Quantum Cryptography

In traditional cryptography, encryption is achieved through mathematical algorithms that rely on the computational complexity of factoring large numbers or other mathematical problems. In contrast, quantum cryptography uses the properties of quantum mechanics to create unconditionally secure communication channels.

One of the key principles of quantum cryptography is the fact that measuring a quantum system can disturb it. This means that any attempt to eavesdrop on a quantum communication channel will be immediately detectable, as the act of measurement will alter the state of the system being observed.

Quantum cryptography typically involves the exchange of qubits, which are the quantum equivalent of classical bits. The qubits are encoded with the information to be transmitted and are sent over a communication channel. By exchanging qubits, the two parties can establish a shared secret key, which can be used to encrypt and decrypt messages.

There are several different techniques used in quantum cryptography, including quantum key distribution (QKD), quantum teleportation, and quantum secure direct communication (QSDC). QKD is perhaps the most well-known and involves the exchange of single photons, which are used to generate a shared secret key.

Overall, quantum cryptography has the potential to revolutionize the way that secure communication is achieved, offering unbreakable encryption that is guaranteed to be secure against even the most sophisticated attacks.Quantum cryptography is cryptography augmented or enhanced by quantum means.

Cryptanalyses

Cryptanalysis is the study of analyzing and breaking cryptographic systems with the aim of deciphering the original message without knowing the secret key or the algorithm used to encrypt it. Cryptography is the science of creating secure communication channels, whereas cryptanalysis is the science of breaking them.

The goal of cryptanalysis is to find weaknesses in cryptographic systems that can be exploited to extract the original message. Cryptanalysts use various techniques to break encrypted messages, including brute-force attacks, frequency analysis, side-channel attacks, and differential cryptanalysis.

Brute-force attacks involve trying all possible combinations of keys until the correct one is found. This approach is effective against simple encryption schemes, but it quickly becomes infeasible as the size of the key increases.

Frequency analysis involves analyzing the frequency of occurrence of letters, words, or other patterns in the encrypted message. By comparing the frequency distribution of the encrypted message to that of the original language, a cryptanalyst can infer information about the original message.

Side-channel attacks involve exploiting weaknesses in the physical implementation of a cryptographic system. For example, a cryptanalyst might use power analysis to measure the power consumption of a device during encryption, which can reveal information about the secret key.

Differential cryptanalysis is a statistical method for breaking encryption schemes that rely on substitution and permutation operations. The technique involves analyzing the differences between pairs of plaintexts and ciphertexts to deduce information about the secret key.

In summary, cryptanalysis is an important field of study for understanding the strengths and weaknesses of cryptographic systems. By identifying vulnerabilities and weaknesses, cryptanalysts can help improve the security of cryptographic systems and ensure that sensitive information remains secureQuantum cryptography is a subfield of quantum information science that utilizes the principles of quantum mechanics to achieve secure communication. It provides a method for two parties to communicate in a way that is guaranteed to be private and tamper-proof.

What are important quantum means?

(i) Complementarity: the impossibility of value definiteness for two or more complementary shares or observables. It is still possible to hold one share or observable value definite. But this renders other shares or observables value indefinite.

(ii) Entanglement: the relational encoding of multi-paricle states in a way that only relational, joint, properties are defined. The states of the single constituents of such an entangled multi-paritite state are undefined, that is, they are value indefinite: without any value before measurement. Measurement of single particle properties destrays entanglement.

(III) Coherence and parallelism: a quantum state can simultaneously be is any number of classically mutually exclusive states in parallel.

(IV) Contextuality: this notion is used for many different quantum features, most prominently for nonclassical or even nonexistent value assignments. it has also been used to express the conditionality of quantum observables on the context of measurement - that is, onthe complete disposition of the measurement apparatus, and on what other observables are implicitly measured along the primary observable.

All of these features and considerations are subject to, and relative to the assumption of quantum mechanics. That is, one cannot exclude the possibility of some "post-quantum" physics that would either invalidate quantum theory, or would contain quantum mechanics as as subset, thereby potentially challange quantum means by "post-quantum" means - for instance, "hidden parameter models". Currently this possibility appears remote but should be kept in mind. Any attempt in this direction would be in contradiction to the laws of physics presently accepted as canonical.

Attempts in quantum cryptanalysis include, but are not limited to:

(i) the evaluation of quantum cryptanalytic attacks on cryptocurrencies by (relative to transaction processing) "fast" computation of the private key from the public key of digital signatures:

(ii) the search for and development of quantum cryptographic protocols for digital signatures which are save to quantum cryptanalytic attacks.

(iii) the search for and development of (quantum) cryptographic protocols which are novel and asymmetric (e.g. based on hypergraph theory);

(iv) certification and due diligence of existing realizations of quantum communication protocols;

(v) search into improved quantum comunication protocols.

To give a taste of the type of challenges concrete quantum cryptographic protocols are confronted with:

(i) Due to complementary, there are no localized single-quantum states presumed in idealized theoretical protocol descriptions. Multi-particle states may give rise to cryptanalytic attacks and eavesdropping.

(ii) Almost paradoxically quantum cryptography starts from, or is often motivated by, the possibility to compromise a classical communication channel. Yet at the same time many proofs of "unconditional security" of quantum cryptographic protocols presume a save, uncompromised classical commuication channel! This is already evident in the pioneering BB84 paper by Charles Bennett and Gilles Brassard in 1984: What is called "active eavesdropping" there refers to the possibility for a cryptanalytic man-in-the-middle attackby compromising both the classical as well asthe quantum channel.

For these reasons it is prudent to consider quantum cryptography as a means to grow a pre-existing commen key.

Randomness

Randomness is a fundamental concept in quantum research and refers to the unpredictability of the outcomes of quantum measurements. In quantum mechanics, the state of a system is described by a wave function that contains information about all possible outcomes of a measurement. However, the act of measuring a quantum system disturbs its state, causing it to collapse into one of the possible outcomes. The outcome of a measurement is inherently random and cannot be predicted with certainty.

This inherent randomness in quantum mechanics has important implications for quantum research and applications. For example, randomness is used to generate secure cryptographic keys through the process of quantum random number generation (QRNG). QRNG relies on the unpredictability of quantum measurements to produce a stream of random bits that can be used for cryptographic purposes. 

Overall, the role of randomness in quantum research is a fascinating and important topic, with implications especially for cryptography.  

More services Qrand can offer:

(i) certification and due diligence of existing random number generators an random sequences;

(ii) improvement and upgrade - e.g. normalization, see later (iv) - of existing random sequences, relative to pre-defined goals and tasks;

(iii) production of n-ary (n>1 but finite) random sequences; e.g., by recording detector clicks from quantum systems, which are insome coherent superposition (aka linear combination in Hilbert space) and subject to quantum features such as complementarity, nonlocality, and contextuality;

(iv) un-biasing by normalization of n-ary sequences to eliminate bias from such sequences because of unavoidable imperfections (e.g., thermal drift, misalignments) by modern advanced coding techniques.