On the Complexity of Collision Resistant Hash Functions: New and Old Black-Box Separations

Nir Bitansky; Akshay Degwekar

doi:10.1007/978-3-030-36030-6_17

On the Complexity of Collision Resistant Hash Functions: New and Old Black-Box Separations

Nir Bitansky^*, Akshay Degwekar

^*Corresponding author for this work

School of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The complexity of collision-resistant hash functions has been long studied in the theory of cryptography. While we often think about them as a Minicrypt primitive, black-box separations demonstrate that constructions from one-way functions are unlikely. Indeed, theoretical constructions of collision-resistant hash functions are based on rather structured assumptions. We make two contributions to this study: 1.A New Separation: We show that collision-resistant hashing does not imply hard problems in the class Statistical Zero Knowledge in a black-box way.2.New Proofs: We show new proofs for the results of Simon, ruling out black-box reductions of collision-resistant hashing to one-way permutations, and of Asharov and Segev, ruling out black-box reductions to indistinguishability obfuscation. The new proofs are quite different from the previous ones and are based on simple coupling arguments.

Original language	English
Title of host publication	Theory of Cryptography - 17th International Conference, TCC 2019, Proceedings
Editors	Dennis Hofheinz, Alon Rosen
Publisher	Springer
Pages	422-450
Number of pages	29
ISBN (Print)	9783030360290
DOIs	https://doi.org/10.1007/978-3-030-36030-6_17
State	Published - 2019
Event	17th International Conference on Theory of Cryptography, TCC 2019 - Nuremberg, Germany Duration: 1 Dec 2019 → 5 Dec 2019

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11891 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	17th International Conference on Theory of Cryptography, TCC 2019
Country/Territory	Germany
City	Nuremberg
Period	1/12/19 → 5/12/19

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10.1007/978-3-030-36030-6_17

Cite this

Bitansky, N., & Degwekar, A. (2019). On the Complexity of Collision Resistant Hash Functions: New and Old Black-Box Separations. In D. Hofheinz, & A. Rosen (Eds.), Theory of Cryptography - 17th International Conference, TCC 2019, Proceedings (pp. 422-450). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11891 LNCS). Springer. https://doi.org/10.1007/978-3-030-36030-6_17

Bitansky, Nir ; Degwekar, Akshay. / On the Complexity of Collision Resistant Hash Functions : New and Old Black-Box Separations. Theory of Cryptography - 17th International Conference, TCC 2019, Proceedings. editor / Dennis Hofheinz ; Alon Rosen. Springer, 2019. pp. 422-450 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "The complexity of collision-resistant hash functions has been long studied in the theory of cryptography. While we often think about them as a Minicrypt primitive, black-box separations demonstrate that constructions from one-way functions are unlikely. Indeed, theoretical constructions of collision-resistant hash functions are based on rather structured assumptions. We make two contributions to this study: 1.A New Separation: We show that collision-resistant hashing does not imply hard problems in the class Statistical Zero Knowledge in a black-box way.2.New Proofs: We show new proofs for the results of Simon, ruling out black-box reductions of collision-resistant hashing to one-way permutations, and of Asharov and Segev, ruling out black-box reductions to indistinguishability obfuscation. The new proofs are quite different from the previous ones and are based on simple coupling arguments.",

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Bitansky, N & Degwekar, A 2019, On the Complexity of Collision Resistant Hash Functions: New and Old Black-Box Separations. in D Hofheinz & A Rosen (eds), Theory of Cryptography - 17th International Conference, TCC 2019, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11891 LNCS, Springer, pp. 422-450, 17th International Conference on Theory of Cryptography, TCC 2019, Nuremberg, Germany, 1/12/19. https://doi.org/10.1007/978-3-030-36030-6_17

On the Complexity of Collision Resistant Hash Functions : New and Old Black-Box Separations. / Bitansky, Nir; Degwekar, Akshay.

Theory of Cryptography - 17th International Conference, TCC 2019, Proceedings. ed. / Dennis Hofheinz; Alon Rosen. Springer, 2019. p. 422-450 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11891 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - The complexity of collision-resistant hash functions has been long studied in the theory of cryptography. While we often think about them as a Minicrypt primitive, black-box separations demonstrate that constructions from one-way functions are unlikely. Indeed, theoretical constructions of collision-resistant hash functions are based on rather structured assumptions. We make two contributions to this study: 1.A New Separation: We show that collision-resistant hashing does not imply hard problems in the class Statistical Zero Knowledge in a black-box way.2.New Proofs: We show new proofs for the results of Simon, ruling out black-box reductions of collision-resistant hashing to one-way permutations, and of Asharov and Segev, ruling out black-box reductions to indistinguishability obfuscation. The new proofs are quite different from the previous ones and are based on simple coupling arguments.

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Bitansky N, Degwekar A. On the Complexity of Collision Resistant Hash Functions: New and Old Black-Box Separations. In Hofheinz D, Rosen A, editors, Theory of Cryptography - 17th International Conference, TCC 2019, Proceedings. Springer. 2019. p. 422-450. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-36030-6_17

On the Complexity of Collision Resistant Hash Functions: New and Old Black-Box Separations

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