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Applied Optics

Optical Hash function based on two-beam interference

Hongji Lai, Wenqi He, Xiang Peng

Published Aug 21, 2013• 6 citations
Publisher

Abstract

An approach for constructing an optical Hash function, also known as a one-way cryptosystem, based on two-beam interference (OHF-TBI) is proposed. The purpose of this method is creating the "digital fingerprint" of any precoding message with arbitrary length. This approach consists of three steps, in which the main step is a one-way processing procedure with a compression mechanism. To achieve the function of one-way property and compressibility, we designed a cascaded process on the basis of the two-beam interference principle and phase-truncation operation. The performance of the mentioned OHF-TBI is verified by theoretical analysis and a set of numerical simulations.

DOI
10.1364/ao.52.006213

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An approach for constructing an optical Hash function, also known as a one-way cryptosystem, based on two-beam interference (OHF-TBI) is proposed. The purpose of this method is creating the "digital fingerprint" of any precoding message with arbitrary length. This approach consists of three steps, in which the main step is a one-way processing procedure with a compression mechanism. To achieve the function of one-way property and compressibility, we designed a cascaded process on the basis of the two-beam interference principle and phase-truncation operation. The performance of the mentioned OHF-TBI is verified by theoretical analysis and a set of numerical simulations.
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A novel asymmetric cryptosystem based on coherent superposition, which is free from silhouette problem, is proposed. Being different from the phase-truncated Fourier transform-based cryptosystem, the encryption process uses equal modulus decomposition (EMD) to create an effective trapdoor one-way function. As a result, the proposed method achieves high robustness against the special attack based on iterative Fourier transform. Simulation results are presented to prove the validity of the proposed system.
In the letter we define the notion of a quantum resistant ( -resistant) hash function which consists of a combination of pre-image (one-way) resistance ( ε -resistance) and collision resistance ( δ -resistance) properties. We present examples and discussion that supports the idea of quantum hashing. We present an explicit quantum hash function which is ‘balanced’, one-way resistant and collision resistant and demonstrate how to build a large family of quantum hash functions. Balanced quantum hash functions need a high degree of entanglement between the qubits. We use a phase transformation technique to express quantum hashing constructions, which is an effective way of mapping hash states to coherent states in a superposition of time-bin modes. The phase transformation technique is ready to be implemented with current optical technology.
We present a version of quantum hash function based on non-binary discrete functions. The proposed quantum procedure is "classical-quantum", that is, it takes a classical bit string as an input and produces a quantum state. The resulting function has the property of a one-way function (pre-image resistance), in addition it has the properties analogous to classical cryptographic hash second pre-image resistance and collision resistance. This function can be naturally used in a quantum digital signature protocol.
Quantum digital signatures (QDSs), generating correlated bit strings among three remote parties for signatures through quantum law, can guarantee nonrepudiation, authenticity, and integrity of messages. Recently, a one-time universal-hashing QDS framework, exploiting the quantum asymmetric encryption and universal hash functions, has been proposed to significantly improve the signature rate and ensure unconditional security by directly signing the hash value of long messages. However, similar to quantum key distribution, this framework utilizes keys with perfect secrecy by performing privacy amplification that introduces cumbersome matrix operations, thereby consuming large computational resources, causing delays, and increasing failure probability. Here, we prove that, different from private communication, imperfect quantum keys with partial information leakage can be used for digital signatures and authentication without compromising the security while having eight orders of magnitude improvement on signature rate for signing a megabit message compared with conventional single-bit schemes. This study significantly reduces the delay for data postprocessing and is compatible with any quantum key generation protocols. In our simulation, taking two-photon twin-field key generation protocol as an example, QDS can be practically implemented over a fiber distance of 650 km between the signer and receiver. For the first time, this study offers a cryptographic application of quantum keys with imperfect secrecy and paves a way for the practical and agile implementation of digital signatures in a future quantum network.
We present a version of quantum hash functions based on non-binary discrete functions. The proposed quantum procedure is 'classical-quantum', that is, it takes a classical bit string as an input and produces a quantum state. The resulting function has the property of a one-way function (pre-image resistance); in addition it has properties analogous to classical cryptographic hash second pre-image resistance and collision resistance. We also show that the proposed function can be naturally used in a quantum digital signature protocol.