Unbiased bits from sources of weak randomness and probabilistic communication complexity
SIAM Journal on Computing - Special issue on cryptography
Unconditional security in quantum cryptography
Journal of the ACM (JACM)
Quantum computation and quantum information
Quantum computation and quantum information
On the (non)Universality of the One-Time Pad
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
On the Impossibility of Private Key Cryptography with Weakly Random Keys
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Independent Unbiased Coin Flips From A Correlated Biased Source: A Finite State Markov Chain
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
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The lack of perfect randomness can cause significant problems in securing communication between two parties. McInnes and Pinkas [13] proved that unconditionally secure encryption is impossible when the key is sampled from a weak random source. The adversary can always gain some information about the plaintext, regardless of the cryptosystem design. Most notably, the adversary can obtain full information about the plaintext if he has access to just two bits of information about the source (irrespective on length of the key). In this paper we show that for every weak random source there is a cryptosystem with a classical plaintext, a classical key, and a quantum ciphertext that bounds the adversary's probability p to guess correctly the plaintext strictly under the McInnes-Pinkas bound, except for a single case, where it coincides with the bound. In addition, regardless of the source of randomness, the adversary's probability p is strictly smaller than 1 as long as there is some uncertainty in the key (Shannon/min-entropy is non-zero). These results are another demonstration that quantum information processing can solve cryptographic tasks with strictly higher security than classical information processing.