On Basing One-way Permutations on NP-hard Problems under Quantum Reductions

On Basing Size-Verifiable One-Way Functions on NP-Hardness

We prove that if the hardness of inverting a size-verifiable one-way function can be based on NP-hardness via a general (adaptive) reduction, then NP ⊆ coAM. This claim was made by Akavia, Goldreich, Goldwasser, and Moshkovitz (STOC 2006), but was later retracted (STOC 2010). Akavia, Goldreich, Goldwasser, and Moshkovitz [AGGM06] claimed that if there exists an adaptive reduction from an NP-com...

On the Impossibility of Basing Public-Coin One-Way Permutations on Trapdoor Permutations

One of the fundamental research themes in cryptography is to clarify what the minimal assumptions to realize various kinds of cryptographic primitives are, and up to now, a number of relationships among primitives have been investigated and established. Among others, it has been suggested (and sometimes explicitly claimed) that a family of one-way trapdoor permutations (TDP) is sufficient for c...

On the Impossibilities of Basing One-Way Permutations on Central Cryptographic Primitives

We know that trapdoor permutations can be used to construct all kinds of basic cryptographic primitives, including trapdoor functions, public-key encryption, private information retrieval, oblivious transfer, key agreement, and those known to be equivalent to one-way functions such as digital signature, private-key encryption, bit commitment, pseudo-random generator and pseudo-random functions....

On the Impossibilities of Basing One-Way Permutations on Central Cryptographi Primitives

Universal Test for Quantum One-Way Permutations

The next bit test was introduced by Blum and Micali and proved by Yao to be a universal test for cryptographic pseudorandom generators. On the other hand, no universal test for the cryptographic onewayness of functions (or permutations) is known, though the existence of cryptographic pseudorandom generators is equivalent to that of cryptographic one-way functions. In the quantum computation mod...