Digital Signature

1
Digital Signature

• You want to sign a document.
• Three conditions.
• 1. The receiver can verify the identity of the
  sender.
• 2. The sender cannot later repudiate the content
  of the message.
• 3. The receiver cannot make the message up.

2
Using Public key / Private Key

• To send P, Alice send E_B(D_A(P)).
• Bob receives, decode it with his private key to
  get D_A(P), encode it with Alices public key to
  get P.

3
Digital Signature

• If Alice later denies she sent the message P, Bob
  can show P and D_A(P). A third party can check if
  he can get P with D_A(P) and Alices private key.
  If yes, Alice is lying because bob does not know
  Alices private key and have no way to make up
  D_A(P).

4
Is problem solved?

• How can Alice and Bob know each others public
  key?
• Can Alice send a message to Bob to ask him to
  send her pkB?
• No. Tom may intercept this message and return
  Alice a message with his key or some junk.

5
Solution?

• Ask someone with authority, say, C.
• Alice asks C can you tell me the public key of
  Bob?
• C replies Here you are, pkB.
• Will this work?
• No. Because how can Alice be sure that this
  message is from C and not from Tom?

6
Solution

• Because C is well-known, Alice remembers his
  public key.
• So when C sends Alice the reply, he signs it
  with his private key D_skC(pkB, I am sending you
  the public key of Bob as you requested).
• When Alice gets this message, she knows that this
  must be from C and can be trusted.

7
Problems?

• If everyone must contact C before the session
  begins, can C still handle it?
• Note that the RSA algorithm involves
  multiplications of large numbers and is slow.

8
Solution

• In fact, C does not have to answer the reply in
  real time.
• He can send Bob a certificate like D_skCI
  hereby certificate that this key
  belongs to Bob. Bobs IP address is and
  his email is _at__at__at__at_.
• Later, when Bob wants to prove he is indeed Bob,
  he can just present this to Alice.
• Actually, it is D_skCSHA_1I hereby certificate
  that this key belongs to Bob. Bobs
  IP address is and his email is _at__at__at__at_. and
  C is called Certificate Authority (CA).

9
Optimizations

• Still, signing all these certificates is too much
  for a single machine.
• There is PKI (Public Key Infrastructure) as a
  tree. You have a root, Regional Authorities, and
  CAs.
• A node certifies the nodes under it by signing.
• Chain of trust.