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Cryptography General Interview Questions

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Naor and Shamir developed what they called visual secret sharing schemes, which are an interesting visual variant of the ordinary secret sharing schemes.

Roughly speaking, the problem can be formulated as follows: There is a secret picture to be shared among n participants. The picture is divided into n transparencies (shares) such that if any m transparencies are placed together, the picture becomes visible, but if fewer than m transparencies are placed together, nothing can be seen. Such a scheme is constructed by viewing the secret picture as a set of black and white pixels and handling each pixel separately. See for more details. The schemes are perfectly secure and easily implemented without any cryptographic computation. A further improvement allows each transparency (share) to be an innocent picture (e.g. a picture of a landscape or a picture of a building), thus concealing the fact that secret sharing is taking place. 

Informally, an interactive proof is a protocol between two parties in which one party, called the prover, tries to prove a certain fact to the other party, called the verifier. An interactive proof usually takes the form of a challenge-response protocol, in which the prover and the verifier exchange messages and the verifier outputs either "accept" or "reject" at the end of the protocol. Besides their theoretical interests, interactive proofs have found applications in cryptography and computer security such as identification and authentication. In these situations, the fact to be proved is usually related to the prover's identity, e.g., the prover's private key.

The following properties of interactive proofs are quite useful, especially in cryptographic applications:

Completeness: The verifier always accepts the proof if the prover knows the fact and both the prover and the verifier follow the protocol.
Soundness: The verifier always rejects the proof if the prover does not know the fact, as long as the verifier follows the protocol.
Zero knowledge: The verifier learns nothing about the fact being proved (except that it is correct) from the prover that he could not already learn without the prover. In a zero-knowledge proof, the verifier cannot even later prove the fact to anyone else.

A typical round in a zero-knowledge proof consists of a "commitment" message from the prover, followed by a challenge from the verifier, and then a response to the challenge from the prover. The protocol may be repeated for many rounds. Based on the prover's responses in all the rounds, the verifier decides whether to accept or reject the proof. 

Consider two questions that may be asked by a computer user as he or she views a digital document or on-line record. (1) Who is the author of this record - who wrote it, approved it, or consented to it? (2) When was this record created or last modified?

In both cases, the question is one about exactly this record-exactly this sequence of bits - whether it was first stored on this computer or was created somewhere else and then copied and saved here. An answer to the first question tells who & what: who approved exactly what is in this record? An answer to the second question tells when & what: when exactly did the contents of this record first exist?

Both of the above questions have good solutions. A system for answering the first question is called a digital signature scheme. Such a system was first proposed in and there is a wide variety of accepted designs for an implementation of this kind of system.

DNA computing, also known as molecular computing, is a new approach to massively parallel computation based on ground-breaking work by Adleman. He used DNA to solve a seven-node Hamiltonian path problem, a special case of an NP-complete problem that attempts to visit every node in a graph exactly once. (This special case is trivial to solve with a conventional computer, or even by hand, but illustrates the potential of DNA computing.)

A DNA computer is basically a collection of specially selected DNA strands whose combinations will result in the solution to some problem. Technology is currently available both to select the initial strands and to filter the final solution. The promise of DNA computing is massive parallelism: with a given setup and enough DNA, one can potentially solve huge problems by parallel search. This can be much faster than a conventional computer, for which massive parallelism would require large amounts of hardware, not simply more DNA. 

Quantum cryptography is a method for secure key exchange over an insecure channel based on the nature of photons. Photons have a polarization, which can be measured in any basis, where a basis consists of two directions orthogonal to each other. If a photon's polarization is read in the same basis twice, the polarization will be read correctly and will remain unchanged. If it is read in two different bases, a random answer will be obtained in the second basis, and the polarization in the initial basis will be changed randomly.

The following protocol can be used by Alice and Bob to exchange secret keys.

Alice sends Bob a stream of photons, each with a random polarization, in a random basis. She records the polarizations.
Bob measures each photon in a randomly chosen basis and records the results.
Bob announces, over an authenticated but not necessarily private channel (e.g., by telephone), which basis he used for each photon.
Alice tells him which choices of bases are correct. 

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