Parent-identifying set system is a kind of combinatorial structures with applications to broadcast encryption. In this paper we investigate the maximum number of blocks $$I_2(n,4)$$ I 2 ( n , 4 ) in a 2-parent-identifying set system with ground set size n and block size 4. The previous best-known lower bound states that $$I_2(n,4)=\varOmega (n^{4/3+o(1)})$$ I 2 ( n , 4 ) = Ω ( n 4 / 3 + o ( 1 ) ) . We improve this lower bound by showing that $$I_2(n,4)= \varOmega (n^{3/2-o(1)})$$ I 2 ( n , 4 ) = Ω ( n 3 / 2 - o ( 1 ) ) using techniques in additive number theory.

中文翻译：

---

在块大小为 4 的 2-parent-identifying 集合系统上

亲子识别集系统是一种应用于广播加密的组合结构。在本文中，我们研究了具有地面集大小为 n 和块大小为 4 的 2-parent-identifying set 系统中块的最大数量 $$I_2(n,4)$$I 2 ( n , 4 )。已知下界表明 $$I_2(n,4)=\varOmega (n^{4/3+o(1)})$$ I 2 ( n , 4 ) = Ω ( n 4 / 3 + o ( 1 ) ) 。我们通过证明 $$I_2(n,4)= \varOmega (n^{3/2-o(1)})$$ I 2 ( n , 4 ) = Ω ( n 3 / 2 - o (1) ) 使用加性数论中的技术。