1. A system, comprising: at least one processor; a memory communicatively coupled to the at least one processor, the memory having stored therein computer-executable instructions configured to implement the system including: a cryptographic component configured to secure data in accordance with a cryptographic protocol; and a randomized exponentiation component configured to at least one of decrypt the data or generate a digital signature, based at least in part on an exponentiation of the data with an exponent associated with the data based at least in part on a cryptographic algorithm comprising a right-to-left square-and-multiply algorithm, where a value of the data is randomized based at least in part on a value of a random number, wherein the randomized exponentiation component is further configured to perform a result values check after the exponentiation of the data with the exponent to determine whether the exponentiation is performed without error, and provide a final result of the exponentiation as an output when there is no error in the exponentiation of the data and provide an output comprising an error message when there is an error in the exponentiation of the data.