Randomized RSA-based cryptographic exponentiation resistant to side channel and fault attacks

A method, comprising:

• employing at least one processor executing computer executable instructions stored on a computer readable storage medium to implement the following acts:
• exponentiating data using an exponent based at least in part on a cryptographic algorithm comprising a right-to-left square-and-multiply algorithm, a value of the data is randomized based at least in part on a random number;
• performing a result values check on preliminary exponentiation results generated after exponentiating the data to determine whether the exponentiation is performed without error;
• and
• providing an output, wherein, when a result of the result values check indicates there is no error in the exponentiation of the data, the output comprises a final result of the exponentiation calculated based at least in part on an inverse value of the random number and a portion of the preliminary exponentiation results, and wherein, when the result of the result values check indicates there is an error in the exponentiation of the data, the output is an error message.

A computer readable storage medium comprising computer executable instructions that, in response to execution by a computer system, cause the computing system to perform operations comprising:

• randomizing a binary value associated with information based at least on part on a random number to generate a randomized binary value;
• exponentiating the randomized binary value with an exponent based at least in part on a right-to-left square-and-multiple algorithm;
• performing a result values check on preliminary results generated after exponentiating the data to determine whether the exponentation of the randomized binary value is performed without error;
• and
• providing an output, wherein, when a result of the result values check indicates there is no error in the exponentiation of the randomized binary value, the output comprises a final data value of the exponentiation calculated based at least in part on an inverse value of the random number and a portion of the preliminary results, and wherein, when the result of the result values check indicates there is an error in the exponentiation of the randomized binary value, the final data value is not calculated and the output comprises specified data other than the final data value.