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We consider the problem of designing secure and private codes for distributedmatrix-matrix multiplication. A master server owns two private matrices andhires worker nodes to help compute their product. The matrices should remaininformation-theoretically private from the workers. Some of the workers aremalicious and return corrupted results to the master. We design a framework forsecurity against malicious workers in private matrix-matrix multiplication. Themain idea is a careful use of Freivalds' algorithm to detect erroneous matrixmultiplications. Our main goal is to apply this security framework to schemeswith adaptive rates. Adaptive schemes divide the workers into clusters and thusprovide flexibility in trading decoding complexity for efficiency. Our newscheme, SRPM3, provides a computationally efficient security check per clusterthat detects the presence of one or more malicious workers with highprobability. An additional per worker check is used to identify the maliciousnodes. SRPM3 can tolerate the presence of an arbitrary number of maliciousworkers. We provide theoretical guarantees on the complexity of the securitychecks and simulation results on both, the missed detection rate as well as onthe time needed for the integrity check.

Secure Private and Adaptive Matrix Multiplication Beyond the Singleton Bound