## Order-Preserving Symmetric Encryption

Citations: | 25 - 0 self |

### BibTeX

@MISC{Boldyreva_order-preservingsymmetric,

author = {Ra Boldyreva and Nathan Chenette and Younho Lee},

title = {Order-Preserving Symmetric Encryption},

year = {}

}

### OpenURL

### Abstract

We initiate the cryptographic study of order-preserving symmetric encryption (OPE), a primitive suggested in the database community by Agrawal et al. (SIGMOD ’04) for allowing efficient range queries on encrypted data. Interestingly, we first show that a straightforward relaxation of standard security notions for encryption such as indistinguishability against chosen-plaintext attack (IND-CPA) is unachievable by a practical OPE scheme. Instead, we propose a security notion in the spirit of pseudorandom functions (PRFs) and related primitives asking that an OPE scheme look “as-random-as-possible ” subject to the order-preserving constraint. We then design an efficient OPE scheme and prove its security under our notion based on pseudorandomness of an underlying blockcipher. Our construction is based on a natural relation we uncover between a random order-preserving function and the hypergeometric probability distribution. In particular, it makes black-box use of an efficient sampling algorithm for the latter. 1

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Citation Context ...rt codes were used, for example, during World War I [3]. A more formal treatment of the concept of order-preserving symmetric encryption (OPE) was proposed in the database community by Agrawal et al. =-=[1]-=-. The reason for new interest in such schemes is that they allow efficient range queries on encrypted data. That is, a remote untrusted database server is able to index the (sensitive) data it receive... |

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Citation Context ...sed in practice (e.g. range queries) has remained open. The work of [24] suggested enabling efficient range queries on encrypted data not by using OPE but so-called prefix-preserving encryption (PPE) =-=[31, 5]-=-. Unfortunately, as discussed in [24, 2], PPE schemes are subject to certain attacks in this context; particular queries can completely reveal some of the underlying plaintexts in the database. Moreov... |

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Citation Context ...work extends a recent line of research in the cryptographic community addressing efficient (sub-linear time) search on encrypted data, which has been addressed by [2] in the symmetric-key setting and =-=[6, 10, 7]-=- in the public-key setting. However, these works focus mainly on simple exact-match queries. Development and analysis of schemes allowing more complex query types that are used in practice (e.g. range... |

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Citation Context ...deed, subsequent to its publication, [1] has been referenced widely in the database community, and OPE has also been suggested for use in in-network aggregation on encrypted data 1in sensor networks =-=[30]-=- and as a tool for applying signal processing techniques to multimedia content protection [13]. Yet a cryptographic study of OPE in the provable-security tradition never appeared. Our work aims to beg... |

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Citation Context ...work extends a recent line of research in the cryptographic community addressing efficient (sub-linear time) search on encrypted data, which has been addressed by [2] in the symmetric-key setting and =-=[6, 10, 7]-=- in the public-key setting. However, these works focus mainly on simple exact-match queries. Development and analysis of schemes allowing more complex query types that are used in practice (e.g. range... |

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Citation Context ... the target-applications require. (Such an approach was taken previously in the case of deterministic public-key encryption [6, 10, 7], on-line ciphers [5], and deterministic authenticated encryption =-=[27]-=-.) Weakening IND-CPA. One approach is to try to weaken the IND-CPA definition appropriately. Indeed, in the case of deterministic symmetric encryption this was done by [8], which formalizes a notion c... |

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Citation Context ...bove for a VOL-PRG adversary making 1 query, and then the proposition follows by a standard hybrid argument. Now, to instantiate the VIL-PRF F in the TapeGen construction, we suggest OMAC (aka. CMAC) =-=[21]-=-, which is also blockcipher-based and introduces no additional assumption. Then the secret-key for TapeGen consists only of that for OMAC, which in turn consists of just one key for the underlying blo... |

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Citation Context ...dy this situation. Related Work. Our work extends a recent line of research in the cryptographic community addressing efficient (sub-linear time) search on encrypted data, which has been addressed by =-=[2]-=- in the symmetric-key setting and [6, 10, 7] in the public-key setting. However, these works focus mainly on simple exact-match queries. Development and analysis of schemes allowing more complex query... |

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Citation Context ...sed in practice (e.g. range queries) has remained open. The work of [24] suggested enabling efficient range queries on encrypted data not by using OPE but so-called prefix-preserving encryption (PPE) =-=[31, 5]-=-. Unfortunately, as discussed in [24, 2], PPE schemes are subject to certain attacks in this context; particular queries can completely reveal some of the underlying plaintexts in the database. Moreov... |

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Citation Context ...GD are the running-times of the sampling algorithms for the respective distributions), but we show that it is O(log M) · THGD on average. We note that the hypergeometric distribution was also used in =-=[19]-=- for sampling pseudorandom permutations and constructing blockciphers for short inputs. The authors of [19] were unaware of the efficient sampling algorithms for HG [22, 23] and provided their own rea... |

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Citation Context ...e works focus mainly on simple exact-match queries. Development and analysis of schemes allowing more complex query types that are used in practice (e.g. range queries) has remained open. The work of =-=[24]-=- suggested enabling efficient range queries on encrypted data not by using OPE but so-called prefix-preserving encryption (PPE) [31, 5]. Unfortunately, as discussed in [24, 2], PPE schemes are subject... |

5 |
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Citation Context ... and OPE has also been suggested for use in in-network aggregation on encrypted data 1in sensor networks [30] and as a tool for applying signal processing techniques to multimedia content protection =-=[13]-=-. Yet a cryptographic study of OPE in the provable-security tradition never appeared. Our work aims to begin to remedy this situation. Related Work. Our work extends a recent line of research in the c... |

4 | Algorithm 668: H2PEC: Sampling from the hypergeometric distribution - Kachitvichyanukul, Schmeiser - 1988 |

1 |
Cem Say and A. Kutsi Nircan. Random generation of monotonic functions for Monte Carlo solution of qualitative differential equations. Automatica
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Citation Context ... result may also be of independent interest, since the more general question of what functions can be lazy-sampled is interesting in its own right, and it may find other applications as well, e.g. to =-=[12]-=-. We first uncover a connection between a random order-preserving function and the hypergeometric (HG) probability distribution. 4.1 The Hypergeometric Connection To gain some intuition we start with ... |

1 |
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Citation Context ... an efficient sampling algorithm for the NHG distribution. Unfortunately, the existence of such an algorithm seems open. It is known that NHG can be approximated by the negative binomial distribution =-=[26]-=-, which in turn can be sampled efficiently [16, 14], and that the approximation improves as M and N grow. However, quantifying the quality of approximation for fixed parameters seems difficult. Instea... |