Safe mode index outsourcing method and system under single malicious cloud server

The invention discloses a safe mode index outsourcing method and a safe mode index outsourcing system under a single malicious cloud server. The method comprises the steps as follows: step1, a user T calls a sub-program Rand for six times to obtain six random pairs; step 2, the user T splits a mode index which needs to calculate according to the random pairs returned by the sub-program Rand, and simultaneously, the user T selects a random value r and multiplies the index of the mode index by r to obtain a new mode index, and splits the new mode index; step 3, the user T requests a server U to separately calculate the values which needs to calculate after splitting; step 4, the user T multiplies a random value which is related to ua and which is remained by the T by a result which is related to the ua and which is returned by the server U, and multiplies the results for r times to obtain a verification result 1; and the user T multiplies a random value which is related to ura and which is remained by the T by a result which is related to the ura and which is returned by the server U to obtain a verification result 2; comparing the result 1 and the result 2, and judging that the server could accurately perform calculation if the result 1 and the result 2 are equal to each other.