Cryptography Definition and 11 Discussions

Cryptography, or cryptology (from Ancient Greek: κρυπτός, romanized: kryptós "hidden, secret"; and γράφειν graphein, "to write", or -λογία -logia, "study", respectively), is the practice and study of techniques for secure communication in the presence of third parties called adversaries. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages; various aspects in information security such as data confidentiality, data integrity, authentication, and non-repudiation are central to modern cryptography. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, electrical engineering, communication science, and physics. Applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords, and military communications.
Cryptography prior to the modern age was effectively synonymous with encryption, converting information from a readable state to unintelligible nonsense. The sender of an encrypted message shares the decoding technique only with intended recipients to preclude access from adversaries. The cryptography literature often uses the names Alice ("A") for the sender, Bob ("B") for the intended recipient, and Eve ("eavesdropper") for the adversary. Since the development of rotor cipher machines in World War I and the advent of computers in World War II, cryptography methods have become increasingly complex and its applications more varied.
Modern cryptography is heavily based on mathematical theory and computer science practice; cryptographic algorithms are designed around computational hardness assumptions, making such algorithms hard to break in actual practice by any adversary. While it is theoretically possible to break into a well-designed system, it is infeasible in actual practice to do so. Such schemes, if well designed, are therefore termed "computationally secure"; theoretical advances, e.g., improvements in integer factorization algorithms, and faster computing technology require these designs to be continually reevaluated, and if necessary, adapted. There exist information-theoretically secure schemes that provably cannot be broken even with unlimited computing power, such as the one-time pad, but these schemes are much more difficult to use in practice than the best theoretically breakable but computationally secure schemes.
The growth of cryptographic technology has raised a number of legal issues in the information age. Cryptography's potential for use as a tool for espionage and sedition has led many governments to classify it as a weapon and to limit or even prohibit its use and export. In some jurisdictions where the use of cryptography is legal, laws permit investigators to compel the disclosure of encryption keys for documents relevant to an investigation. Cryptography also plays a major role in digital rights management and copyright infringement disputes in regard to digital media.

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  1. Rzbs

    I Space group symmetry

    What does mean spinel structure has F d3m space group? I know F is for face centred cubic, 3 is 3-fold symmetry and m is mirror, but I don't know what means "d"?
  2. S

    Nobel prize in physics for quantum cryptography?

    Is it likely that this year's Nobel prize could be awarded to the field of quantum cryptography with Charles H Bennet, Gilles Brassard and Artur Ekert as possible nobel laureate candidates?
  3. S

    Comp Sci RSA system with p=17, q=11 and e=3. Find m corresponding to c=156

    OFFICIAL SOLUTION: d=e^(-1) mod 160=107 mp= c^(d) mod p=7 mq:=c^(d) mod q=7 MY THOUGHTS: I understand how d = 107, but I got that by using m = (17-1)(11-1) = 160. What I don't understand is the next two lines (from the official solution). I am aware of the P = C^d mod n (decryption) formula...
  4. N

    Man in the middle attack

    I have some curiosity about MIM attack in a paper that I have been found before. The diagram shows the MIM attack between Alice and Bob: I found that the sentences state: "We consider that the transmittance of the quantum channel is t. If Alice sends pulses with a mean photon number of N...
  5. H

    Number Theory Cryptanalysis books?

    Hey guys, I just bought the book Elementary Cryptanalysis: A Mathematical Approach by Abraham Sinkov, yet before I start it, I would like to know if there are any prerequisites I should know about as I am 16 and I still haven't even taken all of high school mathematics although I am self...
  6. The Inner Workings of an Enigma Machine

    The Inner Workings of an Enigma Machine

    Ever wonder how the famous Enigma Machine worked? Mathematician and cryptography expert Dr. James Grime takes one apart to demonstrate how it created complex codes.
  7. T

    Learning number theory for cryptography

    Hi everyone, I am trying to learn the underlying number theory concepts behind cryptography, and I was wondering if anyone knows of good resources for learning about number theory as applied to cryptography. I was hoping to practice writing proofs as well. Thanks!
  8. J

    Cryptographic attacks as minimization of degree 4 polynomial

    Cryptography is based on reason-result chains like hash functions: which are inexpensive to propagate in the intended direction, but seem hard to reverse. However, decomposing them into satisfaction of simple (direction-agnostic) relations like 3-SAT clauses, may bring a danger of existence of...
  9. S

    Is DEHP a kind of Multivariate hard problem?

    Please correct me if I am wrong. To my understanding , given a '##m##' multivariate set of equations in '##n##' variables in a integer field '##F##' is hard to solve, even in case of ##MQ(multiquadratic)## usually with field having characteristic as '##2##'. Where in case of ##DEHP(Diophatine...
  10. C

    What can be different options for a MS in applied Math ?

    Where all can I apply to pursue a MS in applied Math after acquiring a BS in Math as I am not interested in doing a PhD.
  11. ant0n

    How would observation of the state of qubits affect them?

    Firstly, I apologise for any lack of understanding, incorrect assumptions or misinterpretations of the very little I know about physics, quantum mechanics & quantum computing. I am not an academic, scientist or mathematician, but a software engineer with an interest in quantum computing and...