By Jean-Sébastien Coron, David Naccache, Julien P. Stern (auth.), Michael Wiener (eds.)
Crypto ’99, the 19th Annual Crypto convention, was once backed through the overseas organization for Cryptologic study (IACR), in cooperation with the IEEE computing device Society Technical Committee on protection and privateness and the pc technological know-how division, collage of California, Santa Barbara (UCSB). the overall Chair, Donald Beaver, used to be liable for neighborhood association and registration. this system Committee thought of 167 papers and chosen 38 for presentation. This year’s convention application additionally integrated invited lectures. i used to be happy to incorporate within the application UeliM aurer’s presentation “Information Theoretic Cryptography” and Martin Hellman’s presentation “The Evolution of Public Key Cryptography.” this system additionally integrated the normal Rump consultation for casual brief displays of latest effects, run by way of Stuart Haber. those lawsuits comprise the revised types of the 38 papers permitted through this system Committee. those papers have been chosen from the entire submissions to the convention in response to originality, caliber, and relevance to the sphere of cryptology. Revisions weren't checked, and the authors undergo complete accountability for the contents in their papers.
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Additional info for Advances in Cryptology — CRYPTO’ 99: 19th Annual International Cryptology Conference Santa Barbara, California, USA, August 15–19, 1999 Proceedings
Therefore, the first m − n − 1 vectors of any reduced basis of b⊥ are likely to be short lattice points of (x1 , . . , xn , k)⊥ , and their expected length is given by the previous expression. For these vectors, the approximate length of the corresponding pu is: √ n m/4 × (m/2)n/2 1/(m−n−1) n m(m − n − 1)/4. And condition 4 is likely to be satisfied if and only if this length is significantly smaller than Λ(v⊥ ), that is: √ n m/4 × (m/2)n/2 1/(m−n−1) n m(m − n − 1)/4 √ M 1/n (n/3)1/(2n) n. For sufficiently large m and n, the condition simplifies to: mn(m − n − 1)/4 M 1/n (3) The left-hand part is not large.
Um−1 ) be a reduced basis of b⊥ . Then the first m − (n + 1) vectors u1 , . . , um−(n+1) are orthogonal to each xj and k. One cannot expect that more than m − (n + 1) vectors are orthogonal, because ¯ x has dimension (n + 1). If the condition is satisfied, the (n + 1)-dimensional L lattice (u1 , . . , um−(n+1))⊥ contains each of the xj ’s and k. And one can see ¯ x , because they are orthogonal lattices of equal that it is in fact the lattice L dimension, with one containing the other. Hence, the first step is as follows: 1.
Clearly, the vector (β1 , . . , βn ) modulo M satisfies the first m solutions of the system. If m is sufficiently large, it must be the unique solution (α1 , . . , αn ). Hence, in order to solve the system, it suffices to compute a basis of the orthogonal lattice L⊥ , which can be done in polynomial time. 4 Sparse Hidden Subset Sums If the hidden subset sum is sparse, that is κ n/2, the condition (3) gets slightly better. Indeed, when one picks at most κ weights in each subset sum, one can show that E( k 2 ) ≈ mκ2 /16 and E( xj 2 ) ≈ mκ/n.
Advances in Cryptology — CRYPTO’ 99: 19th Annual International Cryptology Conference Santa Barbara, California, USA, August 15–19, 1999 Proceedings by Jean-Sébastien Coron, David Naccache, Julien P. Stern (auth.), Michael Wiener (eds.)