Next-bit test

Abstract: 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 one-wayness of functions (or permutations) is known, although the existence of cryptographic pseudorandom generators is equivalent to that of cryptographic one-way functions. In the quantum computation model, Kashefi, Nishimura and Vedral gave a sufficient condition of (cryptographic) quantum one-way permutations and conjectured that the condition would be necessary. In this paper, we affirmatively settle their conjecture and complete a necessary and sufficient condition for quantum one-way permutations. The necessary and sufficient condition can be regarded as a universal test for quantum one-way permutations, since the condition is described as a collection of stepwise tests similar to the next bit test for pseudorandom generators.

Abstract: The next bit test was shown by Yao to be a universal test for sources of unbiased independent bits. The aim of this paper is to provide a rigorous methodology of how to test other properties of sources whose output distribution is not necessarily uniform. We prove the surprising result that the natural extension of the next bit test, even in the simplest case of biased independent bits, is no longer universal: We construct a source of biased bits, whose bits are obviously dependent and yet none of these bits can be predicted with probability of success greater than the bias. To overcome this difficulty, we develop new universal tests for arbitrary models of (potentially imperfect) sources of randomness.

Abstract: The next bit test as introduced by Blum and Micali was shown by Yao to be a universal test for sources of unbiased independent bits The aim of this paper is to provide a rigorous methodology for testing sources whose output distributions are not necessarily uniform We first show that the natural extension of the next bit test, even in the simplest case of biased independent bits, is no longer universal: we construct a source of biased bits, whose bits are obviously dependent and yet none of these bits can be predicted with probability of success greater than the bias To overcome this difficulty, we develop new universal tests for arbitrary models of (potentially imperfect) sources of randomness These new tools contribute to the theoretical as well as practical study of sources of randomness

Abstract: 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 one-wayness 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 model, Kashefi, Nishimura and Vedral gave a sufficient condition of (cryptographic) quantum one-way permutations and conjectured that the condition would be necessary. In this paper, we relax their sufficient condition and give a new condition that is necessary and sufficient for quantum one-way permutations. Our condition can be regarded as a universal test for quantum one-way permutations, since our condition is described as a collection of stepwise tests similar to the next bit test for pseudorandom generators.