2021/12/27 by Asaf Cohen, Neri Merhav, Cohen, Asaf +1
Computer Science · Engineering · #Cryptography and Security (cs.CR) #Digital Media Forensic Detection #Distributed #FOS: Computer and information sciences #Information Theory (cs.IT) #Parallel #Wireless Communication Security Techniques #Wireless Signal Modulation Classification #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.2112.13594
openalex publication_date 2021/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider the problem of guessing a sequence subject to a distortion constraint. Specifically, we assume the following game between Alice and Bob: Alice has a sequence \bx of length n. Bob wishes to guess \bx, yet he is satisfied with finding any sequence \bx which is within a given distortion D from \bx. Thus, he successively submits queries to Alice, until receiving an affirmative answer, stating that his guess was within the required distortion. Finding guessing strategies which minimize the number of guesses (the guesswork), and analyzing its properties (e.g., its ρ--th moment) has several applications in information security, source and channel coding. Guessing subject to a distortion constraint is especially useful when considering contemporary biometrically--secured systems, where the "password" which protects the data is not a single, fixed vector but rather a ball of feature vectors centered at some \bx, and any feature vector within the ball results in acceptance. We formally define the guessing problem under distortion in four different setups: memoryless sources, guessing through a noisy channel, sources with memory and individual sequences. We suggest a randomized guessing strategy which is asymptotically optimal for all setups and is five--fold universal, as it is independent of the source statistics, the channel, the moment to be optimized, the distortion measure and the distortion level.