Science topic

# Cryptography - Science topic

A topic for the discussion of research into Cryptography and Cryptanalysis.
Questions related to Cryptography
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Cryptography efficiency
Dear Isaac Obiri,
You may want to look over the following data below:
A Study of Hyperelliptic Curves in Cryptography
Elliptic curves are some specific type of curves known as hyper elliptic curves. Compared to the integer factorization problem(IFP) based systems, using elliptic curve based cryptography will significantly decrease key size of the encryption. Therefore, application of this type of cryptography in systems that need high security and smaller key size has found great attention. Hyperelliptic curves help to make key length shorter. Many investigations are done with regard to improving computations, hardware and software implementation of these curves, their security and resistance against attacks. This paper studies and analyzes researches done about security and efficiency of hyperelliptic curves.
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Hyper-and-elliptic-curve cryptography
This paper introduces ‘hyper-and-elliptic-curve cryptography’, in which a single high-security group supports fast genus-2-hyperelliptic-curve formulas for variable-base-point single-scalar multiplication (for example, Diffie–Hellman shared-secret computation) and at the same time supports fast elliptic-curve formulas for fixed-base-point scalar multiplication (for example, key generation) and multi-scalar multiplication (for example, signature verification).
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An (imaginary) hyperelliptic curve of genus over a field is given by the equation where is a polynomial of degree not larger than and is a monic polynomial of degree. From this definition it follows that elliptic curves are hyperelliptic curves of genus 1. In hyperelliptic curve cryptography is often a finite field. The Jacobian of, denoted, is a quotient group, thus the elements of the Jacobian are not points, they are equivalence classes of divisors of degree 0 under the relation of linear equivalence. This agrees with the elliptic curve case, because it can be shown that the Jacobian of an elliptic curve is isomorphic with the group of points on the elliptic curve.[1] The use of hyperelliptic curves in cryptography came about in 1989 from Neal Koblitz. Although introduced only 3 years after ECC, not many cryptosystems implement hyperelliptic curves because the implementation of the arithmetic isn't as efficient as with cryptosystems based on elliptic curves or factoring (RSA). The efficiency of implementing the arithmetic depends on the underlying finite field, in practice it turns out that finite fields of characteristic 2 are a good choice for hardware implementations while software is usually faster in odd characteristic.[2].
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Greetings all,
I am a Phd student starting on my thesis journey to hopefully do good to the libraries, furthermore, lets say the main theme focus suggested by the ministy of higher education is the corporate governance and IPO instead of internal financing. and since I am highly interested in Blockchain I believe such techonology would serve corporate governance in wide range of ways, since it shares same characteristics with it (Transparency, cryptography, security etc), My question is what problem can we solve on the IPO in particular? can we assume blockchain adoption is same as corporate governance ? what variables can we use? the preferable study case (empirical ? ) I would be happy to find some insights since it is broad new topic and we need to shed lights on. thanks in advance
Look into DAOs or decentralized autonomous organizations
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I'm working on modifying the TDES cipher and the implementation will be in pure python (only builtin libraries used), and need to compare the results with the standard pure python implementation of the original TDES and other ciphers . Is there a repository containing such pure implementations (in python) without re-implementing them from scratch?
Why do you need a python version to start with? Python is close enough to C, certainly for the language elements used in symmetric cryptography that a "find and replace" on an existing C example will do most of the work.
The golden standard for refence values is of course FIPS-46, but OpenSSL is unlikely to deviate ;-) Another very commonly used code base is libtomcrypt.
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What is the background story of calculating the value of d in the RSA algorithm of Cryptography and Network Security?
The value of d is required for decryption. I want to know the derivation of finding d. The equation of finding d is d = e-1mod Φ(n).
Consider an example: P = 17, q = 7, n = 119, φ (n) = 96, e = 5. From here I want to find the value of d in my hand. How can I do this?
The idea! The idea of RSA is based on the fact that it is difficult to factorize a large integer. The public key consists of two numbers where one number is multiplication of two large prime numbers. And private key is also derived from the same two prime numbers. So if somebody can factorize the large number, the private key is compromised. Therefore encryption strength totally lies on the key size and if we double or triple the key size, the strength of encryption increases exponentially. RSA keys can be typically 1024 or 2048 bits long, but experts believe that 1024 bit keys could be broken in the near future. But till now it seems to be an infeasible task.
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It is widely claimed, without any hesitation or disclaimer, that quantum computers (QC) can (or well, will be soon able to) break cryptography by factorizing large numbers. However, to my knowledge, largest number ever factorized by a quantum computer is 21 (= 7 x 3) for Shors algorithm, and to make things worse, this world record hasn't been improved for a whole decade!
Some larger numbers were factorized too, but not like "give me a number and I will factorize it". Rather, it was done by starting from a known solutuion and figuring out if this particular case could be programmed in to the QC - which is basically cheating, or at least not a useful factorization process.
So what is stopping the game? What are the factors that limit the size (measured in number of bits) of an arbitrary numer that can be factorized by a QC? Are they just a technologic annoyance or is there a fundamental obstacle that invalidades QC from ever factoring large numbers?
Quantum computers work with quantum gates, just like classical computers work with classical gates. In both cases the gates are ``logical''-their material implementation just respects the logic.
For classical computers it's known how to design logical circuits that can realize any computation-and how to construct real circuits that implement this; for quantum computers this isn't, yet, known at comparable level of detail.
Factoring a number means two things: (a) Deciding whether it's a prime or not; and, (b) Determining its factors. The two problems are, actually, independent, since it is possible to solve (a), without solving (b)-of course, solving (b) provides an answer to (a).
What was realized, before quantum algorithms were even imagined, was that it was possible to define the probability that, given a number N, another number, a, could be one of its factors. This led to classical factoring algorithms and quantum algorithms.
With 50 bits one can represent all integers from 0 to 250-1. So any such integer is a string of 50 bits. So it's necessary to translate the statements of problems (a) and (b) into operators on such strings. It might be useful to start with smaller numbers, to understand how things work. Shor's algorithm is presented here: https://en.wikipedia.org/wiki/Shor%27s_algorithm and this might be a good place to start. It solves problem (b) by realizing a way for computing the probability that some number is, or not, a factor of the number one wants to factor.
In general, the bits will be entangled, of course.
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2 Logistic chaotic sequences generation, we are generating two y sequence(Y1,Y2) to encrypt a data
2D logistic chaotic sequence, we are generating x and y sequence to encrypt a data
whether the above statement is correct, kindly help in this and kindly share the relevant paper if possible
after reading an article baesd on quantum image encryption I think these two chaotic sequences are used for a key generation, not for encryption.
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Good day Dear Researchers. Please I would want to ask a question on cryptography. Am trying to use hybrid cryptography to secure a system, that is 3DES AND AES. Is it possible to merge both algorithms to have a unique algorithm. Or we encrypt the plaintext using the first algorithm (3DES) then the output is encrypted again using the next algorithm (AES). PLEASE, WHICH IS BETTER AND WHY?? AND WHICH IS POSSIBLE AND WHY??
Dear Chibueze Nwamouh Ubochi,
Find below several professional opinions to your question:
Integrating AES, DES, and 3-DES Encryption Algorithms for Enhanced Data Security
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Why would anyone choose 3DES over AES in software?
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Combination of more than one crypto algorithm
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Dear colleagues and experts
When I encrypt audio using one of the chaotic map for example logistic map and then DNA cryptography rules, how can I estimate the keyspace of all system
Thanks
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Kindly visit the article, and share your honest thoughts in any communication style, even if you are not an expert. Feel free to submit your thoughts here, or under the comments section of the article.
Looking forward to hear your thoughts. Let the fun debates begin!
Best,
M. R.
hi,
In cryptography, a key derivation function (KDF) is a cryptographic algorithm that derives one or more secret keys from a secret value such as a main key, a password, or a passphrase using a pseudorandom function (which typically uses a cryptographic hash function or block cipher).Ġasaq; a provably secure key derivation method that, when given access to a true random number generator (TRNG), allows communicating parties, that have a pre-shared secret password p, to agree on a secret key k that is indistinguishable from truly random numbers with a guaranteed entropy.The derivation key index is used to locate the derivation key (i.e. the master DES key) for the issuer BIN, as derived by the online switch in case of EMV cards. .
best wishes..
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Hi all,
Does PUF stop side channel attacks?? If so, how does PUF stop side channel analysis based on timing differences or power differences??
It does not stop side channel attack. In contrast, one of the problems of PUF is the side channel attack itself.
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I was able to create a compound chaotic system which is given satisfying results so far when used to generate substitution boxes. However, I want to improve the values of NL, SAC, BIC, DP and LP. I need recommendations on how to improve these values. What I am thinking is to use values generated by the proposed chaotic system as an input for elliptic curve. Problem is that I am not much familiar with ECC. Please help in this regard. Thank you!
P.S. I want to achieve results much better than AES S-box in all criteria.
Hi
It is always better to mention the full forms such as Avalanche Effect, Bit Independence etc of the matrices instead of BIC, SAC etc so that it will be easier for people to understand and respond.
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I am interested in the usefulness of zero knowledge proof in verifying an algorithm (for bias, privacy, data processing, and general deployment process). Have you come across examples of it in regulatory compliance?
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May you please name some good books on Blockchain technology?
Dear Jay Kamlesh Dave,
Here there are some more:
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Today's network security is mainly based on public-key cryptography. It is expected that these algorithms will be faster to break for attackers with quantum computers. Especially in case of collecting vehicle data in central storage systems, which could be used to support autonomous driving or to solve crimes, security plays a major role. This raises the question of the application of Post-Quantum Cryptography. In which time frame are realizations seen and also the costs of the application?
I want to share this talk with you: " Drive (Quantum) Safe! –Towards Post-Quantum Security for Vehicle-to- Vehicle Communications; " which is presented at CAST e.V. Workshop “Quantentechnologie und Quantencomputer-resistente Sicherheit” 2021 (virtual). The link is here https://ninabindel.de/presentations-2.
In short, they concluded that Falcon-512 is the most suitable NIST PQC finalist for V2V and illustrate how Falcon can be incorporated.
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Some recent events point that IBM got a 27 qubit computer (https://www.ibm.com/blogs/research/2020/09/ibm-quantum-roadmap/), and maybe 10 years from now one with one million qubits (see same source). Speculations aside, the fact is that quantum entanglement does proves a remarkable advancement in cryptography, among many other applications.
On the other hand let us recapitulate that the Riemann hypothesis (RH) is still out there, unsolved, and that its proof (or disproof) might lead to an understanding on how to factorize much faster than now. We know that today's internet security is based on prime cryptography, and hence its very close connection to a proof of the RE, even if that proof is only existential (the tools for proving it may show a way for faster factorization, and hence to decrypt in way that can't be done now).
It seems that quantum cryptography might arrive much faster than the solution to the RE, and hence the question. As concerns of cryptography, RE would appear that it has lost its most important motivation to be researched, at least commercially speaking. Thus, RE would remain as a pure mathematical problem ( a very tough one, though), connected, perhaps, with many other mathematical statements that are assumed true, if RE is proven true. So, the question is:
Is RE still relevant for some foreseeable practical applications, other that cryptography?
Yes, it's relevant for a lot of things, if you're into math, of course.
I have a sketch of a proof for it in my profile, go check it out.
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Respected research fellows,
I am working on logistic chaotic map for generating numbers from 0-255 (in non-repetitive manner), so far I am successful in generating numbers but there are so many repetition of values. I need some help please! Following is python snippet I am using to generate these numbers.
def sbox(x, r, size):
i = []
for j in range(size):
x=r*x*(1-x)
i.append(int((x* pow(10,14))%256))
return i
print(sbox(0.9058,3.9,256))
This will eventually go towards Substitution Box creations.
Karima Amara Korba Thank you ma'am. I already found a solution but I am working on it. I will share it with the research community once I am successful.
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Hello all, I'm an undergraduate student and currently I'm interested to learn more about Cryptographic for Network Security. I want to know is there any paper or journal that quickly summarize whether each Encryptions Algorithm has their own behaviour that maybe works better for its different purposes?
Like some algorithms are best-used for Cloud Computing, some others are for an E-Commerce website, some others for Social Media application, etc. that would lead to decision making of which are more suitable for algorithm for every project.
Thanks before!
RSA
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My friend and I wrote a research paper on computer science (cryptography). The article is a simple contribution. We need someone to join us and do a good grammar correction for the theory part. In addition, an improvement may be proposed to the proposed contribution.
my respects
Dear Seddiq Abd Al-Rahman
I will be interested in that.
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Hi, I am looking forward for collaborators (academic and research work) who are interested to work in the following area:
Quantum Attacks
Quantum Computing
Quantum Artificial Intelligence
Post-quantum Cryptography
Internet of Drones
Blockchain and Quantum Computing
Hello Sir,
I am interested in the suggested topics. My domain is cloud computing security using cryptographic techniques. I have few publications in this domain. Please have a look.
Regards
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I want to generate a Lyapunov-exponents-Diagram for my new chaotic map using matlab code. i am unable understand the concept which some of the matlab codes used to get Lyapunov-exponents-Diagram for any chaotic map . kindly help me
You may get some ideas here. Just apply the same for your chaotic map.
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NIST randomness test is very important for any encryption algorithm. I want Matlab code for NIST test.
I have tested the image using different test suites in the following paper. (Not only NIST)
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The recent Sveriges Riksbank Prize in Economic Sciences or Nobel prize (as commonly known) was actually awarded to an economist (Fama) who claimed that markets are efficient and any prediction of it's movement is fruitless. Isn't the Bitcoin price random too?
Furthermore, we can even fit Robert Schiller's theory into it. There is clearly a long-term trend and crazy volatility. Also, Bitcoin tries modelling the ideal world scenario of no transaction fee as used when designing theory like CAPM.
With such similarities, why isn't research being done in the Bitcoins? There's so little to read. We pretty much end up with Satoshi's paper which is more cryptography and less economics.
Bitcoin (not asset backed cryptocurrencies) is nothing more and nothing less than unlicensed gambling. Instead, central bank cryptocurrencies -- digital regular money issued by government -- will lead change.
Details are in my book: Bitcoin: The Mother of all Scams. https://www.amazon.com/gp/product/B095NMLM2F
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in the principe of the cryptographie RSA
Next, you may check the answer given by Dana A. Jacobsen in this post:
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I want to know the execution times of the following cryptographic primitives involved in ECC:
2. ECC point multiplication
3. ECDSA signing time
4. ECDSA signature verification time
2) It depends by the elliptic curve that you are considering, i.e. secp160r1, secp192r1, ecc. (and the respective Koblitz version).
3) It depends if you are considering pre-computations or not.
4) It depends if you are estimating these costs in C or Python or another generic language. By the way, from my experience you should work in C to estimate how much time requires an ECC operation. As a standard library to make these experiments, I can suggest you OpenSSL.
5) The best option is to measure the time and the energy consumption by adopting an oscilloscope.
6) Further you need to repeat the tests (i.e. 10,000 times) and compute the mean + interval confidence at 95%.
7) An example here (Section VI A):
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what is the new idea it can implemented security and cryptography for IoT ?
@Thenmozi Sundaram, very good point on the energy consumption issue inherent to Blockchain processing.
This would be irrealistic to expect a "thin client" type of IoT node to replicate and update the list of transactions having occured until t, at every time t. This is however what a fully Distributed Ledger system would have to do.
Hence a massive downsampling is needed to implement such a Distributed Ledger Technology in IoT:
-time downsampling, restricting transaction list update to more spaced times...
-hierarchical downsampling whereby nodes would be aggregated, especially at the Edge, where sensors input real world measurement data, in IoT nodes cluster, and one update per cluster would replace one update per IoT node.
-then you need to address data protection within the clusters, when the different nodes aggregated in a cluster need to share or exchange data.
You may use block coding for the local cluster aspects of data.
The above sketches a possible path towards your goal.
Is it compatible with the problem you have in mind?
Let me know
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Hii,
I'm doing MBA in cloud computing, please suggest me some topic to do thesis on cloud cryptography, If possible on aviation cloud implementation.
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The future of blockchain-based internet solutions
Blockchain is defined as a decentralized and distributed database in the open source model in a peer-to-peer internet network without central computers and without a centralized data storage space, used to record individual transactions, payments or journal entries encoded using cryptographic algorithms.
In current applications, blockchain is usually a decentralized and dispersed register of financial transactions. It is also a decentralized transaction platform in a distributed network infrastructure. In this formula, blockchain is currently implemented into financial institutions.
Some banks are already trying to use blockchain in their operations. if they did not do it, other economic entities, including fintechs, implementing blockchain could become more competitive in this respect. However, cryptocurrencies and a secure record of transactions are not the only blockchain applications. Various potential blockchain applications are being considered in the future.
Perhaps these new, different applications already exist in specific companies, corporations, public institutions or research centers in individual countries. In view of the above, the current question is: In what applications, besides cryptocurrency, blockchain in your company, organization, country, etc.?
I invite you to the discussion
Thank you very much
Best wishes
Thank you very much for your answer and confirmation of my theses. Thank you very much for your valuable participation in our discussion. Yes, I agree with you on this point that improving risk management processes is a key issue and that the decentralized finance (DeFi) sector will continue to grow in the future.
Best regards,
Dariusz Prokopowicz
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cryptography is a technique for securing the message through various ways such as cipher and algorithms so that Intruders or attackers don't steal or replicate our data.
Choice is a plenty But any choice has to deal with attributes like time, efficiency and cost.
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I'm looking to talk with people that match that description. Any suggestions or advice is greatly appreciated.
I hope you feel very well. Yes I know a very good researcher:
Dr. Mohamed Mahmoud CHEMS-EDDIN
Good luck.
You can contact him for discussing your purpose.
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Number theory is among cryptography foundations, but sometimes it is hard for students to understand the theory, mostly due the lack of previous skills and knowledge of that mathematical theory by students.
Have you dealt with that problem? Have you faced other problems while teaching number theory? How to overcome them?
This is a good question! I was trying to figure that out a couple years ago.
The best approach I found was Coursera's course from USC San Diego - Intro to Discrete Math for CS Specialization with the 4th course being Number Theory and Crypto. The first two courses give enough grounding for those students that don't have enough of the correct mathematical background for Number Theory. I think they need something pretty accessible to not be overwhelmed. People often have such a love of crypto that they slog through with just a really basic and algorithm specific understanding of number theory - which really won't help them in the long run if they are going to do cryptanalysis etc. Dan Boneh's refresher on Probability is really short and helpful as well.
Please post here if you find a good solution.
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the avalanche effect
# Python program to measure avalanche effect for cryptographic algorithms
a = 546313 # first_cipher
b = 37385 # second_cipher after chanage one bit
# print bitwise XOR operation
a_xor_b = a ^ b
print("a ^ b =", a_xor_b)
# Base 2(binary)
bin_a_xor_b = bin(a_xor_b)
print("the result in decimal =", bin_a_xor_b)
# next steps to count 1s in binary number
one_count = 0
for i in bin_a_xor_b:
if i == "1":
one_count+=1
print ("the 1s numbers is=", one_count)
# next steps to calculate equation of avalanche effect
len_a = len(bin(a))
len_b = len(bin(b))
# if to ensure divide by the longest binary string
if (len_a) >= (len_b):
AVA = (one_count/ len (bin(a))) * 100
else:
AVA = (one_count/ len (bin(b))) * 100
print ("avalanche effect =", AVA, "%")
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Visual cryptography scheme (VCS) used to encrypt the secret image in visual form by splitting it into k shares, then be transmitted securely via communication channels to n participants. When all the k shares stacked ,the original secret image is visible.
Although this scheme has important features, but suffers from major problems such as the codebook is very difficult to manage and design , generate meaningless share that is not carry any visual information, loss contrast and pixel expansion that results increase size and poor quality of recover image and suffers from cross interference problem .
In order to obtain better quality of the shares with carrying visual information, it is important to enlarge the area of visual cryptography (VC) through proposition scheme to create halftone share that carrying meaningful information to increase visual quality and security, this scheme called Halftone Visual Cryptography (HVC)
The main idea of (HVC) scheme is realization visual cryptography" via digital halftone technique depending on the Blue noise concept to generated k shares more pleasant to human eyes and more flexible shares management. Halftone Visual Cryptography (HVC) methods are still endure unsolved problems like the visual quality of shares , large pixel expansion, difficulty design codebook and cross interference in reconstruction secret image and construction share images.
thanks a lot
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I am new to Cryptography field and try to implement Threshold Implementation. In Decomposition of SBox into composition of two quadratic SBox. I am not getting how to split SBox input of 4bit into 12bit input of G1,G2,G3 respectively. And also how to form ANF(Algebraic Normal Form)equation to get G(x) and F(x).
I am attaching image of SBox decomposition also for reference.
Please can someone explain it .
I don't agree with Mohammed Salem Atoum , in my opinion blockchain have nothing to do with this task.
Mahima Bhatnagar , I'm not quite sure what do you mean by Threshold Implementation (maybe due to our different native languages terminology or missed context) - providing more verbose specification would help me or other colleagues to answer the question more specifically.
As far as it seemed from figure the input of G1, G2, G3 is 8 bit (12 bit - whole device's block), but it still doesn't help though, because the rightmost part of the figure contradicts its center part. It is more likely that authors of the figure made a mistake or missed something while describing the center part (SBox decomposition).
Regarding ANF - the particular result should heavily depend on the particular SBox case. Try to build a Cayley's table for it or something similar and then build respective ANF. There are a lot of materials regarding ANF designing within discrete mathematics handbooks.
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I am new to Cryptography field and try to implement Threshold Implementation. In Decomposition of SBox into composition of two quadratic SBox. I am not getting how to split SBox input of 4bit into 12bit input of G1,G2,G3 respectively. And also how to form ANF(Algebraic Normal Form)equation to get G(x) and F(x).
I am attaching image of SBox decomposition also for reference.
Please can someone explain it with a small example .
use different polynomial equation for each parts
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Hello fellow researchers;
I want to generate the AES cipher Sboxes, and I couldn't figure out how to do it; I know that we take 4X4 bytes state matrix, where each byte can be expressed as a polynomial ; and then we calculate the multiplicative inverse of that byte mod x^8+x^4+x^3+x+1; then we multiply it by the matrix A and XOR it with a constant c.
A = [1 0 0 0 1 1 1 1] and c = [0
[1 1 0 0 0 1 1 1] 1
[1 1 1 0 0 0 1 1] 1
[1 1 1 1 0 0 0 1] 0
[1 1 1 1 1 0 0 0] 0
[0 1 1 1 1 1 0 0] 0
[0 0 1 1 1 1 1 0] 1
[0 0 0 1 1 1 1 1] 1]
And as I understand the multiplicative inverse of 1 is 1 and for 0 is not defined; so what would a byte turn into? for example x = 00011001, what is b such that x . b mod x^8+x^4+x^3+x+1 =1 ?
hello
you can see me in the next september, and i can give you a book where a good explanation has been done about what do you looking for.
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Dear colleagues
I want to ask, where can I obtain the original versions of classic photos that are traditionally used for image encryption?
Examples include the Lenna figure, vegetables, baboon, cameraman, rice, etc.
Is there any source to get all such images, and maybe try out new ones, that aren't bound by any copyright.
Apart from the above, I want to see if there are any copyright free images of other types, like fingerprints, x-ray images, satelite images, that can be used as examples in image encryption papers.
Dear Dr Lazaros,
You many many such standard & benchmark image dataset at
Regards,
Musheer
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WHAT IS A MDS MATRIX (MDS in AES finalists) and how can we achieve diffusion through it?
The term MDS originates from coding theory, codes for which the Singleton bound is met are called MDS (maximal distance separable) codes. A matrix is MDS if all its square sub-matrices are nonsingular. Though its characterization is also given by branch number (see https://tosc.iacr.org/index.php/ToSC/article/view/8364/7713). MDS matrices are matrices with a property that even a small change in input costs a maximum change in its output results. Through this property, we can achieve maximum diffusion. For more details, see the above-refered paper.
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In my master's Degree I proposed a way to extend the existing privacy enhancing technologies used in Instant messaging in order for the users to be able to publish user-driven services:
This MSc Thesis I want to continue it over into a PhD as a step to implement it. From my point of view it requires lots of research that may also have scientific value as well.
The research I am interested to do it via a MEXT Scholarchip in Japan. But so far what I found only few researchers that either are qualified in cryptography or in cyber security:
But still I have hard time to look over univercities that do a complete research in Privacy Enhancing technologies or in Cybersecurity in Japan. Therefore, I want to ask:
- Which Universities in Japan do research in a related field (Cryptography, Cyber security, Internet Privacy) and which ones would you reccomend and why?
- Should I keep looking for professors-only and create a database with contact info or it is reccomend to look for univercities as well?
The Japan government is keen to attract more international students, and has set a target of having 300,000 foreign students in the country by 2020 (it reached the 100,000 mark in 2003). As a result, universities are focusing on making life easier for foreign students, from the application process all the way through to finding a job after graduation.
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Hash Question (Use Sage): The following describes the simple hash function: Choose p, q primes and compute N = pq. Choose g relatively prime to N and less than N. Then a number n is hashed as follows: H = gn mod N If there is an m that hashes to the same value as n, then gm ≡ gn mod N so gm-n ≡ 1 mod N which implies that m –n ≡ 0 mod φ (N) So breaking this amounts to finding a multiple of φ (N), which is the hard problem in RSA. Write a function that takes a bit length n and generates a modulus N of bitlength n and g less than N and relatively prime to it. Show the output of your function from part (a) for a few outputs. Using N, g, n as arguments write a function to perform the hashing. For parts (d)-(f) compute the simple hash: N = 600107, g = 154835, n = 239715 N = 548155966307, g = 189830397891, n = 44344313866 N = 604766153, g = 12075635, n = 443096843 Write a function that creates a collision given p and q. Show that your function works for a couple of examples.
Nice Habakuk Kibagendi.
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I have to calculate the NPCR and UACI of the binary image. How it will be different from grayscale images.
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I want a hardware which support MATLAB code code for my data hiding algorithm . Kindly suggest me the hardware board which support MATLAB code.
Dear all
I need a base paper to implement my algorithm in hardware. if anyone working in this area kindly share those details
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I am looking for mathematical methods or techniques discussed on solving number triangles such as simple case pascal triangle. For example, one finds sequence of numbers that form a pascal triangle pattern. The formula to generate those numbers are hypothetically unknown. Is there a method in mathematics to derive the formula that will generate those numbers. (example, methods in cryptography )
Thanks Ait Mansour El Houssain.
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I am doing research on comparative analysis of ID based cryptographic protocols like ElGamal, RSA, DSA etc. How can compare these protocols with the properties without doing any objective experiment?
You need to choose the properties for comparing. It could be size of the keys, or size of additional data, computational and memory complexity, complexity for cryptanalysis (with different attack model), mathematical problems in the base of protocols, application of protocols in different standards.
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I have introduced some factorization for the infinite Hilbert Operator based on the Cesaro, generalized Cesaro and Gamma matrices in the following papers:
1-H. Roopaei, Factorization of Cesàro and Hilbert matrices based on generalized Cesàro
matrix, Linear Multilinear Algebra, 68 (1) (2020), 193-204.
2-H. Roopaei, Factorization of the Hilbert matrix based on Cesàro and Gamma matrices,
Results Math., 75 (1) 3, 2020. DOI: 10.1007/s00025-019-1129-1.
Now, my questions are:
1-Is there any other factorization for the Hilbert matrix based on the Hausdorff operators? and in especial case of Hausdorff classes, based on Euler or Holder operators?
2- As I know the infinite Hilbert operator is used in Cryptography and Image processing. Is there any mathematicians in this group who can introduce some good references?
Dear Reza
The reference that you sent me is my own publication.
Best regards
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I want to know why is it that XOR is ignored in the computation cost of a security protocol? And is there any reference there which can prove that it is insignificant so can be ignored?
Like in a certain research paper it is stated that "In the proposed scheme, we take the
cost of concatenation (||) operations and XOR (⊕) evaluated as insignificant." why is this?
based on complexities measurements (Big- O , Theta and Omega), Bit-wise Primitive operators (such as XOR) has lower time complexity compared to +, - , *, /
for example (reference):
Complexities of primitive operators (logical and math) using different processors compared in :
bit- wise operators such as XOR got minimum complexity time.
Thus, if XOR is ignored (as refereed in the question context), it means XOR considered as O(1) or constant ( relative to other higher computation primitive operators, typically used in encryption and decryption as necessary .
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I would like to use bilinear pair concept for designing a secure data.
e(u,v)=2power(u*v)
from this we can prove G1xG1-->G2
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I wanted to know if it is possible to generate random numbers using GAN and what mathematical background is necessary.
If a GAN can accept Non-Parallel data then it has the ability to generate random numbers.
1. They may have a sequence in past to predict new numbers. OR
2. Just a random sequence .
I worked with non parallel voice data using GAN and it worked, then this has also the ability to work for random numbers as well. But this method may not be the best choice as there are other models SVM,LSTM(for exmple). But your question is "whether we can ?" Then you can give it a try.
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I developed a new cryptographic algorithm (block cipher) based on RADG and using chaos (tent Map) with key of 256 bit, the design of the RADG is no more fixed as it was, the design totally depends on the chaos seed X and TM parameter μ , which is vary .
I built the cipher/Decipher code and it works perfectly .
what standard test/validation programs should I use to prove validity ?
1. Key Analysis (Key Space Analysis, Key Sensitivity Test)
2. Statistical Analysis (Correlation Coefficients Analysis, Correlation Distribution(Similarity) of The Adjacent Pixels , Histograms Analysis)
3. Differential Analysis
4. Information Entropy
5. other test like the Histogram Deviation, The Irregular Deviation, Encryption Quality Metric, The Avalanche Effect Metric)
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Why is there not detailed material on this subject? Anybody, to begin with, can take initiative.
The term „Whitebox Cryptography“ is probably a marketing invention and a contradiction in itself. The Greek source of the term crypto refers to “secret/hidden” which is not really the case in what is called “Whitebox Cryptography”. The term “Whitebox” refers to the fact that nothing is really hidden. I would prefer this technique to be called obfuscation instead of using the term “crypto”. Modern Cryptography is based on secrets called keys and algorithms using said keys to transform plaintext into a message unreadable without access (not knowledge) to said key material. Given the key material is kept secret and only authorized access is granted mathematical methods can be applied to prove the strength of function. The technique some call “Whitebox Cryptography” cannot be mathematically assessed since all details needed to transform a message back to plain text is contained in the transmitted message. The technique relies on proprietary mechanisms for both directions of the transformation which an attacker can also reverse engineer from one or multiple transmitted message(s) (with more or less efforts). The major difference between Cryptography and obfuscation is that given proper access control to secret key material cryptography can be secured against external AND internal attackers while the mechanisms of obfuscation are always known by multiple individuals. Still obfuscation is helpful since it uses up external attacker’s time for attack preparation. It is used when a message is to be sent to a party while it was not possible to yet share secrets.
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I’m doing a project on ”Applying graph theory on symmetric cryptography”. As a part of it, I’ve been given an algorithm to calculate the time complexity using Big O notation. I have got an answer of O(l(n^2)). Note that here n ≤ l.
But the answer should be O(l^3).
Can I argue that O(l(n^2)) ≤ O(l(l^2)) = O(l^3)?
If L =O(n) which is the case that there are only constant number of blocks and for example L=n/3 and there are 3 blocks exactly. Then n *L^2 =O(n^3)
L cannot exceed n (when there is only one block) and can be even smaller (which is exactly the definition of O(n)).
It will help to learn analysis of algorithms and understand asymptotic analysis of algorithms' complexity to do this things right!!
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Bijection Functions used for Internal Encoding in Look Up Tables in White-Box Cryptography, but it suffers from few attacks, so to avoiding these attacks can we replace it by any other functions or optimization algorithm?
Thanks Sir
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For Security Purpose in Smart Devices we generally used Symmetric Key Cryptography (DES, AES) for its lightweight, but for increasing security can we think about public key Cryptography too?
as u know the IoT devices have some constraints in power, processing data, memory, so because of these constraints i don't propose using RSA. you can use the lightweight version encryption than RSA like ECC or DTLS. ECC is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields.
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In socialist millionaire problem, two millionaires learns whether their wealth are same or not without revealing detail wealth. It is a step in protocol where Qa = g^x and Qb = g^y, where x and y are wealth, g is base of the discrete logarithm. a) Is it not computational overhead on users if value of x and y are huge? b) If I want to replace x and y as string in place of numbers, then how may I do it?
Peter Breuer Thank you Dr. Peter for your answer. May you please let us know how may we replace the integer x with a string message?
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best in worldwide usage and applications, and best in extensibility
Both RSA Cryptosystem and Elgamal Cryptosystem are secure enough to use.
Actually, if we looking for the best one, we need to determine the application space.
Sincerely,
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Do you think bot's like this https://tradesanta.com/en have theoretical support?
It's posible to predict the market fluctuations?
It's interesting question, I will tray answer asap.
Kind regards,
Milica Slijepcevic
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Encryption-decryption algorithm based on Cryptography module using Fernet key instance
Dear Dariusz,
Thank you very much for pointing out the issues of the security breaches, looking at the database as the storage aspect. What do you think could be the best mechanism to protect the biometric data in the database server.
Any link to the papers and the books is welcomed
Kind regards
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Encoding of biometric data to arithmetic for use in cryptography
Bio-hashing and cancellable biometric approach can help in some extend
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In ECDH, when two person wants to share private key, they first select a point G on elliptic curve and after that, each of them pick a random integer a and b, respectively, and multiply with G. After the multiplication each of them shares aG and bG with each other and after that, they multiply again using their keys a(bG) and b(aG), respectively, and creates a shared key between themselves. However, if one person wants to communicate with a group of person (more than 2) using a shared key utilizing ECDH, how he can use this method? because each of the person may choose different integer while establishing the key.
How to employ ECDH in key exchange with a group of people?
Hi Dr. Anik Islam Abhi
Sincerely
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Dear colleagues,
As I am new in the domain of teaching courses, so it takes too much of time to prepare my course, saying for example: cryptography course, web development,..etc,... So, my problem is that, for every short period, there is something of new especialy in web development, (e.g., new programming languages, new packages, new technologies,....soon so forth), so my question is that, really I can not cope with myself to update my course for every short time,.., so by doing that I come to loose so much of time and efforts, which guide to a negative impact on the time preserved for my research investigation?!
So, any advice is so welcome !
Best regards.
Amina, I recommend using a good textbook which comes with lecture slides and labs with instructor's manuals. For cryptography, "Cryptography and Network Security" by Stallings 7th edition is pretty good! It is from 2017, so should have all the latest updates included
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hello everyone,
recently i am learning phase of understanding ns3 simulator.
Just out of curiosity, can we integrate cryptography module to it??
I mean can we secure a program with any of the available encryption schemes??
Thank you
Yes download ns-allinone and add any new module with C code for any of the well known cryptography algorithms.. Refer https://www.nsnam.org/docs/manual/html/new-modules.html
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I need a topic on Cryptography/ Network security for Ph.D study
Hi Pantuvo Tsoke
"enhanced elliptic curve scalar multiplication"
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The binary image as shown in the figure
Hi,
visual cryptography, pixel expansion and contrast are two ... contrast of the recovered binary secret images is only a half of the original secret . In Visual cryptography mainly visual information is encrypted .it takes a secret image as input, and outputs share images that shares are having visual.
Best Wishes..
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I am doing my Mtech Project on Secure AODV routing protocol I need a way to show Simulation in NS2 ? Please anyone provide me how to implement my algorithm and Simulate the result in NS2.
Hi.,Try to use in MANET environments ... with the help of protocol stack and NS mobile node in NS2 simulation. NS2 help in commands and getting output from simulation after running tcl file.
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I am working on ECG cryptography and authentication for Body Area Networks. I seek knowledge on how to get the algorithms implemented. I mean the language or libraries to use for implementations and respective results.
Ms Preeti,
the data set for ECG cryptography can be obtained from Bonn university site at the below link
http://epileptologie-
you can also employ discrete chaos for realization of new ecg cryptographic method.
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Currently working on e-voting using cryptographic Techniques. I Would like to implement RSA and also to know how SHA works technically with RSA.
Dear Timos Mukoko,
to answer this question illustratively, I would like to refer to some figures in the following literature sources:
[1] Anatol Badach: TLS – Transport Layer Security
See here in particular the figures: 4132 (TLS Importance), 4134 (TLS Handshake) und 4140 (Structure of Shiper Suites)
[2] Dr. Erwin Hoffmann: Was ist neu bei TLS 1.3? TSLv1.3 – 21nd Century Internet Transmission Security
See especially the pages: 3, 4, 8, 11 und 16
By using asymmetric cryptographic algorithm RSA and SHA (Secure Hash Algorithm), connection-oriented communication can be secured over TCP connections - especially communication in distributed web applications with HTTP.
In order to be able to secure communication over TCP connections, for example in distributed web applications and the use of HTTP, TLS was developed. Among other things, the security protocol TLS regulates the way in which RSA and SHA are used.
As shown in Fig. 4134 in [1], according to TLS, the two communicating partners - the TLS client and the TLS server - agree on the principles by which they secure the communication. These principles are specified in the form of a cipher suite. Each cipher suite has the structure shown in Fig. 4140.
Each cipher suite consists of the following three parts:
• Key Exchange and Authentication: Specifying the method by which the key exchange and the authentication - when establishing a TLS connection - run between client and server.
• Encryption: Specifying the cryptographic method used to encrypt the data of an application protocol transported via the TLS connection.
• Hash: Specify the hash function to verify the integrity of the transported data of an application at the destination.
When using RSA, for Key Exchange (only „key material“ exchange!) and Authentication, and SHA (for Data Integrity Checking), the cipher suites can take the form:
TLS_RSA_WITH_3DES_EDE_CBC_SHA
The "good" cipher suites are registered with the IANA. Their listing can be found at the web address
Best regards and much success
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In quantum key distribution (QKD) optical fiber networks, the quantum channel (QCh) is used for establishing and updating secure keys which are used to encrypt data [1]. Public interaction channel (PICh) is used for exchanging other key related information [1]. Traditional data channel is used for transmitting encrypted data [1].
My question is, what are the modulation schemes to be used for QCh and PICh?
I could not find information regarding the modulation scheme in any of the published articles I read. Please answer this question or suggest some articles that contain this information.
Please note that I am not looking for modulation schemes used for transmitting traditional data.
Thanks
[1] Zhao, Y., Cao, Y., Wang, W., Wang, H., Yu, X., Zhang, J., Tornatore, M., Wu, Y. and Mukherjee, B., 2018. Resource allocation in optical networks secured by quantum key distribution. IEEE Communications Magazine, 56(8), pp.130-137.
Dear Anuj, the point raised by you is really timely. From your points, it is understood that traditional methods will not help much. However, I would like to say QAM may be an option along with orbital angular momentum multiplexing. Just have a look at the articles attached.
b)
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Hello all,
I have been wondering about differences between true random number generator and pseudo-random number generator.
In my system there are three main components; clock signal ,push button, and output (LED). When the button is pressed, the LED simultaneously represents the state of the clock signal and remains the last state while the button is released. For instance, I release my finger when the LED is 'ON' so, it is on until the next pushing and vice versa. let's say the period of the clock is relatively fast so human is not able to know whether the current state is 0 or 1.
However, I got be confused that is my system a TRNG or PRNG. First, i thought it is a TRNG because the randomness is only determined by human decision. Therefore in this case I may say the source of randomness is non-deterministic However, the second thought can be raised that what if the clock can also be considered as a source then the randomness is likely not random ( non-deterministic) anymore
Notably, the real system is much more complicated, for an ease of discussion i just briefly explain the principle of the system.
Korakot
Dear Korakot Boonyaphon,
The difference between true random number generators(TRNGs) and pseudo-random number generators(PRNGs) is that TRNGs use an unpredictable physical means to generate numbers (like atmospheric noise), and PRNGs use mathematical algorithms (completely computer-generated).
Pseudo-RNG's are sets of algorithms (i.e. logical instructions for by a computer program) that utilize mathematical formulas to produce a certain sequence of numbers that will appear random, or at least will have the effect of randomness. Other RNG's use pre-calculated tables instead of mathematical formulas, but either way table or formula, the objective is still the same.
A lot of research has been done (and is still ongoing) on RNG's insomuch that our modern algorithms used for Pseudo-RNG's produce number sequences that do exactly mimic truly random sequences. But that may be the outcome of today's research there is still room for improvement since the results of Pseudo-RNG's are really "pseudo".
Comparing the results of a Pseudo-RNG with that from a True-RNG will prove useful. If you list down the results of a Pseudo-RNG mimicking dice rolls the numbers will really appear as if they are random. But statistical analysis will prove that the numbers produced by a Pseudo-RNG is not really random but is rather predetermined. Thus its results can be measured and standardized, and, we can say, controlled.
True-RNG's behave differently since the results are truly random and unpredictable. If we try to get a computer to produce a really random sequence of numbers then the computer must base its numbers on a naturally occurring physical phenomenon, which may include the radioactive decay of isotopes, static in the airwaves, and the waves of the sea. True-RNG's will not really be cost-efficient if you compare it to Pseudo-RNG's. True-RNG's will be subject to wear and tear since all things natural will really be subject to entropy. A Pseudo-RNG will not be subject to such physical phenomena.
Another efficiency of a Pseudo-RNG is that you can reproduce the same sequence of numbers in another time by simply knowing the starting point of the sequence (thus it is also periodic and the sequence will repeat itself in due time). This better facilitates inspections done by casino control boards. But you can be sure that the sequence of numbers produced by a Pseudo-RNG, though periodic, the time to reproduce the same sequence will eventually take a really long time that unless you acquire the actual algorithms, the correct sequence will be very difficult (almost impossible) to crack.
Many online casinos have settled for Pseudo-RNG's for its cost-efficiency, periodicity, and efficiency. These are good reasons to choose this type of random number generator, though a True-RNG will also have its own benefits as well.
With Best Wishes,
Samir G. Pandya
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Hi,
As per the definition of logic obfuscation, obfuscated circuit stays in obfuscated mode upon global reset (i.e. initial state) and generates incorrect output; upon receiving correct initialization sequence it enters into functional mode and generates intended outputs.
This is fine with respect to the design that does not connected with any further critical systems. If at all, the obfuscated logic needs to be connected to further safety critical systems, won't incorrect value generated in obfuscated mode affects the critical systems??
In such case, how to apply logic obfuscation??
You can read the literature yourself and come up with your own conclusions. It would do you good, you would sound less like a non-expert rambling about something you have very little clue about. I am done here.
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There are many algorithms used to build a secure transmission system but with the advancements in programming field most of them are now breakable.
The question now is : what the best algorithm used for securing text ?
In addition to what Peter presents, my answer to the original question might be, "it depends." The best cipher today is generally accepted to be AES, by NIST anyway. A block cipher, which can also be used in "counter mode," to encrypt and decrypt continuous streams of data. Could be text or anything else.
The computationally somewhat more efficient ciphers may be symmetric key stream ciphers. Functionally, they work much like AES when used in counter mode, but depend only on good quality pseudo-random number generators (PRNG). You need a PRNG with seeds that consist of many bits, like 128-bit seeds or better, to achieve good results.
Not sure if this link still works, because the partial government shutdown won't let me use it at the moment, to see what updates may have been introduced lately:
Quoting from that link, while it was working:
Currently, the use of AES in the Output Feedback Mode (OFB) mode and the counter (CTR) mode are approved by NIST as block-cipher based stream ciphers. However, dedicated stream ciphers sometimes have performance advantages, especially for software applications with high throughput requirements, or for hardware applications with constrained resources (such as limited storage, gate count or power consumption). During FY2013, the performance of some of the well-understood stream ciphers (focusing on the eSTREAM finalists) will be studied and compared to the approved block-cipher based stream ciphers. A technical report is being finalized, and is expected to be published soon.
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i want to use artificial intelligent algorithm with cryptography.
Thank you very much
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I want to use ECC in my research.
Many implementations can be found here!
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The BCS in the UK have developed a Blueprint for Cyber Security in Health and Care, and aim to bring together key stakeholders to work together in improving security within the NHS. But are our health and social care systems really fit for the 21st Century, and are they citizen-focused?
If you have an opinion, please consider submitting to a paper to the link provided on this question.
Call for Papers
The development of new electronic services within health and social care provides an opportunity for citizen-focused health care, especially in sharing information across traditional organisational boundaries. With the move to enhanced services, there are also increasing risks, including from data breaches and in the hacking of medical devices.
As health care data often contains sensitive data, there are many risks around the trustworthiness of the security infrastructures used within health and social care and in the methods that can be applied to share information across domains. New regulations, too, such as with GDPR (General Data Protection Regulation), focus on an integrated security approach for incident response, encryption, and pseudoanonymisation and in providing citizens with more control over their data. This will require new approaches to the design of data architectures and the services used within health and social care infrastructures.
This special issue focuses on the latest research within health and social care for cyber security, including the application of new methods to integrate data from each part of the patient journey. It will also focus on the integration of policies and data protection methods, to protect against data breaches, along with allowing data to be used to improve patient safety and in reducing the costs of health care provision.
Potential topics include but are not limited to the following:
- Data breaches and risk models within health and social care
- Detecting and responding to health care data breaches
- New design principles for GDPR requirements within health and social care data
- Models for risk analysing cyber security threats
- Citizen-focused health and social care systems
- Information sharing and secure architectures within health and social care
- Trust, governance, and consent around interagency approaches
- Data sharing models for interagency approaches
- Creating consensus models for health and social care
- Cloud-based architectures for integrated health and social care
- Cryptography for health and social care data
- Integration of cryptography for trust and governance, including methods for anonymization and secure data processing
- Policy integration for data access
- Anonymization and sanitisation of health care data
- Application of blockchain methods within a health care environment
- Attacks on health care devices
- Vulnerabilities in health care devices
It is very important to maintain a high level of cyber security also in the area of computerized health and social care institutions.
Unfortunately, despite the assurances of companies that run social media portals, the information contained on these websites is not always fully secured against the activities of cybercriminals.
In addition, the issue of downloading data from social media portals by large companies to Big Data database systems should be added in order to process them for marketing purposes.
The issue of privacy in social media is very important and is related to the security of personal information. Privacy is at risk in terms of information posted on social media portals.
I invite you to the discussion
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