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Uploading Data Streams To A Resource-rich Cloud Server For Inner Product Evaluation, An Essential Building Block In Many Popular Stream Applications (e.g., Statistical Monitoring), Is Appealing To Many Companies And Individuals. On The Other Hand, Verifying The Result Of The Remote Computation Plays A Crucial Role In Addressing The Issue Of Trust. Since The Outsourced Data Collection Likely Comes From Multiple Data Sources, It Is Desired For The System To Be Able To Pinpoint The Originator Of Errors By Allotting Each Data Source A Unique Secret Key, Which Requires The Inner Product Verification To Be Performed Under Any Two Parties' Different Keys. However, The Present Solutions Either Depend On A Single Key Assumption Or Powerful Yet Practically-inefficient Fully Homomorphic Cryptosystems. In This Paper, We Focus On The More Challenging Multi-key Scenario Where Data Streams Are Uploaded By Multiple Data Sources With Distinct Keys. We First Present A Novel Homomorphic Verifiable Tag Technique To Publicly Verify The Outsourced Inner Product Computation On The Dynamic Data Streams, And Then Extend It To Support The Verification Of Matrix Product Computation. We Prove The Security Of Our Scheme In The Random Oracle Model. Moreover, The Experimental Result Also Shows The Practicability Of Our Design.