# Advances in Cryptology — ASIACRYPT’98: International by Arjen K. Lenstra (auth.), Kazuo Ohta, Dingyi Pei (eds.)

By Arjen K. Lenstra (auth.), Kazuo Ohta, Dingyi Pei (eds.)

ASIACRYPT’98, the overseas convention protecting all elements of idea and alertness of cryptology and data safeguard, is being held at Beijing Friendship inn from October 18 to 22. this is often the fourth of the Asiacrypt meetings. ASIACRYPT’98 is subsidized via the country Key Laboratory of knowledge protection (SKLOIS), college of technology and know-how of China (USTC), and the Asiacrypt steerage Committee (ASC), in cooperation with the foreign organization for Cryptology examine (IACR). The 16-member application Committee geared up the clinical software and thought of 118 submissions. of those, 32 have been authorized for presentation. The authors’ affiliations of the 118 submissions and the 32 authorized papers diversity over 18 and thirteen international locations or areas, respectively. The submitted model of every paper was once despatched to all participants of this system Committee and used to be widely tested by means of not less than 3 committee contributors and/or open air specialists. The evaluation procedure used to be carefully blinded and the anonymity of every submission are maintained till the choice used to be accomplished. We the conventional coverage that every member of this system Committee can be an writer of at so much one permitted paper. those complaints comprise the revised types of the 32 contributed talks in addition to a brief notice written by way of one invited speaker. reviews from this system Committee have been taken under consideration within the revisions. notwithstanding, the authors (not the committee) undergo complete accountability for the contents in their papers.

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**Extra resources for Advances in Cryptology — ASIACRYPT’98: International Conference on the Theory and Application of Cryptology and Information Security Beijing, China, October 18–22, 1998 Proceedings**

**Example text**

Theorem 1. Let N = pq be an n-bit rsa modulus. Let 1 ≤ e, d ≤ φ(N ) satisfy ed = 1 mod φ(N ). There is an algorithm that given the n4 least significant bits of d computes all of d in polynomial time in n and e. We note that the running time of the attack algorithm in the above theorem is linear in e. Consequently, as long as e is not “too large” the attack can be efficiently mounted. For a very small value of e such as e = 3 the attack runs in a reasonable amount of time. For larger values, such as e = 65537, the attack is still feasible, though clearly takes much longer.

An Attack on RSA Given a Small Fraction of the Private Key Bits 27 Theorem 2 applies to public exponents e in the range 2n/4 ≤ e ≤ 2n/2 . Unlike the previous theorem, Theorem 2 makes use of the most significant bits of d. When e is prime, at most half the bits of d are required to mount the attack. Fewer bits are needed when e is smaller. Indeed, if e is close to N 1/4 only a quarter of the msb bits of d are required. The same result holds when e is not prime, as long as we are given the factorization of e and e does not have too many distinct prime factors.

Since k > 2t we know that v = (d − d0 )/k < 1/ . To find v we try all possible candidates in the range [0, 1 ]. For each candidate we compute the candidate value of d and test it out. An Attack on RSA Given a Small Fraction of the Private Key Bits 33 3. Once the correct values of v and k are found d is exposed. Testing each candidate d takes O(n3 ) time and there are O(1/ ) candidates to try out. Theorem 8 works without having to know the factorization of e. Unfortunately, the results are not as strong as in the previous section.