallest is m ø(n) then a is called a
  primitive root
• if p is prime, then successive powers of a
  generate the group mod p
• Not every integer has primitive roots

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Primitive Root Example Power of Integers Modulo
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Discrete Logarithms

• Inverse problem to exponentiation is to find the
  discrete logarithm of a number modulo p
• Namely find x where ax b mod p
• Written as xloga b mod p or xinda,p(b)
• If a is a primitive root then discrete logarithm
  always exists, otherwise may not
• 3x 4 mod 13 has no answer
• 2x 3 mod 13 has an answer 4
• While exponentiation is relatively easy, finding
  discrete logarithms is generally a hard problem

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Diffie-Hellman Setup

• All users agree on global parameters
• large prime integer or polynomial q
• a which is a primitive root mod q
• Each user (e.g. A) generates its key
• choose a secret key (number) xA lt q
• compute its public key yA axA mod q
• Each user publishes its public key

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Diffie-Hellman Key Exchange

• Shared session key for users A and B is KAB
• KAB axA.xB mod q
• yAxB mod q (which B can compute)
• yBxA mod q (which A can compute)
• KAB is used as session key in symmetric
  encryption scheme between A and B
• Attacker needs xA or xB, which requires solving
  discrete log

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Diffie-Hellman Example

• Given Alice and Bob who wish to swap keys
• Agree on prime q353 and a3
• Select random secret keys
• A chooses xA97, B chooses xB233
• Compute public keys
• yA397 mod 353 40 (Alice)
• yB3233 mod 353 248 (Bob)
• Compute shared session key as
• KAB yBxA mod 353 24897 160 (Alice)
• KAB yAxB mod 353 40233 160 (Bob)

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Next Class

• Hashing functions
• Message digests