Chapter

Public-Key Cryptography – PKC 2013

Volume 7778 of the series Lecture Notes in Computer Science pp 89-106

Cryptography Using Captcha Puzzles

  • Abishek KumarasubramanianAffiliated withUniversity of California
  • , Rafail OstrovskyAffiliated withUniversity of California
  • , Omkant PandeyAffiliated withUniversity of Texas at Austin
  • , Akshay WadiaAffiliated withUniversity of California

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Abstract

A Captcha is a puzzle that is easy for humans but hard to solve for computers. A formal framework, modelling Captcha puzzles (as hard AI problems), was introduced by Ahn, Blum, Hopper, and Langford ([1], Eurocrypt 2003). Despite their attractive features and wide adoption in practice, the use of Captcha puzzles for general cryptographic applications has been limited.

In this work, we explore various ways to formally model Captcha puzzles and their human component and explore new applications for Captcha. We show that by defining Captcha with additional (strong but realistic) properties, it is possible to broaden Captcha applicability, including using it to learning a machine’s “secret internal state.” To facilitate this, we introduce the notion of an human-extractable Captcha, which we believe may be of independent interest. We show that this type of Captcha yields a constant round protocol for fully concurrent non-malleable zero-knowledge. To enable this we also define and construct a Captcha-based commitment scheme which admits “straight line” extraction. We also explore Captcha definitions in the setting of Universal Composability (UC). We show that there are two (incomparable) ways to model Captcha within the UC framework that lead to different results. In particular, we show that in the so called indirect access model, for every polynomial time functionality \(\ensuremath{\mathcal{F}}\) there exists a protocol that UC-realizes \(\ensuremath{\mathcal{F}}\) using human-extractable Captcha, while for the so-called direct access model, UC is impossible, even with the help of human-extractable Captcha.

The security of our constructions using human-extractable Captcha is proven against the (standard) class of all polynomial time adversaries. In contrast, most previous works guarantee security only against a very limited class of adversaries, called the conservative adversaries.

Keywords

Captcha concurrent non-malleable zero-knowledge universal composability human-extractable Captcha