Strong white-box cryptography

An apparatus for providing digital signal security comprising:

• a processor;
• a memory, communicatively coupled to the processor, the memory storing instructions comprising instructions for:
• generating at least one output from at least one input according to a secret that uses a white-box implementation of a randomized cryptographic function, the randomized cryptographic function obtained by at least one random operation performed on the whole of a nonrandomized function;
• providing the randomized cryptographic function as a plurality of interconnected logic elements, the interconnection of the plurality of logic elements being comprised of anon-algebraic interconnection of logic elements and an algebraic interconnection of logic elements having obfuscated boundaries between the at least one input and output;
• wherein the non-algebraic plurality of interconnected logic elements comprises a cyclic connection of at least a portion of the plurality of interconnected logic elements that produces an equivalent input-output relationship of a non-cyclic connection of logic elements,
• wherein the logic elements are Boolean circuit gates;
• and
• wherein the randomized cryptographic function has fewer Boolean circuit gates than the whole of the nonrandomized function.

A non-transitory computer readable medium containing program instructions for causing a computer to perform the method of:

• generating at least one output from at least one input according to a secret that uses a white-box implementation of a randomized cryptographic function, the randomized cryptographic function obtained by at least one random operation performed on the whole of a nonrandomized function;
• providing the randomized cryptographic function as a plurality of interconnected logic elements, the interconnection of the plurality of logic elements being comprised of non-algebraic interconnection of logic elements and algebraic interconnection of logic elements having obfuscated boundaries between at the least one input and output;
• wherein the non-algebraic interconnected logic elements comprises a cyclic connection of at least a portion of the plurality of interconnected logic elements,
• wherein the logic elements are Boolean circuit gates;
• and
• wherein the randomized cryptographic function has fewer Boolean circuit gates than the whole of the nonrandomized function.