关键词: 信息安全, 组密钥管理, “1影响n”问题, 多素数RSA, 椭圆曲线分解方法, 中国剩余定理

Abstract: Recently, Lin, Tang and Wang proposed a multi-prime RSA based on a star architecture of key distribution and made use of it to construct a centralized group key management scheme. According to several main security requirements of group key management, from the perspective of cryptographic engineering practice and applying computational number theory, four kinds of attacks against this scheme were proposed: a ring idempotent attack, a chosen plaintext attack，an attack of extracting high order integer roots, and a collusion attack based on the elliptic curve factoring method and Chinese remainder theorem. The mathematical analysis and cryptanalysis indicate that under certain conditions these attacks can be realized efficiently, and it is the characteristic of "without rekeying the key server's encryption exponent" that causes such security risks.

Key words: information security, group key management, “1-affects-n” problem, multi-prime RSA, elliptic curve factoring method, Chinese remainder theorem