Abstract
A key idea in cryptography is using hard functions in order to obtain secure schemes. The theory of hard functions (e.g. one-way functions) has been a great success story, and the community has developed a fairly strong understanding of what types of cryptographic primitives can be achieved under which assumption.
We explore the idea of using moderately hard functions in order to achieve many tasks for which a perfect solution is impossible, for instance, denial-of-service. We survey some of the applications of such functions and in particular describe the properties moderately hard functions need for fighting unsolicited electronic mail. We suggest several research directions and (re)call for the development of a theory of such functions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abadi, M., Burrows, M., Manasse, M., Wobber, T.: Moderately Hard, Memory-Bound Functions. In: Proceedings of the 10th Annual Network and Distributed System Security Symposium (February 2003)
Ajtai, M.: Generating Hard Instances of Lattice Problems. In: 28th Annual Symposium on Theory Of Computing (STOC), pp. 99–108 (1996)
Ajtai, M.: Determinism versus Non-Determinism for Linear Time RAMs. In: STOC 1999, pp. 632–641 (1999)
Ajtai, M.: A Non-linear Time Lower Bound for Boolean Branching Programs. In: FOCS 1999, pp. 60–70 (1999)
Back, A.: Hashcash - A Denial of Servic Counter-Measure, available at http://www.cypherspace.org/hashcash/hashcash.pdf
Beame, P., Saks, M.E., Sun, X., Vee, E.: Super-linear time-space tradeoff lower bounds for randomized computation. In: FOCS 2000, pp. 169–179 (2000)
Bellare, M., Goldwasser, S.: Verifiable Partial Key Escrow. In: Proc. of 4th ACM Symp. on Computer and Communications Security, pp. 78–91 (1997)
Bellare, M., Goldwasser, S.: Encapsulated key escrow. MIT Laboratory for Computer Science Technical Report 688 (April 1996)
Ben-Or, M., Goldreich, O., Micali, S., Rivest, R.L.: A Fair Protocol for Signing Contracts. IEEE Transactions on Information Theory 36/1, 40–46 (1990)
Blum, M.: How to Exchange (Secret) Keys. In: Proc. 15th ACM Symp. on Theory of Computing, pp. 440–447 (1983), ACM TOCS 1(2), 175–193 (1983)
Blum, L., Blum, M., Shub, M.: A Simple Unpredictable Pseudo-Random Number Generator. SIAM J. Comput. 15(2), 364–383 (1986)
Boneh, D., Naor, M.: Timed Commitments. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 236–254. Springer, Heidelberg (2000)
Cai, J.Y., Lipton, R.J., Sedgwick, R., Yao, A.C.: Towards uncheatable benchmarks, Structures in Complexity. In: Proc. Structures in Complexity, pp. 2–11 (1993)
Canetti, R., Goldreich, O., Goldwasser, S., Micali, S.: Resettable Zero-Knowledge, ECCC Report TR99-042 (October 27, 1999), Proc. of 32nd ACM Symp. on Theory of Computing, pp. 235–244 (2000)
Canetti, R., Kilian, J., Petrank, E., Rosen, A.: Concurrent Zero-Knowledge Requires Ω̃(log n) Rounds. In: Proc. of the 33rd ACM Symposium on the Theory of Computing, pp. 570–579 (2001), Full version: Electronic Colloquium on Computational Complexity, Report TR01-050, vol. 8 (2001), Available: www.eccc.uni-trier.de/eccc/
Cleve, R.: Limits on the Security of Coin Flips when Half the Processors Are Faulty. In: Proc. of 18th ACM Symp. on Theory of Computing, pp. 364–369 (1986)
Cleve, R.: Controlled gradual disclosure schemes for random bits and their applications. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 573–588. Springer, Heidelberg (1990)
Cleve, R., Impagliazzo, R.: Martingales, collective coin flipping and discrete control processes (1993) (manuscript), Available: http://www.cpsc.ucalgary.ca/~cleve/papers.html
Damgård, I.: Concurrent Zero-Knowledge in the auxiliary string model. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 418–430. Springer, Heidelberg (2000)
Damgård, I.: Practical and Provably Secure Release of a Secret and Exchange of Signatures. J. of Cryptology 8(4), 201–222 (1995)
Douceur, J.: The Sybil Attack. In: Druschel, P., Kaashoek, M.F., Rowstron, A. (eds.) IPTPS 2002. LNCS, vol. 2429, p. 251. Springer, Heidelberg (2002)
Dolev, D., Dwork, C., Naor, M.: Non-malleable Cryptography. Siam J. on Computing 30(2), 391–437 (2000)
Dwork, C., Goldberg, A., Naor, M.: On Memory-Bound Functions for Fighting Spam. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 426–444. Springer, Heidelberg (2003)
Dwork, C., Naor, M.: Pricing via Processing -or- Combatting Junk Mail. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 139–147. Springer, Heidelberg (1993)
Dwork, C., Naor, M.: Zaps and their applications. In: Proc. 41st IEEE Symp. on Foundations of Computer Science, pp. 283–293 (2000); Also: Electronic Colloquium on Computational Complexity (ECCC)(001) (2002)
Dwork, C., Naor, M., Sahai, A.: Concurrent Zero-Knowledge. In: Proc. of the 30th ACM Symposium on the Theory of Computing, pp. 409–418 (1998)
Dwork, C., Stockmeyer, L.: 2-Round Zero-Knowledge and Proof Auditors. In: Proc. of the 34th ACM Symposium on Theory of Computing, pp. 322–331 (2002)
Even, S., Goldreich, O., Lempel, A.: A Randomized Protocol for Signing Contracts. CACM 28(6), 637–647 (1985)
Feigenbaum, J., Fortnow, L.: Random-Self-Reducibility of Complete Sets. SIAM J. Comput. 22(5), 994–1005 (1993)
Franklin, M., Malkhi, D.: Auditable metering with lightweight security. Journal of Computer Security 6(4) (1998)
Goldreich, O.: Foundation of Cryptography – Basic Tools. Cambridge University Press, Cambridge (2001)
Goldreich, O., Krawczyk, H.: On the Composition of Zero Knowledge Proof Systems. SIAM J. on Computing 25(1), 169–192 (1996)
Goldschlag, D., Stubblebine, S.: Publicly Verifiable Lotteries: Applications of Delaying Functions. In: Hirschfeld, R. (ed.) FC 1998. LNCS, vol. 1465, pp. 214–226. Springer, Heidelberg (1998)
Goldwasser, S.: New directions in cryptography: Twenty some years later. In: Proceedings of 38th Annual Symposium on Foundations of Computer Science, pp. 314–324. IEEE, Los Alamitos (1997)
Impagliazzo, R., Rudich, S.: Limits on the provable consequences of one-way permutations. In: STOC 1989, pp. 44–61(1989)
Juels, A., Brainard, J.: Client Puzzles: A Cryptographic Countermeasure Against Connection Depletion Attacks
Kilian, J., Petrank, E., Rackoff, C.: Lower Bounds for Zero Knowledge on the Internet. In: IEEE 38th Symp. on Foundations of Computer Science, pp. 484–492 (1998)
Luby, M., Micali, S., Rackoff, C.: How to Simultaneously Exchange a Secret Bit by Flipping a Symmetrically-Biased Coin. In: Proc. IEEE Symp. Foundations of Computer Science, pp. 11–21 (1983)
Menezes, A., van Oorschot, P., Vanstone, S.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1996)
Naor, M., Pinkas, B., Sumner, R.: Privacy Preserving Auctions and Mechanism Design. In: Proc. of the 1st ACM conference on E-Commerce, November 1999, pp. 129–139 (1999)
Rivest, R.: Description of the LCS35 Time Capsule Crypto-Puzzle (April 4, 1999), available: http://www.lcs.mit.edu/research/demos/cryptopuzzle0499
Rivest, R., Shamir, A., Wagner, D.: Time lock puzzles and timed release cryptography, Technical report, MIT/LCS/TR-684
Rosen, A.: A note on the round-complexity of concurrent zero-knowledge. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 451–468. Springer, Heidelberg (2000)
Rosenthal, D.H.S., Roussopoulos, M., Maniatis, P., Baker, M.: Economic Measures to Resist Attacks on a Peer-to-Peer Network. In: Proceedings of the Workshop on Economics of Peer-to-Peer Systems (June 2003)
Syverson, P.: Weakly Secret Bit Commitment: Applications to Lotteries and Fair Exchange. In: Proceedings of the 1998 IEEE Computer Security Foundations Workshop (CSFW11) (June 1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Naor, M. (2003). Moderately Hard Functions: From Complexity to Spam Fighting. In: Pandya, P.K., Radhakrishnan, J. (eds) FST TCS 2003: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2003. Lecture Notes in Computer Science, vol 2914. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24597-1_37
Download citation
DOI: https://doi.org/10.1007/978-3-540-24597-1_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20680-4
Online ISBN: 978-3-540-24597-1
eBook Packages: Springer Book Archive