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arXiv 2512.22720cs.CR
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当RSA失效:公钥密码学中素数选择漏洞的利用

When RSA Fails: Exploiting Prime Selection Vulnerabilities in Public Key Cryptography

Davidson College(戴维森学院)

Murtaza Nikzad, Kerem Atas

AI总结:

本文研究了RSA中因素数选择不当导致的漏洞,揭示了嵌入式设备随机数生成薄弱是主要问题,并提出改进措施。

摘要:

本文探讨了在密钥生成过程中因不当选择素数而产生的RSA密码系统中的漏洞。我们分析了两种主要攻击方式:费马因数分解法,它利用了生成的素数过于接近的RSA密钥,以及最大公约数(GCD)攻击,它利用了共享公共素因子的密钥。借鉴Heninger等人关于『挖掘你的P和Q』研究的里程碑成果,该研究发现了超过64,000个易受攻击的TLS主机,以及Böck 2023年对费马因数分解在部署系统中的分析,我们证明这些漏洞在现实世界中的密码学实现中仍然普遍存在。我们的分析揭示了嵌入式设备中随机数生成薄弱是这些失败的主要原因,并讨论了缓解策略,包括正确收集熵和素数验证检查。

英文摘要:

This paper explores vulnerabilities in RSA cryptosystems that arise from improper prime number selection during key generation. We examine two primary attack vectors: Fermat's factorization method, which exploits RSA keys generated with primes that are too close together, and the Greatest Common Divisor (GCD) attack, which exploits keys that share a common prime factor. Drawing from landmark research including Heninger et al.'s ``Mining Your Ps and Qs'' study, which discovered over 64,000 vulnerable TLS hosts, and B{ö}ck's 2023 analysis of Fermat factorization in deployed systems, we demonstrate that these vulnerabilities remain prevalent in real-world cryptographic implementations. Our analysis reveals that weak random number generation in embedded devices is the primary cause of these failures, and we discuss mitigation strategies including proper entropy collection and prime validation checks.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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