This paper examines classical privacy amplification using a universal family of hash functions. In quantum key distribution, the adversary's measurement can wait until the choice of hash functions is announced, and so the adversary's information may depend on the choice. Therefore the existing result on classical privacy amplification, which assumes the independence of the choice from the other random variables, is not applicable to this case. This paper provides a security proof of privacy amplification which is valid even when the adversary's information may depend on the choice of hash functions. The compression rate of the proposed privacy amplification can be taken to be the same as that of the existing one with an exponentially small loss in secrecy of a final key.
This paper examines classical privacy amplification using a universal family of hash functions. In quantum key distribution, the adversary's measurement can wait until the choice of hash functions is announced, and so the adversary's information may depend on the choice. Therefore the existing result on classical privacy amplification, which assumes the independence of the choice from the other random variables, is not applicable to this case. This paper provides a security proof of privacy amplification which is valid even when the adversary's information may depend on the choice of hash functions. The compression rate of the proposed privacy amplification can be taken to be the same as that of the existing one with an exponentially small loss in secrecy of a final key.
Privacy amplification is an indispensable step in the post-processing of quantum key distribution, which can be used to compress the redundancy of shared key and improve the security level of the key. The commonly used privacy amplification is based on the random selection of universal hash functions, which needs the help of an additional random source, while it does not exist in general. In this paper, we propose a privacy amplification scheme based on composite coding, which is an extension of quantum CSS codes to classical linear codes. Compared with the universal hashing function, the proposed scheme does not need other random sources, and the randomness can be completely provided by the qubit string. Furthermore, the information-theoretic bound for the extraction of the key is obvious in composite coding.
Quantum Key Distribution (QKD) protocols typically involve two separate steps of error-verification and privacy amplification. Both steps involve the application of a hash function sampled from a suitable hash family to classical data. A potentially simpler alternative is to implement a single-step hashing procedure, announce and compare a fixed number of bits of its output for error-verification, and retain the remaining bits as the final output key. This reduces the complexity of classical postprocessing, the amount of classical communication, and the amount of randomness needed in the protocol. While this construction has appeared in the literature, a suitable mathematical justification is lacking. In this work, we show that the security of such protocols, under certain simple conditions, follows from a slightly modified notion of secrecy of the protocol without the final error-verification step. In particular, we show that for most entropy-based proofs, the combined protocol can be implemented with no change to the key rate, and a minor change to the security parameter.
We introduce the concept of selectable knowledge, which models the information stored in an arbitrary (e.g., quantum mechanical) device. We then analyze a situation where an entity A holds selectable knowledge about some random variable X and quantify the information A has about the output H(X) of a randomly chosen function H applied to X. This generalizes the setting of privacy amplification by universal hashing. In particular, our result can be used to prove that privacy amplification remains secure even if the enemy possesses quantum instead of classical information.
Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information.
Privacy amplification (PA) is a vital step in the postprocessing stage of quantum key distribution, which can extract a secure key from a source partially leaked to the environment. We propose a PA scheme that uses the square hash (SQH)--modular arithmetic hash (MH) function. In consideration of a potential quantum attacker, we use the trace distance as a metric to measure the closeness between two classical-quantum states. We transform a raw key state to a processed state using this scheme and derive the trace distance between the processed state and the ideal target state. It is proven that the trace distance can be reached as small as desired. Additionally, our approach accelerates the SQH-MH function through the number-theoretic transform, reducing the computational complexity to O(nlogn). On the basis of a CPU, a maximum throughput rate of 1.06 Gbit/s is achieved, and the results show that our algorithm demonstrates good stability of the throughput rate when handling tasks with different compression ratios.
This is the third part of a three-part paper on se- cret-key agreement secure against active adversaries. Here, we con- sider the special case where the legitimate partners already share a mutual string which might, however, be partially known to the adversary. The problem of generating a key in this case has been well studied in the passive-adversary model—for instance, in the context of quantum key agreement—under the name of privacy amplification. We consider the same problem with respect to an ac- tive adversary and propose two protocols, one based on universal hashing and one based on extractors, allowing for privacy ampli- fication secure against an adversary whose knowledge about the initial partially string is limited to one third of the length of this string. Our results are based on novel techniques for au- thentication secure even against adversaries knowing a substantial amount of the secret key. information about . From Eve's point of view, the length of can in this case be roughly equal to the Renyi entropy of . In this paper, we investigate the same problem under the as- sumption that the communication between Alice and Bob is not authenticated. Note that, in contrast to the model where many independent repetitions of the involved random variables are given (15), the same piece of information must be used here both for authentication and as the input for privacy amplifica- tion. Two problems that arise in this context are authentication with an only partially key, and the fact that this authenti- cation leaks information about , hence potentially also about , to the adversary. We show that for our purpose, a new, inter- active, authentication method is better than one-way authentica- tion by strongly universal hashing, and that so-called extractors, requiring fewer random bits (i.e., shorter messages to be com- municated), are a better technique for privacy amplification than