7/28/2019 Accelerating Greater Than-Strong Conditional Oblivious Transfer Multiparty Protocol Using GPU

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Accelerating the Greater Than-Strong Conditional Oblivious Transfer multiparty protocol using Graphics

Processing Units

Axel Y. Rivera, Prarthana L. Gowda, Nikhil Vidyadhar & Mary HallSchool of Computing, University of Utah

Abstract

Greater Than-Strong Conditional Oblivious Transfer (GT-SCOT) is a protocol

used for sharing data between two parties without revealing any private

information. Due to the large number of iterative operations computed

sequentially and the increase in size of the input, the algorithm is

computationally intensive, and hence cannot be used for large credentials or

secure database mining. This work presents an implementation ofGT-SCOT

using Graphics Processing Units (GPU) in order to accelerate the operations

and be able to handle large message sizes. Results show that GPU

implementation achieved a speed up of 7x for messages with size of 1024 bits

using 64 bits of encryption for each bit of the message.

Background

Oblivious Transfer (OT) Secure Multiparty Protocol:

Receiver (R) has a single input X; Sender (S) has two input strings s0 and s1S solves a predicate and sends the result to R

R just learns the secret of his choice linked to the result of computation, sx,

while sender S learns nothing

Homomorphism:

Uses Paillier encryption scheme, which is additively homomorphic

Additive properties:

Multiplicative properties:

Greater Than Conditional Oblivious Transfer (GT-SCOT) Protocol:

Uses the Greater Than (a b) inequality predicate to obliviously exchange

secrets between two users

Algorithm:

m1 and m2 are encrypted

m1 encrypted, m2 plaintext

m1 encrypted, m2 plaintext

m1 encrypted, k constant

$150 $200

100101101 1100100010

93578708349723

56430784933981

.

32677843402389

Operate on theencrypted values

usingHomomorphic

transformations

If > send S0

If 0

if (exponent & 1) equals 1:

result = (result * base) mod modulus

exponent := exponent >> 1

base = (base * base) mod modulus

return result

Arithmetic Operations+, -, x, /

Comparison operations