Summary
In 1998, W. Mao proposed a verifiable encryption scheme. In the scheme Alice shall encrypt two prime numbers P and Q and disclose N = PQ. Bob shall verify the correctness of the encryption under an agreed public key. In the short paper, we show that Alice can only disclose \(N=PQ\ \mbox{mod}\ q\), where q is the order of the cryptographic group used for zero-knowledge proof. Actually, the proof of bit-length proposed can only show the bit-length of the residue \(\hat P\in \mathcal{Z}_q\) in stead of \(P\in \mathcal {Z}\). To fix the scheme, it’s sure that the order of the cryptographic group should be unknown by the prover. That means we should introduce another RSA modulus and base the Mao’s scheme on RSA setting instead of the original ElGamal setting.
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References
Bellare, M., Goldwasser, S.: Verifiable partial key escrow. In: Proceedings of 4th ACM Conference on Computer and Communications Security, April 1997, pp. 78–91. ACM Press, New York (1997)
Boudot, F.: Efficient Proofs that a Committed Number Lies in an Interval. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 431–444. Springer, Heidelberg (2000)
Boudot, F., Traore, J.: Efficient Publicly Verifiable Secret Sharing Schemes with Fast or Delayed Recovery. In: Varadharajan, V., Mu, Y. (eds.) ICICS 1999. LNCS, vol. 1726. Springer, Heidelberg (1999)
Chan, A., Frankel, Y., Tsiounis, Y.: Easy Come–Easy Go Divisible Cash. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 561–575. Springer, Heidelberg (1998)
Chan, A., Frankel, Y., Tsiounis, Y.: Easy Come Easy Go Divisible Cash. Updated version with corrections, GTE Tech. Rep. (1998), http://www.ccs.neu.edu/home/yiannis/
Cao, Z., Liu, L.: Boudot’s Range-Bounded Commitment Scheme Revisited. In: Qing, S., Imai, H., Wang, G. (eds.) ICICS 2007. LNCS, vol. 4861, pp. 230–238. Springer, Heidelberg (2007)
Camenisch, J., Michels, M.: Separability and Efficiency for Generic Group Signa- ture Schemes. In: Wiener, M.J. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 413–430. Springer, Heidelberg (1999)
Camenisch, J., Michels, M.: Proving in Zero-Knowledge that a Number is the Product of Two Safe Primes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 106–121. Springer, Heidelberg (1999)
Fujisaki, E., Okamoto, T.: Statistical Zero Knowledge Protocols to Prove Modular Polynomial Relations. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 16–30. Springer, Heidelberg (1997)
Fiat, A., Shamir, A.: How to prove yourself: Practical solution to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987)
Guillou, L., Quisquater, J.: A practical zero-knowledge protocol fitted to security microprocessor minimizing both transmission and memory. In: Günther, C.G. (ed.) EUROCRYPT 1988. LNCS, vol. 330, pp. 123–128. Springer, Heidelberg (1988)
Mao, W.: Guaranteed Correct Sharing of Integer Factorization with Off-Line Shareholders. In: Imai, H., Zheng, Y. (eds.) PKC 1998. LNCS, vol. 1431, pp. 60–71. Springer, Heidelberg (1998)
Micali, S.: Fair public key cryptosystems. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 113–138. Springer, Heidelberg (1993)
Okamoto, T.: Threshold key-recovery system for RSA. In: Christianson, B., Lomas, M. (eds.) Security Protocols 1997. LNCS, vol. 1361, pp. 191–200. Springer, Heidelberg (1998)
Rabin, M.: Digital signatures and public-key functions as intractable as factorization. MIT Laboratory for Computer Science, Technical Report, MIT/LCS/TR–212 (1979)
Rivest, R., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM 21(2), 120–126 (1978)
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Liu, L., Cao, Z. (2008). Security Analysis of One Verifiable Encryption Scheme. In: Lee, R. (eds) Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing. Studies in Computational Intelligence, vol 149. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70560-4_15
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DOI: https://doi.org/10.1007/978-3-540-70560-4_15
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