**Proofs of Space: When Space is of the Essence**

*Giuseppe Ateniese and Ilario Bonacina and Antonio Faonio and Nicola Galesi*

**Abstract: **Proofs of computational effort were devised to control denial of service attacks. Dwork and Naor (CRYPTO ’92), for example, proposed to use such proofs to discourage spam. The idea is to couple each email message with a proof of work that demonstrates the sender performed some computational task. A proof of work can be either CPU-bound or memory-bound. In a CPU-bound proof, the prover must compute a CPU-intensive function that is easy to check by the verifier. A memory-bound proof, instead, forces the prover to access the main memory several times, effectively replacing CPU cycles with memory accesses.
In this paper we put forward a new concept dubbed proof of space. To compute such a proof, the prover must use a specified amount of space, i.e., we are not interested in the number of accesses to the main memory (as in memory-bound proof of work) but rather on the amount of actual memory the prover must employ to compute the proof. We give a complete and detailed algorithmic description of our model. We develop a comprehensive theoretical analysis which uses combinatorial tools from Complexity Theory (such as pebbling games) which are essential in studying space lower bounds.

**Category / Keywords: **foundations / Space Complexity, Proof of Work, Pebbling Game, Random Oracle Model

**Original Publication**** (with major differences): **SCN 2014

**Date: **received 1 Dec 2013, last revised 3 Jul 2014

**Contact author: **afaonio at gmail com

**Available format(s): **PDF | BibTeX Citation

**Version: **20140703:194705 (All versions of this report)

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