1. A Light-weight Oblivious Transfer Protocol Based on Channel Noise
Albert Guan

2. Outline Introduction Related Work Oblivious Transfer Protocol
Comparison
Conclusions

3. Introduction Design fundamental tools in cryptography Applications
Oblivious transfer (OT)
Applications
Secure multiparty computation
Private information retrieval

4. Secure Multiparty Computation
Millionaires problem
Suppose A has wealth x, B has wealth y
They want to know whom is richer
Without revealing their actual wealth
f (x, y) = 1, if x > y
f (x, y) = 0, otherwise

5. Secure Multiparty Computation
Parties P1,…,Pn
Parties Pi has private input xi
The parties want to jointly compute a function y = f(x1,…, xn)
Each parties Pi knows only y, nothing else.

6. Private Information Retrieval
Server holds x1, x2,…, xn
User wants to retrieve xi
Server can’t learn which xi is retrieved.
User only learn xi , nothing else.

7. Definition of the problem
Oblivious-Transfer (OT)
A: sender has two secrets m0 and m1
B: receiver has choice c
Goal:
B learns only mc,
A doesn’t know c

8. Security Models Computationally secure Statistically secure
Attacker does not have enough computing resources to break the system.
If quantum computers are available, most of the commonly used public key cryptosystems (e. g. RSA) can be broken.
Statistically secure
The probability for the attacker to break the system is negligible even with unlimited computing resources.
Our protocol is statistically secure.

9. Related Work Rabin's oblivious transfer protocol [Rabin 83]
Based on computational hard problem
Factoring large integer
Computationally secure
Heavy computation
long integer arithmetic

10. Related Work Erasure channel model [Imai et al. 06]
receiver either receives the bit or it was not received
Channel delay model [Cheong et al. 11]
Packets deliver with some delay
Security doesn’t depend on computationally hard problems

11. Our Work Design protocols
Security does not depends on computationally hard problems
Only need XOR and hash operations
Suitable for sensors or any devices with low computational power

12. Our Work Based on noise in communication channel
Channel noise is a good random source
Unpredictable

13. Binary Symmetric Channel
b, with prob. 1 – p BSp(b) = 1 – b, with prob. p Pr[b’ = 0 | b = 0] = Pr[b’ = 1 | b = 1] = 1 – p Pr[b’ = 1 | b = 0] = Pr[b’ = 0 | b = 1] = p

14. Oblivious Transfer (OT)
Beacon node
M =
A B
X = Y = Z
Z = { |1 ≤ i ≤ n/2} if |{i | }| < n/4
abort
, , {1, 2,…, n/2}
∩ = ϕ, | | = | | = n/4
Sc = {i | }

15. Oblivious Transfer (OT)
A B f, ,

16. Security of the oblivious transfer protocol
Theorem 1 A has no information about B’s choice c. Proof This follows from the fact that the sets and give A no information on c since the bits are flipped by the channel independently. The sender A cannot control the bits received by B.

17. Security of the oblivious transfer protocol
Theorem 2 B has no information about , the other secret he does not choose.
Proof since the secret correspond to the index set , which is contain some inconsistent parity bits, thus B can’t reconstruct the string

18. Comparison (oblivious transfer)
scheme Hao’s Cheong’s Crepeau’s Our Message 1 bit 1 bit 1 bit multi-bit Based on noise delay noise noise Overhead O(n²) O(n log n) O(n³) O(n) n : security parameter

19. Conclusions
Design efficient and lightweight protocols for oblivious transfer.
Security does not depends on computationally hard problems
Suitable for sensors or any devices with low computational power