Abstract
In CRYPTO’ 93 Lim and Lee provided a valuable investigation of public key encryption systems secure against adaptive chosen ciphertext attacks. In this paper we identify several insecurities of both their RSA and El Gamal based schemes. We first demonstrate that the RSA based scheme is insecure under an adaptive chosen ciphertext attack. We also point weaknesses in the design of both their RSA and El Gamal based schemes regarding the use of pseudorandom-generators, and in particular show that their choice of pseudorandom-generators for the RSA based scheme may be insecure even with respect to a known ciphertext only attack.
They further claim that their schemes are particularly useful in the context of group-oriented cryptosystems due to the unique verification method used. (In fact their scheme is the only group-oriented practical encryption claimed to be secure against chosen ciphertext attacks). Group oriented cryptosystems distribute the decryption process amongst a multiple of individuals in order to provide a mechanism in which no single person is trusted. We further demonstrate that both their schemes are completely insecure in this setting.
Research was performed while the author was at GTE Laboratories Incorporated.
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Keywords
- Hash Function
- Pseudorandom Generator
- Cryptographic Hash Function
- Decryption Oracle
- Choose Ciphertext Attack
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
W. Alexi, B. Chor, O. Goldreich and C. P. Schnorr, RSA and Rabin functions: certain parts are as secure as the whole, SIAM J. Computing vol. 17(2). 1988.
T. M. Apostol Introduction to analytic number theory, Springer-Verlag, New York, 1976.
M. Bellare and P. Rogaway, Random Oracles are Practical: a paradigm for designing efficient protocols, ACM, 1-st Comp. and Com. Sec. 1993.
I. Damgård, Towards practical public key cryptosystems secure against chosen ciphertext attacks, Advances in Cryptology-Proc. of Crypto’ 91.
Y. Desmedt, Society and group oriented cryptography: a new concept, Advances in Cryptology, Proc. of Crypto’ 87, Springer-Verlag, 1988.
Y. Desmedt and Y. Frankel, Threshold cryptosystems, Advances in Cryptology, Proc. of Crypto’ 89 Springer-Verlag, 1990.
W. Diffie and M. Hellman, New Directions in Cryptography, IEEE Trans. on Information Theory 22(6), 1976, pp. 644–654.
D. Dolev, C. Dwork and M. Naor, Non-Malleable Cryptography, Proc. of the 23rd Annual ACM Symposium on the Theory of Computing, 1991, pp. 542–560.
T. El Gamal, A Public key cryptosystem and a signature scheme based on discrete logarithm, IEEE Trans. on Information Theory 31, 465–472, 1985.
M.K. Franklin and M.K. Reiter, Adaptive Chosen Ciphertext Security for RSA from G-Q Signatures, Preliminary manuscript.
O. Goldreich S. Goldwasser and S. Micali, How to Construct Random Functions, J. of the ACM 33 (1986), pp. 792–807.
S. Goldwasser and S. Micali, Probabilistic Encryption, J. Com. Sys. Sci. 28 (1984), pp 270–299.
C. H. Lim and P. J. Lee, Another method for attaining security against adaptive chosen ciphertext attacks, Advances in Cryptology-Proc. of Crypto’ 93.
M. Naor and M. Yung, Public-key cryptosystem provably secure against chosen ciphertext attack, Proc. of the 22nd Annual Symposium on the Theory of Computing, 1990, pp. 427–437.
M. O. Rabin, Digital Signatures and Public Key Functions as Intractable as Factoring, Technical Memo TM-212, Lab. for Computer Science, MIT, 1979.
C. Rackoff, and D. Simon, Non-Interactive Zero-Knowledge Proof of Knowledge and Chosen Ciphertext Attacks, Advances in Cryptology-Proc. of Crypto’ 91.
R. Rivest, A. Shamir and L. Adleman, A Method for Obtaining Digital Signature and Public Key Cryptosystems, Comm. of ACM, 21 (1978), pp 120–126.
Y. Zheng and J. Seberry, Immunizing public key cryptosystems against chosen ciphertext attacks, IEEE Jour. on Selected Areas in Communications, 11(5), 1993, pp. 715–724. (Also in: Advances in Cryptology-Proc. of Crypto’ 92).
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Frankel, Y., Yung, M. (1995). Cryptanalysis of the Immunized LL Public Key Systems. In: Coppersmith, D. (eds) Advances in Cryptology — CRYPT0’ 95. CRYPTO 1995. Lecture Notes in Computer Science, vol 963. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44750-4_23
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