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Efficient fault-tolerant scheme based on the RSA system. Author: N.-Y. Lee and W.-L. Tsai IEE Proceedings Presented by 詹益誌 2004/03/02. Outline. Introduction The scheme of Zhang Security flaw in the scheme of Zhang Improvement of the Zhang scheme Security analysis Conclusions.
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Efficient fault-tolerant scheme based on the RSA system Author: N.-Y. Lee and W.-L. Tsai IEE Proceedings Presented by 詹益誌 2004/03/02
Outline • Introduction • The scheme of Zhang • Security flaw in the scheme of Zhang • Improvement of the Zhang scheme • Security analysis • Conclusions
Introduction • Zhang scheme can simultaneously deal with error detection and data correction. • But Zhang scheme can suffer from an attack by a malicious receiver. • This paper proposes improvement to the Zhang scheme to repair the security flaw.
The scheme of Zhang • User A: • User B: • User B wants to send a message M to a user A. • Step1: translate the message M into an n*m plaintext matrix X:
The scheme of Zhang • Step2: Construct another (n+1)*(m+1) matrix • Step3: compute an (n+1)*(m+1) ciphered matrix Ch:
The scheme of Zhang • A received the Ch and decrypts Ch. So A will get • Data can be corrected by
Security flaw in the scheme of Zhang • Transform the into • Compute • New plaintext matrix is: • Compute • the new matrix is constructed
Improvement of the Zhang scheme • Step1: translate the message into matrix X. • Step2: construct another matrix Xh • Step3: generate the signature
Improvement of the Zhang scheme • Step4: Construct an ciphered matrix Ch*. B first computes • Step5: transmit Ch* to A.
Improvement of the Zhang scheme • A receive Ch*, and decrypts by use own private key: • Then, A obtains the plaintext matrix Xh:
Improvement of the Zhang scheme • A verifies the validity of B’s signature by computing: • and checking • If rure, A compute • And checks • If true, the signature is valid.
Security analysis • A attacker will generate a different message for the existing signature. He will first choose x11,…,x1,m-1 and then find a x1m, which must satisfy
Security analysis • If an attacker wants to view the content of the plaintext matrix, he has to first get ZC. • If an attacker wants to generate a valid signature for any message, he must compute Zc from Z.
Conclusion • This paper proposed an improved scheme to withstand the attack.