Basic cryptography

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Basic cryptography
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Basic cryptography

• Pseudorandom numbers and sequences.
• Encryption and Decryption.
• Symmetric Encryption.
• Block ciphers.
• Stream ciphers.
• Asymmetric Encryption.
• Hash functions.
• Message Digest.
• Digital signature.
• Dual Signatures.
• Blind Signatures.
• Digital Certification.
• Attacks on encryption schemes.
• Attacks on protocols.

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Pseudorandom numbers and sequences

• Random number generation is an important
  primitive in many cryptographic mechanisms.
• In cryptographic applications, one of the
  following steps must be performed
• From a finite set of n elements (e.g., 1,
  2,,n), select an element at random.
• From the set of all sequences (strings) of length
  m over some finite alphabet A of n symbols,
  select a sequence at random.
• Generate a random sequence (string) of symbols of
  length m over a set of n symbols.

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Pseudorandom numbers and sequences Cont

• Example (random sequence generator) To generate a
  random sequence of 0s and 1s
• A coin could be tossed with a head landing up
  recorded as a 1 and a tail as a 0.
• It is assumed that the coin is unbiased, which
  means that the probability of a 1 on a given toss
  is exactly 1/2.
• This method would be of little value in a system
  where random sequences must be generated quickly.

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Encryption and Decryption

• Plaintext is denoted by P.
• Ciphertext is denoted by C.
• The encryption function E operates on P to
  produce C.
• E(P) C
• The decryption function D operates on C to
  produce P.
• D(C)P.
• A cryptographic algorithm is also known as
  cipher.
• Modern ciphers uses key K in both encryption and
  decryption
• E(K, P)C
• D(K,C)P.

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Symmetric Encryption

• Both parties must first possess a copy of a
  single secret key SK.
• Most used symmetric encryption techniques
• DES, Triple DES, IDES and AES.
• Symmetric Encryption classification
• Stream ciphers.
• Block ciphers.

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Block ciphers

• A block cipher is an encryption scheme which
  breaks up the plaintext messages to be
  transmitted into strings (called blocks) of a
  fixed length, and encrypts one block at a time.
• Most well-known symmetric-key encryption
  techniques are block ciphers.
• Two important classes of block ciphers are
• Substitution ciphers are block ciphers which
  replace symbols (or groups of symbols) by other
  symbols or groups of symbols.
• Transposition ciphers which simply permutes the
  symbols in a block.

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Stream ciphers

• They are very simple block ciphers having block
  length equal to one.
• What makes them useful is the fact that the
  encryption transformation can change for each
  symbol of plaintext being encrypted.
• In situations where transmission errors are
  highly probable, stream ciphers are advantageous
  because they have no error propagation.
• They can also be used when the data must be
  processed one symbol at a time (e.g., if the
  equipment has no memory or buffering of data is
  limited)

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Asymmetric encryption

• Was developed to solve the problem of key
  distribution with symmetric encryption.
• Asymmetric encryption uses two keys, Pubic key PK
  which is published to everyone, and Secret
  (private) key SK which is never revealed.
• Most used Asymmetric techniques
• RSA and Elliptic curve.

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Asymmetric encryption Cont

• Formal description
• In public-key encryption systems each entity A
  has a public key e and a corresponding private
  key d.
• In secure systems, the task of computing d given
  e is computationally infeasible.
• The public key defines an encryption
  transformation Ee, while the private key defines
  the associated decryption transformation Dd.
• Any entity B wishing to send a message m to A
  obtains an authentic copy of As public key e,
  uses the encryption transformation to obtain the
  ciphertext c Ee(m), and transmits c to A.
• To decrypt c, A applies the decryption
  transformation to obtain the original message m
  Dd(c).

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Symmetric-key vs. public-key cryptography

• Advantages of symmetric-key cryptography
• Can be designed to have high rates of data
  throughput.
• Keys for symmetric-key ciphers are relatively
  short.
• symmetric-key ciphers can be composed to produce
  stronger ciphers. Simple transformations which
  are easy to analyze, but on their own weak, can
  be used to construct strong product ciphers.
• Disadvantages of symmetric-key cryptography
• In a two-party communication, the key must remain
  secret at both ends.
• In a large network, there are many key pairs to
  be managed. Consequently, effective
  Key-management requires the use of an
  unconditionally trusted third party.

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Symmetric-key vs. public-key cryptography Cont

• Advantages of public-key cryptography
• Only the private key must be kept secret.
• The administration of keys on a network requires
  the presence of only a functionally trusted third
  party, which might only be required in an
  off-line manner, as opposed to in real time.
• Depending on the mode of usage, a private
  key/public key remain unchanged for considerable
  periods of time, e.g., many sessions (even
  several years).
• The key used to describe the public verification
  function is typically much smaller than for the
  symmetric-key counterpart.
• In a large network, the number of keys necessary
  may be considerably smaller than in the
  symmetric-key scenario.
• Disadvantages of public-key encryption
• Throughput rates for the most popular public-key
  encryption methods are several orders of
  magnitude slower than the best known
  symmetric-key schemes.
• Key sizes are typically much larger than those
  required for symmetric-key encryption.
• No public-key scheme has been proven to be
  secure. The most effective public-key encryption
  schemes found to date have their security based
  on the presumed difficulty of a small set of
  number-theoretic problems.

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Hash functions

• A hash function is a computationally efficient
  function mapping binary strings of arbitrary
  length to binary strings of some fixed length,
  called hash-values.
• For a hash function which outputs n-bit
  hash-values (e.g., n 128 or 160) and has
  desirable properties, the probability that a
  randomly chosen string gets mapped to a
  particular n-bit hash-value is 2n.
• The basic idea is that a hash-value serves as a
  compact representative of an input string.
• The most common cryptographic uses of hash
  functions are with digital signatures and for
  data integrity.

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Message Digest

• Message Digesting or Hashing is a technique used
  to insure integrity of the message (to find out
  if the message has been changed). Hash algorithms
  are one way function.
• MAC Message Authentication Code, is generated as
  its faster to encrypt the small hash then the
  complete message.
• MD5 and SHA are the most used hash functions.

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Digital signature

• The purpose of DS is to bind an entity identity
  to a message.
• Signer is the entity who signed the message.
• Verifier is the entity who receives the message
  and verify the DS.
• DS requirements
• Data origin authentication of the signer.
• Non-repudiation.

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Digital Signature Cont

• Digital signatures in practice
• Should be easy to compute by the signer (the
  signing function should be easy to apply)
• Should be easy to verify by anyone (the
  verification function should be easy to apply)
• Should have an appropriate lifespan, i.e., be
  computationally secure from forgery until the
  signature is no longer necessary for its original
  purpose.

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Dual Signatures

• Dual signatures are used to link an identity with
  the content of a particular message.
• Used when a sender A wants to send 2 messages (m1
  and m2) to B (wants m1) and C (wants m2), while
  assuring both B and C that a second linked
  message exist.

M2
M1
Senders SK
Hash
Hash
Dual Sig
Digest1
Digest2
Hash
Sign
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Blind Signatures

• Its a method for allowing a person to sign a
  message without being able to see its content.
• Its like signing the outside of an envelope
  (which contain a carbon paper) with the signature
  going through the envelop and signing the letter
  inside it.

Message
Envelope containing the Message and carbon paper
Blinding process
Sent to signer
Envelope removed
Signed envelope
Signed Message
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Digital Certification

• Digital Certificates are the electronic
  counterparts to passports or membership cards.
• Digital Certificate used to prove identity.
• Digital Certificates, bind an identity to a pair
  of electronic keys that can be used to encrypt
  and sign digital information.
• A Digital Certificate is issued by a
  Certification Authority (CA) and signed with the
  CA's private key.
• Certification Authorities
• CA are trustworthy persons or organizations that
  issue certificates to applicants whose identity
  has in some way been verified by the CA.
• Certificates are verified through a hierarchy of
  these CAs. Each certificate is linked to the
  certificate of the CA that signed it.
• By following this hierarchy, or verification
  path, to a known, trusted CA, you can be assured
  that a certificate is valid.

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Digital Certification Cont

• The typical implementation of digital
  certification involves the following process
• Alice sends a certification request containing
  her name and her public key to a CA.
• The CA creates a special message (m) from Alice's
  request, which constitutes most of the data in
  the certificate.
• The CA signs the message with its private key,
  obtaining a separate signature (sig) in the
  process.
• Then the CA returns the message m and the
  signature sig to Alice the two parts together
  form a certificate.
• Alice sends the certificate to Bob to convey
  trust in her public key.
• Bob verifies the signature sig using the CA's
  public key. If the signature is verified, he
  accepts Alice's public key.

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Digital Certification Cont

• A Digital Certificate typically contains the
• Owner's public key.
• Owner's name.
• Expiration date of the public key.
• Name of the issuer the CA that issued the
  Digital Certificate.
• Serial number of the Digital Certificate.
• Digital signature of the issuer.

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Attacks on encryption schemes

• The objective of the following attacks is to
  systematically recover plaintext
  fromciphertext,or even more drastically, to
  deduce the decryption key.
• A ciphertext-only attack is one where the
  attackers tries to deduce the decryption key or
  plaintext by only observing ciphertext. Any
  encryption scheme vulnerable to this type of
  attack is considered to be completely insecure.
• A known-plaintext attack is one where the
  attackers has a quantity of plaintext and
  corresponding ciphertext. This type of attack is
  typically only marginally more difficult to
  mount.
• A chosen-plaintext attack is one where the
  attackers chooses plaintext and is then given
  corresponding ciphertext. Subsequently, the
  attackers uses any information deduced in order
  to recover plaintext corresponding to previously
  unseen ciphertext.
• An adaptive chosen-plaintext attack is a
  chosen-plaintext attack wherein the choice of
  plaintext may depend on the ciphertext received
  from previous requests.

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Attacks on protocols

• The following is a partial list of attacks which
  might be mounted on various protocols.
• Known-key attack. In this attack an attacker
  obtains some keys used previously and then uses
  this information to determine new keys.
• Replay attack. In this attack an attacker records
  a communication session and replays the entire
  session at some later point in time.
• Impersonation. Here an attackers assumes the
  identity of one of the legitimate parties in a
  network.
• Dictionary. This is usually an attack against
  passwords. Typically, a password is stored in a
  computer file as the image of an unkeyed hash
  function. When a user logs on and enters a
  password, it is hashed and the image is compared
  to the stored value. An attacker can take a list
  of probable passwords, hash all entries in this
  list, and then compare this to the list of true
  encrypted passwords with the hope of finding
  matches.