Boolean function control gates for securely executing on a public computer code that operates on encrypted data

A non-transitory computer-readable medium carrying one or more sequences of instructions, wherein execution of the one or more sequences of instructions by a first set of one or more processors causes the first set of one or more processors to perform the steps of:

• receiving first data indicating a sequence of only reversible Boolean function control gates including a first segment for decrypting permutation encrypted data to produce decrypted data, a second segment for operating on the decrypted data to produce one or more resulting decrypted data, and a third segment for encrypting the resulting decrypted data using permutation encryption to produce permutation encrypted resulting data, wherein a Boolean function control gate affects no more than one bit that is called a target bit;
• storing second data that indicates rules for replacing a first sequence of two reversible Boolean function control gates operating on an input N-bit word with a second sequence of one or more reversible Boolean function control gates that produce the same output N-bit word;
• using the second data to propagate at least one Boolean function control gate from the first segment to a number J of gates distance into the Boolean function control gates for the second segment or beyond and at least one Boolean function control gate from the third segment to a number K of gates distance into the Boolean function control gates for the second segment or before to produce an obfuscated sequence of reversible Boolean function control gates;
• and
• sending obfuscated instructions based on the obfuscated sequence of reversible Boolean function control gates to a second set of one or more processors for execution.

A system comprising:

• a first set of at least one processor;
• and
• at least one memory including one or more sequences of instructions, the at least one memory and the one or more sequences of instructions configured to, with the at least one processor, cause an apparatus to perform at least the following,
• receiving first data indicating a sequence of only reversible Boolean function control gates including a first segment for decrypting permutation encrypted data to produce decrypted data, a second segment for operating on the decrypted data to produce one or more resulting decrypted data, and a third segment for encrypting the resulting decrypted data using permutation encryption to produce permutation encrypted resulting data, wherein a Boolean function control gate affects no more than one bit that is called a target bit;
• storing on the computer-readable medium second data that indicates rules for replacing a first sequence of two Boolean function control gates operating on an input N-bit word with a second sequence of one or more Boolean function control gates that produce the same output N-bit word;
• using the second data to propagate at least one Boolean function control gate from the first segment to a number J of gates distance into the Boolean function control gates for the second segment or beyond and at least one Boolean function control gate from the third segment to a number K of gates distance into the Boolean function control gates for the second segment or before to produce an obfuscated sequence of reversible Boolean function control gates;
• and
• sending obfuscated instructions based on the obfuscated sequence of reversible Boolean function control gates to a second set of at least one processor for execution.