Ｌｕｃａｓ 公钥密码体制是数论中的Ｌｕｃａｓ 序列与公钥密码体制思想的有效结合。在此基础上，讨论了该体制的安全性问题。通过对几种破译该体制的攻击途径的分析，证明了Ｌｕｃａｓ 体制是一种建立在两种密码假设基础之上的公钥密码体制，从而保证了很高的有效性和安全性 Lucas public key cryptosystem is an effective combination of Lucas sequence and public key cryptosystem in number theory. On this basis, the security of the system is discussed. The analysis of several attack ways to decipher the system proves that the Lucas system is a public key cryptosystem based on two kinds of cryptographic assumptions, thus ensuring high validity and security