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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

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
Outline
  • Introduction
  • The scheme of Zhang
  • Security flaw in the scheme of Zhang
  • Improvement of the Zhang scheme
  • Security analysis
  • Conclusions
introduction
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
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 zhang1
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 zhang2
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
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
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 scheme1
Improvement of the Zhang scheme
  • Step4: Construct an ciphered matrix Ch*.

B first computes

  • Step5: transmit Ch* to A.
improvement of the zhang scheme2
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 scheme3
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
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 analysis1
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
Conclusion
  • This paper proposed an improved scheme to withstand the attack.