Multiplicative Complexity of XOR Based Regular Functions

XOR-AND Graphs (XAGs) are an enrichment of the classical AND-Inverter (AIGs) with XOR nodes. In particular, XAGs networks composed by ANDs, XORs, and inverters. Besides several emerging technologies applications, often exploited in cryptography-related applications based on multiplicative complexity a Boolean function. The function is minimum number AND gates (i.e., multiplications) that sufficient to represent over basis {AND, XOR, NOT}. fact, minimization important for high-level cryptography protocols such as secure multiparty computation, where processing more expensive than gates. Moreover, it indicator degree vulnerability circuit, small corresponds high algebraic attacks. this paper we study functions characterized two particular regularities, called autosymmetry D-reducibility. exploit these regularities decreasing nodes XAGs. experimental results validate proposed approaches.