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.
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...
I would like to invite your members to participate in the ZPrize competition. ZPrize is an industry-wide competition, modeled after the XPrize, to accelerate zero-knowledge cryptography. We have over 39 leading zero-knowledge technology companies contributing to this effort donating $7 million...
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"?
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?
Conditions of the problem:
y =/= a^2 (mod pq)
-y =/= a^2 (mod pq)
p = 3 (mod 4)
q = 3 (mod 4)
(a) We assume y is both square (mod p) and (mod q). Then,
b^2 = y (mod p)
b^2 = y (mod q)
b^2 = y + pk
b^2 = y + qr
pk = qr ?
(should we assume b is the same between the two equations?)
(b)
-y = d^2...
Here is my attempt
When we raise both sides to the power (p-1)/2, we get
x^(p-1)= -1^[(p-1)/2](modp)
Looking at p=3(mod4), the possible values of p are
{3, 7, 11, 19, 23, 31...}.
Putting these values of p into (p-1)/2 we get odd integers.
{1, 3, 5, 9, 11, 15...}.
So we have
x^(p-1) =...
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...
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...
May I know how to solve the equation as below:
(1) y2 = x3 + x + 1 mod 17
Finding Inverses
Finding Points on the Curve
(2) y2 = x3 + 3x + 1 mod 13
Finding Inverses
Finding Points on the Curve
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...
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.
I've been trying to solve this question for quite a while now. I watched a ton of videos on RSA. But whenever I try to solve it I get weird answers. Can some pls give me a hint or their method of solving it. An answer to the question also would be fine.
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!
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...
I was just reading a cryptography book and have a question about something the author states I highlighed the statement in yellow and included a pictures.
So I was wondering if the function could be written as E(M,K) = C instead of Ek(M)=C since the fact that E is dependent on K. If not why...
In a recent article (I've lost the reference, but it doesn't matter) it said that employing entangled photons is superior to the usual one way transmission of photons from Alice to Bob for creating a one time pad. It gave no justification for this claim. Can anyone provide me with one?
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...
Hey! :o
I am taking the course cryptography this semester and I will have a presentation at the end of the semester.
Could you give me some information about the following topics:
- An electronic voting system
- Lattices and lattice reduction
What are these topics about??
Which one...
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...
+David West
Heres What I got as far as the hash is concerned.
Heres my indexing functions
First We Have this function for fast indexing of the hash.
ZequebaHashB[bvc_, yvc_, avc_] :=
{Drop[Flatten[Reap[
Module[{a34 = bvc, a35 = yvc, rt2 = avc, z75, zler},
z75 = 1;
zler...
I'm finishing a B.S. in math and have been getting a bit more into physics lately. I'm on track for a second major in either physics or Russian, but not super concerned about finishing - I'm applying to grad programs in pure math. I'm particularly interested in algebraic geometry, combinatorics...
The recent case 'datagate' suggests me to prose to You a question I didn.t resolve completely. Let's suppose that we have a plaintext $p_{n}$ and we code it with a key $k_{n}$ generating a chipertext...
$\displaystyle c_{n} = p_{n} + k_{n}\ (1)$
... where the sum is modulo some 'large...
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...
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...
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
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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.