The Complexity of Online Memory Checking

We consider the problem of storing a large file on a remote and unreliable server. To verify that the file has not been corrupted, a user could store a small private (randomized) “fingerprint” on his own computer. This is the setting for the well-studied authentication problem in cryptography, and the required fingerprint size is well understood. We study the problem of sub-linear authentication: suppose the user would like to encode and store the file in a way that allows him to verify that it has not been corrupted, but without reading the entire file. If the user only wants to read q bits of the file, how large does the size s of the private fingerprint need to be? We define this problem formally, and show a tight lower bound on the relationship between s and q when the adversary is not computationally bounded, namely: s × q = Ω(n), where n is the file size. This is an easier case of the online memory checking problem, introduced by Blum et al. in 1991, and hence t...

• Type: Conference
• Year: 2005
• Where: FOCS
• Authors: Moni Naor, Guy N. Rothblum
• Keywords: FOCS 2005, Lower Bound, One-way Functions, Theoretical Computer Science, Well-studied Authentication Problem