Advances in Cryptology — ASIACRYPT 2000: 6th International by Alex Biryukov, Adi Shamir (auth.), Tatsuaki Okamoto (eds.)

By Alex Biryukov, Adi Shamir (auth.), Tatsuaki Okamoto (eds.)

ASIACRYPT 2000 used to be the 6th annual ASIACRYPT convention. It used to be sp- sored by way of the foreign organization for Cryptologic study (IACR) in - operation with the Institute of Electronics, info, and verbal exchange Engineers (IEICE). The ?rst convention with the identify ASIACRYPT came about in 1991, and the sequence of ASIACRYPT meetings have been held in 1994, 1996, 1998, and 1999, in cooperation with IACR. ASIACRYPT 2000 used to be the ?rst convention within the sequence to be backed by means of IACR. The convention got a hundred and forty submissions (1 submission used to be withdrawn via the authors later), and this system committee chosen forty five of those for presen- tion. prolonged abstracts of the revised models of those papers are incorporated in those court cases. this system additionally incorporated invited lectures through Thomas Berson (Cryptography in every single place: IACR individual Lecture) and Hideki Imai (CRYPTREC undertaking – Cryptographic assessment venture for the japanese digital Government). Abstracts of those talks are incorporated in those proce- ings. The convention application additionally incorporated its conventional “rump consultation” of brief, casual or impromptu shows, kindly chaired by means of Moti Yung. these p- sentations are usually not re?ected in those lawsuits. the choice of this system was once a hard activity as many prime quality submissions have been got. this system committee labored very not easy to guage the papers with appreciate to caliber, originality, and relevance to cryptography. i'm tremendous thankful to this system committee participants for his or her en- mous funding of time and e?ort within the di?cult and gentle technique of overview and selection.

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Additional info for Advances in Cryptology — ASIACRYPT 2000: 6th International Conference on the Theory and Application of Cryptology and Information Security Kyoto, Japan, December 3–7, 2000 Proceedings

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Oorschot, S. Vanstone, “Handbook of Applied Cryptography”, CRC Press, 1997. 13. T. Okamoto and D. Pointcheval, “PSEC-3: Provably Secure Elliptic Curve Encryption Scheme”, Submission to IEEE P1363a, 2000. 14. P. v Oorschot, M. J. Wiener, “On Diffie-Hellman Key Agreement With Short Exponents”, Proc. Eurocrypt ’96, LNCS 1070, Springer-Verlag, 1996. 15. PKCS1, “Public Key Cryptography Standard No. 0”, RSA Labs. 16. D. Pointcheval, “Chosen-Ciphertext Security for any One-Way Cryptosystem”, Proc. PKC ’2000, LNCS 1751, Springer-Verlag, 2000.

For instance, one can take the 2 max(m1 , m2 ) least significant bits of ∆q1 mod p, so that the space requirement is only 2m1 +1 max(m1 , m2 ) bits instead of 2m1 log2 p. Less bits are even possible, for we can check the validity of the (few) candidates obtained. Note also that the table only depends on p and q: the same table can be used for all ciphertexts. For each ciphertext, one needs to compute at most 2m2 modular exponentiations. For each exponentiation, one has to check whether or not it belongs to the table, which can be done with O(m1 ) comparisons once the table is sorted.

We transform the multiplicative rounding problem into a linear problem, provided that p satisfies Why Textbook ElGamal and RSA Encryption Are Insecure 37 the additional assumption p − 1 = qrs where s ≥ 2m is such that discrete logs in subgroups of Z∗p of order s can be efficiently computed. For instance, if pe11 · · · pekk is the prime factorization of s, discrete logs in a cyclic group of order s can be √ k computed with O( i=1 ei (log s + pi )) group operations and negligible space, using Pohlig-Hellman and Pollard’s ρ methods (see [12]).

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