# The Dual Receiver Cryptosystem a by pengtt

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```									The Dual Receiver Cryptosystem
and its Applications

Presented by Brijesh Shetty
Overview
Concept

 Interesting Applications
 Combined Cryptosystem
 Useful Puzzle Solving

 Encryption Scheme

 Ciphertext can be decrypted by two

 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.
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
- The Scheme

 Some Definitions

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
- The Scheme

 Some Definitions

Cryptosystem scheme
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
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

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

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

 Some Definitions

Cryptosystem scheme
Overview
Concept

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

 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?

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
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)
]
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 

```
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