Abstract
An interesting challenge for the cryptography community is to design authentication protocols that are so simple that a human can execute them
without relying on a fully trusted computer. We propose several candidate authentication protocols for a setting in which the human user can
only receive assistance from a semitrusted computer  a computer that stores information and performs computations correctly
but does not provide confidentiality. Our schemes use a semitrusted computer to store and display public challenges C_i\in[n]^k.
The human user memorizes a random secret mapping \sigma:[n]\rightarrow \mathbb{Z}_d and authenticates by computing responses f(\sigma(C_i)) to
a sequence of public challenges where f:\mathbb{Z}_d^k\rightarrow \mathbb{Z}_d is a function that is easy for the human to evaluate. We prove
that any statistical adversary needs to sample m=\tilde{\Omega}\paren{n^{s(f)}} challengeresponse pairs to recover \sigma, for a security
parameter s(f) that depends on two key properties of f. Our lower bound generalizes recent results of Feldman et al. [Feldman'15]
who proved analogous results for the special case d=2. To obtain our results, we apply the general hypercontractivity theorem [O'Donnell'14]
to lower bound the statistical dimension of the distribution over challengeresponse pairs induced by f and \sigma.
Our statistical dimension lower bounds apply to arbitrary functions f:\mathbb{Z}_d^k\rightarrow \mathbb{Z}_d (not just to functions that
are easy for a human to evaluate). As an application, we propose a family of human computable password
functions f_{k_1,k_2} in which the user needs to perform 2k_1+2k_2+1 primitive operations (e.g., adding two digits or remembering a
secret value \sigma(i)), and we show that s(f) = \min{k_1+1, (k_2+1)/2}. For these schemes, we prove that forging passwords is
equivalent to recovering the secret mapping. Thus, our human computable password schemes can maintain strong security guarantees even after
an adversary has observed the user login to many different accounts.
BibTeX  Entry
@InProceedings{blocki_et_al:LIPIcs:2017:8184,
author = {Jeremiah Blocki and Manuel Blum and Anupam Datta and Santosh Vempala},
title = {{Towards Human Computable Passwords}},
booktitle = {8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
pages = {10:110:47},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770293},
ISSN = {18688969},
year = {2017},
volume = {67},
editor = {Christos H. Papadimitriou},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/8184},
URN = {urn:nbn:de:0030drops81847},
doi = {10.4230/LIPIcs.ITCS.2017.10},
annote = {Keywords: Passwords, Cognitive Authentication, Human Computation, Planted Constraint Satisfaction Problem, Statistical Dimension}
}
Keywords: 

Passwords, Cognitive Authentication, Human Computation, Planted Constraint Satisfaction Problem, Statistical Dimension 
Collection: 

8th Innovations in Theoretical Computer Science Conference (ITCS 2017) 
Issue Date: 

2017 
Date of publication: 

28.11.2017 