Abstract: Data is encrypted using only first and second stages of only 3-bit gates, that are linear, and non-linear, respectively. Each 3-bit gate for a function is conjugated by the first stage, i.e., straddled with the first stage and its inverse, to form a set of gates that are replaced using a finite set of substitution rules to form an ordered set of daughter gates. The daughter gates are conjugated by the second stage to form for each output bit of each layer of a daughter gate, a binary decision diagram (BDD). A module chip is formed by combining all BDDs for each daughter gate. The obfuscated module is configured by combining the module chips. The obfuscated module is sent to an unsecured device for execution thereon.

Abstract: Techniques, for secure processing of encrypted data on public resources, include receiving first data, indicating a sequence of reversible Boolean function control (BFC) gates, including a first segment for decrypting, a second segment for operating on the decrypted data, and a third segment for encrypting the resulting data. Second data indicates generic BFC gate rules for replacing a first sequence of two gates operating on an input N-bit word with a second sequence of one or more gates that produce the same output N-bit word. The second data is used to propagate: a gate from the first segment a distance into the second segment or beyond; and, a gate from the third segment a distance into the second segment or before. This produces an obfuscated sequence of reversible gates. Obfuscated instructions based on the obfuscated sequence of gates are sent to the public resources.