Code-Based Conjunction Obfuscation

The pattern-matching problem with wildcards can be formulated as a conjunction where an accepting string is same as the pattern for all non-wild-cards. A scheme of conjunction obfuscation is a algorithm that “encrypt” the pattern to prevent some adversary from forging any accepting string. Since 2013, there are abundant works about conjunction obfuscation which discussed with weak/strong functionality preservation and distributed black-box security. These works are based on generic group model, learning with error assumption, learning with noise assumption, etc. Our work proposes the first conjunction obfuscation with strong functionality preservation and distributed black-box security from a standard assumption. Our scheme with some parameter constraints can also resist some related attacks such as the information set decoding attack and the structured error arrack.