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SingleDatabase Private Information Retrieval with Constant Communication Rate
 In Proceedings of the 32nd International Colloquium on Automata, Languages and Programming
, 2005
"... Abstract. We present a singledatabase private information retrieval (PIR) scheme with communication complexity O(k +d), where k ≥ log n is a security parameter that depends on the database size n and d is the bitlength of the retrieved database block. This communication complexity is better asympt ..."
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Cited by 53 (1 self)
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Abstract. We present a singledatabase private information retrieval (PIR) scheme with communication complexity O(k +d), where k ≥ log n is a security parameter that depends on the database size n and d is the bitlength of the retrieved database block. This communication complexity is better asymptotically than previous singledatabase PIR schemes. The scheme also gives improved performance for practical parameter settings whether the user is retrieving a single bit or very large blocks. For large blocks, our scheme achieves a constant “rate ” (e.g., 0.2), even when the userside communication is very low (e.g., two 1024bit numbers). Our scheme and security analysis is presented using general groups with hidden smooth subgroups; the scheme can be instantiated using composite moduli, in which case the security of our scheme is based on a simple variant of the “Φhiding ” assumption by Cachin, Micali and Stadler [2].
Using LLLReduction for Solving RSA and Factorization Problems: A Survey
, 2007
"... 25 years ago, Lenstra, Lenstra and Lovasz presented their celebrated LLL lattice reduction algorithm. Among the various applications of the LLL algorithm is a method due to Coppersmith for finding small roots of polynomial equations. We give a survey of the applications of this root finding method ..."
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Cited by 16 (0 self)
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25 years ago, Lenstra, Lenstra and Lovasz presented their celebrated LLL lattice reduction algorithm. Among the various applications of the LLL algorithm is a method due to Coppersmith for finding small roots of polynomial equations. We give a survey of the applications of this root finding method to the problem of inverting the RSA function and the factorization problem. As we will see, most of the results are of a dual nature: They can either be interpreted as cryptanalytic results or as hardness/security results.
Parallel Lattice Basis Reduction Using a Multithreaded SchnorrEuchner LLL Algorithm
"... Abstract. In this paper, we introduce a new parallel variant of the LLL lattice basis reduction algorithm. Our new, multithreaded algorithm is the first to provide an efficient, parallel implementation of the SchorrEuchner algorithm for today’s multiprocessor, multicore computer architectures. E ..."
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Cited by 4 (2 self)
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Abstract. In this paper, we introduce a new parallel variant of the LLL lattice basis reduction algorithm. Our new, multithreaded algorithm is the first to provide an efficient, parallel implementation of the SchorrEuchner algorithm for today’s multiprocessor, multicore computer architectures. Experiments with sparse and dense lattice bases show a speedup factor of about 1.8 for the 2thread and about factor 3.2 for the 4thread version of our new parallel lattice basis reduction algorithm in comparison to the traditional nonparallel algorithm. 1
MultiQuery ComputationallyPrivate Information Retrieval with Constant Communication Rate
"... Abstract. A fundamental privacy problem in the clientserver setting is the retrieval of a record from a database maintained by a server so that the computationally bounded server remains oblivious to the index of the record retrieved while the overall communication between the two parties is smalle ..."
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Cited by 1 (1 self)
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Abstract. A fundamental privacy problem in the clientserver setting is the retrieval of a record from a database maintained by a server so that the computationally bounded server remains oblivious to the index of the record retrieved while the overall communication between the two parties is smaller than the database size. This problem has been extensively studied and is known as computationally private information retrieval (CPIR). In this work we consider a natural extension of this problem: a multiquery CPIR protocol allows a client to extract m records of a database containing n ℓbit records. We give an informationtheoretic lower bound on the communication of any multiquery information retrieval protocol. We then design an efficient nontrivial multiquery CPIR protocol that matches this lower bound. This means we settle the multiquery CPIR problem optimally up to a constant factor.
A Strategy for Finding Roots of Multivariate
 in Attacking RSA Variants” n Advances in Cryptology (Asiacrypt 2006), Lecture Notes in Computer Science
, 2006
"... We describe a strategy for finding small modular and integer roots of multivariate polynomials using latticebased Coppersmith techniques. ..."
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We describe a strategy for finding small modular and integer roots of multivariate polynomials using latticebased Coppersmith techniques.
A Parallel LLL using POSIX Threads by
, 2008
"... In this paper we introduce a new parallel variant of the LLL lattice basis reduction algorithm. Lattice theory and in particular lattice basis reduction continues to play an integral role in cryptography. Not only does it provide effective cryptanalysis tools but it is also believed to bring about n ..."
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In this paper we introduce a new parallel variant of the LLL lattice basis reduction algorithm. Lattice theory and in particular lattice basis reduction continues to play an integral role in cryptography. Not only does it provide effective cryptanalysis tools but it is also believed to bring about new cryptographic primitives that exhibit strong security even in the presence of quantum computers. In theory, many aspects of lattices are already wellunderstood. Yet, many practical aspects, like the performance of lattice basis reduction algorithms, are still under investigation. In this paper, we introduce a new parallel lattice basis reduction algorithm that overcomes shortcomings of previously introduced algorithms. First and foremost, our new algorithm is based on the SchnorrEuchner algorithm and as such is the first—to the best of our knowledge—to provide a parallel implementation for the SchnorrEuchner algorithm. Second, using POSIX threads allows us to make effective use of today’s multiprocessor, multicore computer architecture. Developing in a shared memory setting allows us to replace time consuming interprocess communication with synchronization points (barriers) and locks (mutexes). Our implementation of the parallel LLL is optimized for reducing high dimensional lattice bases with big entries that would require a multiprecision