On the Multi-output Filtering Model and Its Applications

In this paper, we propose a novel technique, called multi-output filtering model, to study the non-randomness property of a cryptographic algorithm such as message authentication codes and block ciphers. A multi-output filtering model consists of a linear feedback shift register and a multi-output filtering function. Our contribution in this paper is twofold. First, we propose an attack technique under IND-CPA using the multi-output filtering model. By introducing a distinguishing function, we theoretically determine the success rate of this attack. In particular, we construct a distinguishing function based on the distribution of the linear complexity of component sequences, and apply it on studying \({\textsf {TUAK}}\)’s \(f_1\) algorithm, \( {\textsf {AES} }\), \( {\textsf {KASUMI} }\), \( {\textsf {PRESENT} }\) and PRINTcipher. We demonstrate that the success rate of the attack on \( {\textsf {KASUMI} }\) and \( {\textsf {PRESENT} }\) is non-negligible, but \(f_1\) and \( {\textsf {AES} }\) are resistant to this attack. Second, we study the distribution of the cryptographic properties of component functions of a random primitive in the multi-output filtering model. Our experiments show some non-randomness in the distribution of algebraic degree and nonlinearity for \( {\textsf {KASUMI} }\).