Blockchain-Based Secure Outsourcing of Polynomial Multiplication and Its Application in Fully Homomorphic Encryption

Algorithm 6

Secure outsourcing of polynomial multiplication.

Input: a,b
Output:
(1)	function DISCRETE FOURIER TRANSFORM FOR RESERVED VECTOR (DFTRV) (r, i)
(2)	the length of r
(3)
(4)
(5)	for
(6)
(7)	end for
(8)	return
(9)	end function
(10)	function INVERSE DISCRETE FOURIER TRANSFORM FOR RESERVED VECTOR(IDFTRV) (r, i)
(11)	the length or r
(12)
(13)
(14)	for
(15)
(16)	end for
(17)	return
(18)	end function
(19)	The user picks random parameters and generates
(20)
(21)
(22)	The user calls TASK UPLOAD locally and uploads to the smart contract;
(23)	The smart contract calls TASK ALLOCATION and sends vectors in to nodes;
(24)	The computational nodes compute and call RESULT UPLOAD;
(25)	The smart contract calls RETURN RESULT;
(26)	The user computes and verifies equations (3) and (4) locally;
(27)	The user computes
(28)	The user generates calls TASK UPLOAD locally and uploads to the smart contract;
(29)	The smart contract calls TASK ALLOCATION and sends vectors in to nodes;
(30)	The computational nodes compute and call RESULT UPLOAD;
(31)	The smart contract calls RETURN RESULT;
(32)	The user computes and verifies equations (5)–(7) locally;
(33)	The user sends feedback to the smart contract;
(34)	The smart contract calls VERIFICATION AND PAYMENT.