# What is Cryptography: Definition and 66 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. ### Comp Sci Solve ax+by=GCD(a,b) for RSA Algorithm Cryptography

It starts at 6:16 It's the part where he's pointing his hand in this picture. I didn't get it although it's pretty mechanical, so I'd like to learn that technique as this is really useful in RSA algorithm(rather than having to memorize some values). I've been searching for a method like that...

25. ### Some questions about cryptography

Hi I am a first year student studying mathematics. I have been experimenting with various subjects to find my thing, and I think I am interested in discrete mathematics, particulary in number theory and cryptography. 1) But it seems like, there aren't many companies that are explicitly...
26. ### Can Variable Message Lengths Invalidate Cryptographic Indistinguishability?

Prove that the following definition cannot be satisfied if Π can encrypt arbitrary-length messages and the adversary is not restricted to outputting equal-length messages in experiment PrivKeavA,∏. A prive-key encryption scheme ∏=(Gen, Enc, Dec) has indistinguishable encryptions in the...
27. ### Cryptography, public key and private key

Hello Forum, If Alice wants to send a secret message to Bob, she has to encrypt it first to keep the message secure. Who issues the public key in this case and who uses the private key? thanks fisico30
28. ### What are some applications of prime numbers other than cryptography

I was just wondering what are some applications of prime numbers other than cryptography? Also i heard that there is no certain *equation or prediction of Prime numbers? For example, there is no way to explain prime numbers with an equation. What happens if one was able to find one...
29. ### Mathematicians and cryptography

Hello, This may seem like a random question but I'm doing a essay on cryptography and I'm wondering if anyone could tell me who was the mathematician(s) that done the original work in prime numbers that lead to the development of cryptography and the RSA and whatnot. Sorry if this is vague...
30. ### Prime numbers and cryptography

Hello, this is rather vague but I had a lecture around a year ago about prime numbers and how a mathematician (Hardy or Euler?) found a proof to do with prime numbers and then this lead on to cryptography and internet security... That's all I can particularly remember but I'm wondering on...
31. ### Help with Cryptography | Read & Prerequisites

Dears, Hope everything is going fine with all of you; I hold a Bsc in communications and electronics engineering and a Diploma in Information security; I want to study cryptography, and I decided to have a Msc in Maths for this reason; Kindly, if you can recommend what books to read...
32. ### Need a Comprehensive Cryptography Text

As per the title, I need a cryptography book that does not shy away from math. To me it seems like many crypto books are scared of presenting the theory from a mathematician's perspective. I was recommended Cryptography : Theory and Practice by Stinson, can anyone comment on it? Any help is...
33. ### Linear Algebra Applications: Cryptography

If any of you guys are seeing or saw this app. for linear algebra in your classes, I could use a hand... Homework Statement A Hill 2-cipher is intercepted that starts with the pairs SL HK Find the deciphering and enciphering matrices, given that the plaintext is known to start with the...
34. ### Physics Research in quantum cryptography

Hello! I'm an undergraduate in physics engineering student who's thinking about his future. I would like to work in the field of quantum cryptography or communication with light, or -more or less- to do the same kind of research as Anton Zeilinger. Which kind of MSc and PhD should I take and...
35. ### PhD in Cryptography: Private Sector Career Advice

So I'm getting to the point now where I need to start looking at graduate schools in mathematics. Being a pure math major my original plan has always been to get a phd in pure math and from there attempt to break into academia. But the more I learn about the current academic climate, the more...
36. ### Cryptography - transposition cipher

Suppose m = 6 was encoded with ther permutation \pi = (13)(2546) Decrypt:- EESLSHSALSESLSHBLEHSYEETHRAEOS It turns out that the inverse of \pi is how you decrypt the message and apply the inverse permutaion which is (31)(6452) And the plaintext is she sells seashells... However I am...
37. ### Cryptography - modulo arithmetic

Finding log3(4) in Z(11).. Is that the same as finding log3(4)(mod11)?
38. ### Quantum Cryptography Project Help.

Hello Every one! I am an electric engineering student, Doing my graduation project on the topic of quantum cryptography, i have read the literature and i think that i understand the topic quite well. In the literature review i am talking about classical cryptography, QKD, BB84 protocol, EPR...
39. ### What classes do I need to major in Cryptography?

What classes do I need to major in Cryptography?
40. ### Quantum Cryptography: Classes & Degree Programs

If I want to go into quantum cryptography, what classes should I take and what colleges are there that offer this degree? Thank you so much!
41. ### How Do You Solve an Affine Cipher with Given Mappings?

Homework Statement 7) You are attempting to break an affine cipher. You believe that the ciphertext ‘a’ maps to the plaintext letter ‘E’ and that the ciphertext ‘v’ maps to the plaintext ‘T’. Determine the encryption function used based on these two pieces of information. Homework Equations...
42. ### Hackers exploit quantom cryptography

Simple, ingenious, and effective. http://www.nature.com/news/2010/100829/full/news.2010.436.html http://www.youtube.com/watch?v=VMdf8Xwxvnw&p=5E45CC761E979839&index=2&playnext=2
43. ### How can I break into the NSA's cryptography field before I graduate?

So here is my situation: I am planning on graduating March 2011 with a B.S in Mathematics, as well as a B.S. in Physics. My interest in physics has waned greatly, and my desire to go to grad school for either subject is non-existent right now. I took a look at the NSA, as I heard they hire...
44. ### Is n Prime if Zero Products and Unique Solutions Exist in Modulo n Arithmetic?

I'm having some trouble addressing the following two questions in a text I am going through: 1. Show that n is a prime number iff whenever a,b ∈ Zn with ab=0, we must have that a=0 or b=0. 2. Show that n is a prime number iff for every a,b,c ∈ Zn satisfying a not =0, and ab=ac, we have...
45. ### What Degree Leads to Compsci/ Security/ Cryptography

What undergraduate degree will best prepare a person for one of these fields (comp security/cryptography)? - math - compsci ...out of the two, which one would better benefit me if I pursue a PhD with. I'm most interested in computer security and cryptography. Cryptography is...
46. ### [cryptography] quantum key distribution

I'm reading up on quantum key distribution schemes, mostly: BB84, B92 and the EPR Protocol, and I'm having some problems relating them. Is it correct to say that BB84 is a special case of B92(with extra specific states)? Is it also safe to say that both BB84 and B92 are special cases of EPR...
47. ### What Are the Best Beginner Resources for Learning Quantum Cryptography?

Hi, Can anyone recommend some good websites, or preferably books, which give an introduction to Quantum Cryptography? I'm looking for a level aimed at first year undergrad level, assuming little to no prior knowledge really, except for A-level quantum physics. Any suggestions would be very...
48. ### Programming needed for Cryptography

I was wondering, what types of programming languages are used in the field of Cryptography? I'm a math major with a working knowledge of C/C++, Java, and Python. Would it be worthwhile to learn some assembly languages? Should I learn more high level languages? Or, should I hone my skills in the...
49. ### Debunking the Hype: The Truth About Quantum Cryptography

I am extremely skeptical about quantum cryptography. First all of the articles I have read about the technology use the same mathematical concepts to encrypt and decrypt a message. Nothing about quantum cryptography actually changes physical characteristics of math. That is obvious. There...
50. ### Which books are recommended for learning about RSA public-key cryptography?

public-key cryptography "RSA" Hi all, I want to ask about cryptology, What are the recommended books in this filed and i want to ask about public-key cryptography"RSA", I want some details.