Distributing the power of a government to enhance the privacy of voters
PODC '86 Proceedings of the fifth annual ACM symposium on Principles of distributed computing
A Simple Publicly Verifiable Secret Sharing Scheme and Its Application to Electronic
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Cryptographic Counters and Applications to Electronic Voting
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Randomness Conductors and Constant-Degree Lossless Expanders
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Foundations of Cryptography: Volume 2, Basic Applications
Foundations of Cryptography: Volume 2, Basic Applications
Batch codes and their applications
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Unbalanced Expanders and Randomness Extractors from Parvaresh-Vardy Codes
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Cryptography with constant computational overhead
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Protocols for secure computations
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
A robust and verifiable cryptographically secure election scheme
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Communication Complexity in Algebraic Two-Party Protocols
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Fully homomorphic encryption using ideal lattices
Proceedings of the forty-first annual ACM symposium on Theory of computing
Multi-authority secret-ballot elections with linear work
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
A secure and optimally efficient multi-authority election scheme
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Public key encryption that allows PIR queries
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Evaluating 2-DNF formulas on ciphertexts
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
IEEE Transactions on Information Theory - Part 1
On the (in)security of hash-based oblivious RAM and a new balancing scheme
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
How to fix two RSA-based PVSS schemes: exploration and solution
ACISP'12 Proceedings of the 17th Australasian conference on Information Security and Privacy
Distributed oblivious RAM for secure two-party computation
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
Hi-index | 0.00 |
Searching and modifying public-key encrypted data has received a lot of attention in recent literature. In this paper we revisit this important topic and achieve improved amortized bounds including resolving a prominent open question posed by Boneh et al. [3]. First, we consider the following much simpler to state problem: A server holds a copy of Alice's database that has been encrypted under Alice's public key. Alice would like to allow other users in the system to replace a bit of their choice in the server's database by communicating directly with the server, despite other users not having Alice's private key. However, Alice requires that the server should not know which bit was modified. Additionally, she requires that the modification protocol should have "small" communication complexity (sub-linear in the database size). This task is referred to as private database modification, and is a central tool in building a more general protocol for modifying and searching over public-key encrypted data. Boneh et al. [3] first considered the problem and gave a protocol to modify 1 bit of an N-bit database with communication complexity O(√N). Naturally, one can ask if we can improve upon this. Indeed, the recent work of Gentry [9] shows that under lattice assumptions, better asymptotic communication complexity is possible. However, current algebraic techniques based on any singly homomorphic encryption, or bilinear maps (which includes for example, all known cryptosystems based on factoring and discrete logs) cannot achieve communication better than O(√N) (see [17]). In this paper we study the problem of improving the communication complexity for modifying L bits of an N-bit database. Our main result is a black-box construction of a private database modification protocol to modify L bits of an N-bit database, using a protocol for modifying 1 bit. Our protocol has communication complexity Õ(NβL(1+α)(1-β)), where 0 Nβ, 0 N-bit database. We stress that our amortized protocol improves the communication complexity in all cases when the single bit modification protocol uses any known cryptosystem based on factoring or discrete logs. In addition to our general reduction, we show how to realize an implementation of our amortized protocol under the subgroup decision problem [2]. (We remark that in contrast with recent work of Lipmaa [16] on the same topic, our database size does not grow with every update, and stays exactly the same size.) As sample corollaries to our main result, we obtain the following: - First, we apply our private database modification protocol to answer the main open question of [3]. More specifically, we construct a public-key encryption scheme supporting PIR queries that allows every message to have a non-constant number of keywords associated with it, which is secure under the subgroup decision problem. - Second, we show that one can apply our techniques to obtain more efficient communication complexity when parties wish to increment or decrement multiple cryptographic counters (formalized by Katz et al. [15]). We believe that "public-key encrypted" amortized database modification is an important cryptographic primitive in its own right and will be useful in other applications.