Abstract
In 1985, T. ElGamal proposed a public-key cryptosystem and a signature scheme, in which the difficulty of breaking the system is based on the difficulty of computing a discrete logarithm in a finite group. For the same security level, the size of the ciphertext and the computational time of ElGamal's encryption are double those of the wellknown RSA scheme. In this paper, we propose a public-key cryptosystem based on the discrete logarithm, in which the size of the ciphertext and the computational time are the same as those of the RSA scheme, and the security level is the same as the ElGamal cryptosystem.
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References
W. Diffie and M. E. Hellman.: New Directions in Cryptography, IEEE Trans. Inform. Theory, vol. IT-22, pp. 644–654, Nov. 1976.
R. L. Rivest, A. Shamir and L. Adelman.: A Method for Obtaining Digital Signatures and Public-Key Cryptosystem, Commun. of ACM, vol. 21, No. 2, pp.120–126, Feb. 1978.
R. C. Merkle and M. E. Hellman.: Hiding Information and Signatures in Trapdoor Knapsack, IEEE Trans. Inform. Theory, vol. IT-24, pp. 525–530, Sep. 1978.
T. ElGamal.: A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms, IEEE Trans. Inform. Theory, vol. IT-31, pp. 469–472, July 1985.
C. S. Laih and J. Y. Lee.: Efficient Probabilistic Public-Key Cryptosystem Based on the Diffie-Hellman Problem, Electronics Letters, vol. 26, No. 5, pp. 326–327, March 1990.
S. Pohlig and M. Hellman.: An Improved Algorithm for Computing Logarithms over GF(p) and Its Cryptographic Significance, IEEE Trans. Inform. Theory, vol. IT-24, pp. 106–110, 1978.
K. S. McCurley.: The discrete logarithm problem, in Proc. of Symposia in Applied Mathematics, vol. 42, pp. 49–74, American Mathematical Society, Providence, 1990.
A. M. Odlyzko.: Discrete logarithms in finite fields and their cryptographic significance, Advances in Cryptology, Eurocrypt '84, pp. 224–314, Springer-Verlag, 1985.
D. E. Knuth.: The Art of Computer Programming, vol. II: Seminumerical Algorithms, Addison-Wesley Publishing Company, 1969.
D. E. R. Denning.: Cryptography and Data Security, Addison-Wesley, 1982.
J. M. Carroll.: The binary derivative test: noise filter, crypto aid, and randomnumber seed selector, SIMULATION, Sept. 1989.
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© 1993 Springer-Verlag Berlin Heidelberg
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Harn, L., Yang, S. (1993). Public-key cryptosystem based on the discrete logarithm problem. In: Seberry, J., Zheng, Y. (eds) Advances in Cryptology — AUSCRYPT '92. AUSCRYPT 1992. Lecture Notes in Computer Science, vol 718. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57220-1_85
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DOI: https://doi.org/10.1007/3-540-57220-1_85
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