Abstract
In Eurocrypt'91, Maurer and Yacobi developed a method for building a trapdoor into the one-way function of exponentiation modulo a composite number which enables an identity-based non-interactive key distribution system. In this paper, we provide some improvements of their scheme and then present a modified trapdoor one-way function by combining Maurer-Yacobi's scheme and RSA scheme. We demonstrate that a lot of applications can be constructed based on this modified scheme which are impossible in the original scheme. As examples, we present several protocols based on it, such as identifications, key distributions and signature schemes. We have implemented the Pohlig-Hellman and Pollard's ρ-methods for computing discrete logarithms modulo a composite number, which shows that average running time for computing logarithms is too large to be realizable in practice. Therefore, considering current algorithms and technology, we maintain that it is more efficient and practical to take a certificate-based scheme on which all protocols presented in this paper can be based as well.
This work was supported in part by the Ministry of Science and Technology (MOST) of the Korea.
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References
R.Brent, “An improved Monte Carlo factoring algorithm,” BIT, 20, 1980, pp.176–184.
S.Bengio, G.Brassard, T.G.Desmedt, C.Goutier and J.J.Quisquater, “Secure implementation of identification systems,” J. Cryptology, 4, 3, 1991, pp.175–183.
J.Boyar, D.Chaum, I.Damgard and T.Pedersen, “Convertible undeniable signatures,” Advances in Cryptology — Crypto'90, Lecture Notes in Computer Science (LNCS), Vol.537, Springer-Verlag, 1991.
D.Chaum, “Zero-knowledge undeniable signatures,” Advances in Cryptology — Eurocrypt'90, LNCS, Vol.473, Springer-Verlag, 1991, pp.458–464.
-, “Some weaknesses of ‘Weaknesses of undeniable signatures',” Advances in Cryptology — Eurocrypt'91, LNCS, Vol.547, 1991, pp.554–556.
D.Chaum and H.Antwerpen, “Undeniable signatures,” Advances in Cryptology — Crypto'89, LNCS, Vol.435, Springer-Verlag, 1990, pp.212–216.
D.Coppersmith, A.M.Odlyzko and R.Schroeppel, “Discrete logarithms in GF(p),” Algorithmica, Vol.1, 1986, pp.1–15.
Y.Desmedt, C.Goutier and S.Bengio, “Special uses and abuses of the Fiat-Shamir passport protocol,” Advances in Cryptology — Crypto'87, LNCS, Vol.293, Springer-Verlag, 1988, pp.21–39.
W.Diffie and M.E.Hellman, “New directions in cryptography,” IEEE Trans. Inform. Theory, IT-22, 6, 1976, pp.644–654.
Y.Desmedt and M.Yung, “Weaknesses of undeniable signature schemes,” Advances in Cryptology — Eurocrypt'91, LNCS, Vol.547, 1991, pp.205–220.
L.S.Guillou and J.J.Quisquater, “A practical zero-knowledge protocol fitted to security microprocessor minimizing both transmission and memory,” Advances in Cryptology — Eurocrypt'88, LNCS, Vol.330, Springer-Verlag, 1988, pp.123–128.
-, “A paradoxical identity-based signature scheme resulting from zeroknowledge,” Advances in Cryptology — Crypto'88, LNCS, Vol.403, Springer-Verlag, 1989, pp.216–231.
T.ElGamal, “A public key cryptosystem and a signature scheme based on discrete logarithm,” IEEE Trans. Inform. Theory, IT-31, 1985, pp.469–472.
H.W.Lenstra, “Factoring integers with elliptic curves,” Ann. Math., Vol.126, 1987, pp.649–673.
U.M.Maurer and Y.Yacobi, “Non-interactive public key cryptography,” Advances in Cryptology — Eurocrypt'91, LNCS, Vol.547, 1991, pp.498–507.
T.Okamoto and K.Otha, “How to utilize the randomness of the zero-knowledge proofs,” Advances in Cryptology — Crypto'90, LNCS, Vol.537, Springer-Verlag, 1991.
-, “Divertible zero-knowledge interactive proofs and commutative random self-reducibility,” Advances in Cryptology — Eurocrypt'89, LNCS, Vol.434, Springer-Verlag, 1990, pp.134–149.
K.Ohta, T.Okamoto and A.Fujioka, “Secure bit commitment function against divertibility,” Proc. Eurocrypt'92.
E.Okamoto and K.Tanaka, “Identity-based information security management system for personal computer networks,” IEEE JSAC, Vol.7, No.2, 1989, pp.290–294.
J.M.Pollard, “Theorems on factorization and primality testing,” Proc. Cambridge Philos. Soc., Vol.76, 1974, pp.521–528.
-, “Monte Carlo methods for index computation (mod p),” Math. Comp., 32, 1978, pp.918–924.
S.C.Pohlig and M.E.Hellman, “An improved algorithm for computing logarithms over GF(p) and its cryptographic significance,” IEEE Trans. Inform. Theory, Vol.IT-24, 1978, pp.106–110.
R.L.Rivest, “Remarks on a proposed cryptanalytic attack on the M.I.T. public key cryptosystem,” Cryptologia, Vol.2, No.1, 1978, pp.62–65.
R.L.Rivest, A.Shamir and L.Adleman, “A method of obtaining digital signatures and public key cryptosystem,” Comm. ACM, 21, 2, 1978, pp.120–126.
C.P.Schnorr, “Efficient identification and signatures for smart cards,” Advances in Cryptology — Crypto'89, LNCS, Vol.435, Springer-Verlag, 1990, pp.239–252.
G.J.Simmons and M.J.Norris, “Preliminary comments on the M.I.T. public key cryptosystem,” Cryptologia, Vol.1, No.4, 1977, pp.406–414.
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Lim, C.H., Lee, P.J. (1993). Modified Maurer-Yacobi's scheme and its applications. 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_71
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DOI: https://doi.org/10.1007/3-540-57220-1_71
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