Correcting errors without leaking partial information

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 insu...

• Type: Conference
• Year: 2005
• Where: STOC
• Authors: Yevgeniy Dodis, Adam Smith
• Keywords: Algorithms, Main Open Problem, Private Fuzzy Extractors, Stateless Key Re-use, STOC 2005