### Abstract

This paper explores what kinds of information two parties must communicate in order to correct errors which occur in a shared secret string W. Any bits they communicate must leak a significant amount of information about W - that is, from the adversary's point of view, the entropy of W will drop significantly. Nevertheless, we construct schemes with which Alice and Bob can prevent an adversary from learning any useful information about W. Specifically, if the entropy of W is sufficiently high, then there is no function f(W) which the adversary can learn from the error-correction information with significant probability. This leads to several new results: (a) the design of noise-tolerant "perfectly oneway" hash functions in the sense of Canetti et al. [7], which in turn leads to obfuscation of proximity queries for high entropy secrets W; (b) private fuzzy extractors [11], which allow one to extract uniformly random bits from noisy and nonuniform data W, while also insuring that no sensitive information about W is leaked; and (c) noise tolerance and stateless key re-use in the Bounded Storage Model, resolving the main open problem of Ding [10]. The heart of our constructions is the design of strong randomness extractors with the property that the source W can be recovered from the extracted randomness and any string W′ which is close to W.

Original language | English (US) |
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Title of host publication | Proceedings of the Annual ACM Symposium on Theory of Computing |

Pages | 654-663 |

Number of pages | 10 |

DOIs | |

State | Published - 2005 |

Event | 13th Color Imaging Conference: Color Science, Systems, Technologies, and Applications - Scottsdale, AZ, United States Duration: Nov 7 2005 → Nov 11 2005 |

### Other

Other | 13th Color Imaging Conference: Color Science, Systems, Technologies, and Applications |
---|---|

Country | United States |

City | Scottsdale, AZ |

Period | 11/7/05 → 11/11/05 |

### Fingerprint

### Keywords

- Bounded Storage Model
- Code Obfuscation
- Cryptography
- Entropic Security
- Error-Correcting Codes
- Information Reconciliation
- Randomness Extractors

### ASJC Scopus subject areas

- Computer Vision and Pattern Recognition

### Cite this

*Proceedings of the Annual ACM Symposium on Theory of Computing*(pp. 654-663) https://doi.org/10.1145/1060590.1060688

**Correcting errors without leaking partial information.** / Dodis, Yevgeniy; Smith, Adam.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Annual ACM Symposium on Theory of Computing.*pp. 654-663, 13th Color Imaging Conference: Color Science, Systems, Technologies, and Applications, Scottsdale, AZ, United States, 11/7/05. https://doi.org/10.1145/1060590.1060688

}

TY - GEN

T1 - Correcting errors without leaking partial information

AU - Dodis, Yevgeniy

AU - Smith, Adam

PY - 2005

Y1 - 2005

N2 - This paper explores what kinds of information two parties must communicate in order to correct errors which occur in a shared secret string W. Any bits they communicate must leak a significant amount of information about W - that is, from the adversary's point of view, the entropy of W will drop significantly. Nevertheless, we construct schemes with which Alice and Bob can prevent an adversary from learning any useful information about W. Specifically, if the entropy of W is sufficiently high, then there is no function f(W) which the adversary can learn from the error-correction information with significant probability. This leads to several new results: (a) the design of noise-tolerant "perfectly oneway" hash functions in the sense of Canetti et al. [7], which in turn leads to obfuscation of proximity queries for high entropy secrets W; (b) private fuzzy extractors [11], which allow one to extract uniformly random bits from noisy and nonuniform data W, while also insuring that no sensitive information about W is leaked; and (c) noise tolerance and stateless key re-use in the Bounded Storage Model, resolving the main open problem of Ding [10]. The heart of our constructions is the design of strong randomness extractors with the property that the source W can be recovered from the extracted randomness and any string W′ which is close to W.

AB - This paper explores what kinds of information two parties must communicate in order to correct errors which occur in a shared secret string W. Any bits they communicate must leak a significant amount of information about W - that is, from the adversary's point of view, the entropy of W will drop significantly. Nevertheless, we construct schemes with which Alice and Bob can prevent an adversary from learning any useful information about W. Specifically, if the entropy of W is sufficiently high, then there is no function f(W) which the adversary can learn from the error-correction information with significant probability. This leads to several new results: (a) the design of noise-tolerant "perfectly oneway" hash functions in the sense of Canetti et al. [7], which in turn leads to obfuscation of proximity queries for high entropy secrets W; (b) private fuzzy extractors [11], which allow one to extract uniformly random bits from noisy and nonuniform data W, while also insuring that no sensitive information about W is leaked; and (c) noise tolerance and stateless key re-use in the Bounded Storage Model, resolving the main open problem of Ding [10]. The heart of our constructions is the design of strong randomness extractors with the property that the source W can be recovered from the extracted randomness and any string W′ which is close to W.

KW - Bounded Storage Model

KW - Code Obfuscation

KW - Cryptography

KW - Entropic Security

KW - Error-Correcting Codes

KW - Information Reconciliation

KW - Randomness Extractors

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U2 - 10.1145/1060590.1060688

DO - 10.1145/1060590.1060688

M3 - Conference contribution

AN - SCOPUS:34848837353

SP - 654

EP - 663

BT - Proceedings of the Annual ACM Symposium on Theory of Computing

ER -