A method of performing an equality check in a secure system, including: receiving an input v having a known input property; splitting the input v into t secret shares v_i where i is an integer index and t is greater than 1; splitting an input x into k secret shares x_i where i is an integer index and k is greater than 1; splitting the secret shares x_i into a s chunks resulting in s·k chunks y_j where j is an integer index; calculating a mapping chain t times for each secret share v_i, wherein the mapping chain including s·k affine mappings F_j, wherein y_j and F_j−1(y_j−1) are the inputs to F_j and the F₀(y₀)=v_i; and determining if the outputs have a known output property indicating that the input x equals a desired value.

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