Docstoc

The Dual Receiver Cryptosystem a

Document Sample
The Dual Receiver Cryptosystem a Powered By Docstoc
					The Dual Receiver Cryptosystem
and its Applications




           Presented by Brijesh Shetty
Overview
 Dual Receiver Cryptosystem –
  Concept

 Interesting Applications
     Combined Cryptosystem
     Useful Puzzle Solving
Dual Receiver Cryptosystem

 Encryption Scheme

 Ciphertext can be decrypted by two
  independent receivers!

 Bilinear Diffie Hellman Assumption
  (based on elliptic curves)
Elliptic Curve based Discrete Log
problem
 Given Y = k . P and Y,P
     (i.e P added to itself k times)
  Find k ????
 (P,P)--- g
   (Y,P)--- h
 By definition of Bilinear Curve, we get
     (Y,P)=(kP,P)=(P,P)k=gk
       h = gk    [since (aP,bQ)=(P,Q)ab]
“ Key Escrow ”    (in the context of Dual receiver)




 An arrangement where keys needed
  to decrypt encrypted data must be
  held in escrow by a third party.

 Eg. Govt. agencies can use it to
  decrypt messages which they suspect
  to be relevant to national security.
Dual Receiver Cryptosystem
     A

                 Ciphertext C
                                                 Decrypts to m


                                         B
  Message m

 Encrypt using
 public keys of
                                              B or also
  C B and not learn about the private keys of C can A !! decrypt!
    does C

                                          C
Dual Receiver Cryptosystem
- The Scheme


 Some Definitions

 (Semantically secure) Dual Receiver
  Cryptosystem scheme
Definitions   (Randomised algorithms)



 Key Generation algorithm
    K(k) = (e,d) & (f,g)



 Encryption algorithm
    E e,f (m) = c
Definitions   (contd..)



 Decryption Algorithm D
    Dd,f (c) = m



 Recovery Algorithm R
    Re,g (c) = m
Dual Receiver Cryptosystem
- The Scheme


 Some Definitions

 (Semantically secure) Dual Receiver
  Cryptosystem scheme
   Semantically secure Dual Receiver
   Cryptosystem
         A

                                            (x, xP)
              (u1,u2,u3)              B
Message m                                 private
Random r


                                            (y, yP)
                                      C

  Hx is a hash fn associated with public key xP
   Semantically secure Dual Receiver
   Cryptosystem
       A                          B

                                      (x, xP)

Message m
Random r u1 = rP
           u2 = yP
           u3 = m+ Hx(<xP,yP>r)


                                       (y, yP)
                                  C
Decryption


<u1,u2>x = <rP,yP>x
        = <xP,yP>r         B
        = <P,P>xyr


 U3 + Hx(<xP,yP>r) =   m
Recovery (Second Receiver)


<u1,xP>y = <rP,xP>y
        = <xP,yP>r
         = <P,P>xyr
                           C


 U3 + Hx(<xP,yP>r) =   m
Dual Receiver Cryptosystem
- The Scheme


 Some Definitions

 (Semantically secure) Dual Receiver
  Cryptosystem scheme
Overview
 Dual Receiver Cryptosystem –
  Concept

 Interesting Applications
     Combined Cryptosystem
     Useful Puzzle Solving
Combined Cryptosystem
 We combine using a single key x

     Dual Receiver Encryption

     Signature
Signature (in Combined scheme)


 Same key x .       Hash   I:{0,1}n -> G1
     Sign the hash


    A        σ = x . I(m)
                                 B
Message m
Verification..

B has m, σ
                                   B
            Verify
 <P,   σ   > = <xP, I(m)>



 If they are same both must be equal <P,I(m)>x
Combined Cryptosystem

 What is so special?

 Dual receiver encryption facilitates
  escrow of the decryption capability &
  non escrow of the signature capability
  using the same key!!
 The security of either of the schemes
  is not compromised
Overview
 Dual Receiver Cryptosystem –
  Concept

 Interesting Applications
     Combined Cryptosystem
     Useful Security Puzzles
Useful Security Puzzles
 Application Areas
   When Server wants to rate-limit the
    clients (against DOS attacks)
   Lighten the server’s computational
    burden


 Example : File Server
 File Server (Security Puzzle)
                       Server
         File
         Abcde
                     Ks Eke,Ka(Ks)
          ……




Client             [   ¤¥§~¶
                        …….          ]
                               (C1,C2)



  STORING FILE
  File Server … (Request File)
    Decryption..
 Computation intensive       [  ¤¥§~¶
                                 …….   (C1,C2)
                   Dual Receiver Encrytpion
                                               ]
                                   G, F are hashes
              XOR and hash
                                      Random p
Client                               C1 = Eke,Ka(p)
                                    u1 = Ks+ G(p)
                                  u2 = F(p,Ks,C1,u1)
              C1, Pa                 C2 = [u1,u2]

Compute
DPa,Ke(C1)      TD1                 G(TD1)+u1 = m
                                        Check
                                    u2=F(p,m,c,u1)
Thank you 

				
DOCUMENT INFO