Research Article
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. |
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