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One-Way Functions [
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- Time hierarchies for cryptographic function inversion with advice (Dima Grigoriev, Edward A. Hirsch, Konstantin Pervyshev, ECCC TR05-076)
- On the Power of the Randomized Iterate (Iftach Haitner, Danny Harnik, Omer Reingold, ECCC TR05-135)
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Lossy trapdoor functions []
- [scholar]Lossy Trapdoor Functions and Their Applications (Chris Peikert and Brent Waters, STOC 2008)
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Trapdoor permutations []
- How to sign given any trapdoor permutation (M. Bellare and S. Micali, JACM 92)
- A Trapdoor Permutation Equivalent to Factoring (Pascal Paillier)
- Certifying permutations: Non-interactive zero-knowledge based on any trapdoor permutation (M. Bellare and M. Yung, JoC 1996)
- @Factoring
- @Discrete Logarithm
- @Learning Parity with Noise
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LSRW assumption
- Pseudonym systems (Anna Lysyanskaya, Ronald L. Rivest, Amit Sahai, Stefan Wolf)
- A Cryptographic Framework for the Controlled Release Of Certified Data (Endre Bargerter, Jan Camenisch, Anna Lysyanskaya)
- Concurrent Blind Signatures without Random Oracles (Aggelos Kiayias, Hong-Sheng Zhou, eprint 2005/435)
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Quadratic Residuosity []
- A Low Communication Competitive Interactive Proof System for Promised Quadratic Residuosity (Toshiya Itoh, Masafumi Hoshi, and Shigeo Tsujii, 1993)
- Some combinatorial problems of importance to cryptography (René Peralta, Eiji Okamoto, 1996)
- A Low Communication Competitive Interactive Proof System for Promised Quadratic Residuosity (Toshiya Itoh, Masafumi Hoshi, and Shigeo Tsujii, JoC 1996)
- www.cesg.gov.uk/technology/id-pkc/media/ciren.pdf (An Identity Based Encryption Scheme based on Quadratic Residues)
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Hardness of inversion
- The Cryptographic Impact of Groups with Infeasible Inversion (Susan Rae Hohenberger, MSC Thesis, MIT 2003)
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Phi hiding []
- Computationally Private Information Retrieval with Polylogarithmic Communication (Christian Cachin, Silvio Micali, Markus Stadler, Eurocrypt 1999)
- Efficient Private Bidding and Auctions with an Oblivious Third Party (Christian Cachin, 1999)
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Root extraction/RSA assumption
- On Finding Roots Without Factoring and A Special Purpose Factoring Algorithm (Daniel R. L. Brown, eprint 2005/208)
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- Efficient Cryptographic Schemes Provably as Secure as Subset Sum (Russell Impagliazzo and Moni Naor, Joc 1996)
- Cryptographic Hardness based on the Decoding of Reed-Solomon Codes with Applications (Aggelos Kiayias, Moti Yung, ECCC TR02-017)
- Generalized Compact Knapsacks are Collision Resistant (Vadim Lyubashevsky, Daniele Micciancio, ECCC TR05-142)
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