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Cryptanalysis of Li-Tzeng-Hwang’s Improved Signature Schemes

This paper discusses the cryptanalysis of Li-Tzeng-Hwang’s improved signature schemes based on factoring and discrete logarithms, highlighting potential vulnerabilities and limitations.

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Cryptanalysis of Li-Tzeng-Hwang’s Improved Signature Schemes

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  1. Cryptanalysis of Li-Tzeng-Hwang’s improved signature schemes based on factoring and discrete logarithms ExAnte:Applied Mathematics and Computation 166(2005)pp. 501-505 Arthor :Haifeng Qian, ZhenFu Cao, Haiyong Bao Reporter:黃劭農

  2. Outline • Introduction • Li-Tzeng-Hwang’s improved signature scheme • Cryptanalysis of Li-Tzeng-Hwang’s improved signature scheme • Conclusion

  3. Introduction • Discrete Logarithms • Factoring • Laih-Kuo “A New Signature Scheme Based on Factoring and Discrete Logarithms”. • Li-Tzeng-Hwang’s improved Laih-Kuo’s scheme for shorter keys.

  4. Li-Tzeng-Hwang’s improved signature scheme • Key generation 1.p is a large prime such that a factor of p-1 is product of two large primes p’ and q’. 2.g is an element in GF(p) whose order modulo p is n, where n=p’q’, and G is the multiplicative group generated by g 3.Find u,z satisfying ku2≡-1 mod n and z≡gk mod p, Find u1,k1 satisfying k1u12≡1 mod n 4.Secret key is (u,u1), Public key is (z,k1)

  5. Li-Tzeng-Hwang’s improved signature scheme • Create a signature for message M • Verify signature (K,x,y) for message M the verifier verifies the validity of the signature through the following equation:

  6. Cryptanalysis of Li-Tzeng-Hwang’s improved signature scheme • Universal Forgery exist if FAC problem solved under KSA(Known Signature Attack) • Has 50% in successfully forging a signature on any message in PPT(Probabilistic Polynomial Time) under KSA(Known Signature Attack)

  7. Universal Forgery exist if FAC problem solved.

  8. Has 50% in successfully forging a signature on any message

  9. Conclusion • Li-Tzeng-Hwang’s improved schemes is not equivalent to those of Laih-Kuo’s schemes based on Factoring and Discrete Logarithms. • The attacker would need to solve any difficult problems in forging signature on any message with the probability of 50%.

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