Applied Cryptography - Science topic

Adding to Ed fully seconding what he imho brilliantly summarized above what urgently needs to be done - it’s also fully compatible to iSpace theory, using a simple first order multiplicative integer geometric schema to derive (by now 50+) exact values and integer geometry of constants of nature (!).

I am working with ENT this very day, and I find it to read input files quite well. The command line that I use, when processing my list of One Million Purely Random Digits, is:

ent -c OneMillionPurelyRandomDigits.txt

The text (.txt) file is available on my RG profile page.

In the RSA algorithm, the choice of the public key exponent "e" is an important factor in the security of the system. The most commonly used value for "e" is 65537, but it can be any number that is coprime to the totient of n = p * q (where p and q are two prime numbers). In the example you provided, p = 17 and q = 11, so n = 17 * 11 = 187. The totient of n is (p-1) * (q-1) = 16 * 10 = 160.

Therefore, the public key exponent "e" must be a number that is coprime to 160. In other words, the greatest common divisor (GCD) of "e" and 160 must be equal to 1. The number 7 is a valid choice for "e" because the GCD of 7 and 160 is 1. The number 3 is not a valid choice for "e" in this case because the GCD of 3 and 160 is not 1.

The choice of "e" in the RSA algorithm depends on the values of "p" and "q" and the requirement that "e" must be coprime to the totient of n. The value of "e" can be any number that meets this requirement, but commonly used values are 3, 17, and 65537.

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?

Hello,

the CtF I have experience with have been single day events. That means the event itself is not where any learning is taking place. The important time, for participants as well as organizers, is the preparation. That is also where students learn, but the CtF at the end gives a huge boost for motivation and provides a target to define what to learn.

The topics that can be learned depend on the type of CtF you are playing. The CtF I participated in where focused on application security, very practical implementation and configuration vulnerabilities with the occasional reverse engineering of buggy protocols. It is your, assuming you are the teacher, responsibility to select a fitting curriculum beforehand. But there are plenty of challenges and writeups of historical CtF events out there.

And then CtF provide an opportunity to setup a whole setup for security monitoring and operational processes. But the focus with us normally has been on bug hunting and reverse engineering and that, in my eyes, is not sufficient to motivate a full course in IT-security.

CtF tend to require a lot of preparation and part of it is development of "sport utilities" like efficient flag-submission services or exploit automation, but given that you can engage your students deeper with the prospect of a CtF competition in the end, and the potentials to run a competitive group continuously running over many years, where knowledge and skills can be honed and taught by the experienced students makes up for all the work. And, it is, in my experiences, one of the most fun and most effective ways of standing by while students learn.

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.

As I said, m and c are fixed. Also, I know both of them.

Passwords are about the only form of authentication human beings can use, but the entropy of passwords remembered by humans is very low. Hence, dictionary attacks against passwords are very effective. Several different PAKE protocols can make network protocols safe against both passive and active attackers, but none of them can protect against server compromise - a dictionary attack can always be mounted against the authentication data the server holds.

Secret sharing is used in building secure authentication protocols with weak passwords where the leakage of a single server's data does not allow for dictionary attacks on the password. A simple form of this is used in the real world by Verisign: Server-Assisted Generation of a Strong Secret from a Password. More recent research in to the problem: Provably Secure Threshold Password-Authenticated Key Exchange.

There is no known way to turn primality testing (or composite testing) to prime factorization effectively (in poly time), so this will be really surprising. Any polynomial time prime factorization algorithm will be most surprising results (there is no lower bound that indicates this is impossible, but the mathematical knowledge nowadays leads to sub exponential algorithms far worse than polynomial time). Side comment: The only polynomial time technique for prime factorization is a "Quantum polynomial time" method of Peter Shor (Shor's algorithm) BUT: quantum computers cannot yet be built of reasonable size to be a meaningful candidate to factor numbers that have large factors in them!!! Note that an efficient prime factorization algorithm will have extremely significant effect on modern cryptography as it is practiced!!!

I really appreciate your help, Prof.Thomas Mayerhöfer and Prof.Pablo Acebal !

Maybe this is what you are looking for:

In short, vast majority of today's practical hash functions (including SHA-2 family and SHA.3) do not have a strict proof reducing their properties to some widely acknowledged hard problems. Of course, their designers have some heuristic reasoning, but in practice the hash functions are expected to perform really fast, so you can not use expensive algebraic operations like modular exponentiation in their construction. On the other hand, using something like this seems unavoidable if you want to encode a hard problem somewhere in the function structure.

Dear Majid,

Thank you for your response. I will implement your suggestion. I hope it works well

Cryptography: change the data so it is not readable. Adversary can see there is a data communicated but can’t understand it.

Steganography: hide the very existence of the data. Adversary doesn’t know of a secret communication.

Watermarking: either visible or invisible and used to identify ownership and copyright.

Hi Mohammed. It would be helpful if you include the question signs in your questions.

In order to extract the instrumental profile from your measurements you need to measure a free-of-strain sample first, with a crystalline size small enough to get a good statistic. There's a commercial sample, LaB6, you can get from NIST in the USA. It's very expensive but good to do the job. Another alternative would be preparing a powder from a single crystalline Si wafer, but it's not easy to do without applying some stress. If you can find a way to get rid of the strain in your sample, let's say, to a value below 10^-4, that could be useful as a reference for the instrumental profile.

Once you've measured your reference sample for the instrumental profile you fit the powder diffraction pattern in Xpowder and you store all the values of the reference pattern, which basically consist of the parameters of the Caglioti's formula. Then, the instrumental profile can be extracted from any other sample with a strain higher than the strain in the reference material.

If you change the set-up in the X-Ray diffractometer, the Caglioti's parameters have to be measured again.

You can't get the dislocation density from Xpowder directly. For that purpose I would suggest to take a look at an academic software developed by Mateo Leoni, in Italy. It's called PM2K. You can send an email to him to get a copy of the software.

If you want to develop your own code in Mathematica or Matlab to determine the dislocation density and crystallite size by Warren-Averbach method I can give some directions to get started, just send me an email to hf278@exeter.ac.uk

Best regards.

Your question is not well defined. Differet tasks have different protocols. Authenticated key exchange is indeed a key protocol to span secret authenticated channel between clients and servers or inter servers communication (TLS/ SSL does that). In the mobile domain we have messaging protocols for end-to-ed encryption involving similar methods. All these are used billions of times per day over the Internet. The other various protocols you mention are theoretical ideas mainly (some in some level of use).

Adding to the answer of Ruhul Amin

For Encryption and some related tasks ECC expands the message two times. Furthermore, some of the points (x,y) are missing in almost every ECC curve

Dear Ragupathy,

This document aims to show the very basics of using the Contiki Cooja simulator.

I too, like Vijay Ananda and Majid Bakhtiari believed that our smss travel plain without encryption but the down votes force me to think that may be it is not the case!

WhatsApp support end to end encryption, I know (though dont know what algo is used!). Gmail uses PGP (IDEA) but, sms?????Still doubtful!

Ok. Now how to encode the black and white pixels?i was trying with the mayrices

1 0 0 0             1 0 0 0

1 0 0 0             0 1 0 0

1 0 0 0          0 0 1 0

1 0 0 0  and  0 0 0 1

But it is not working!

I dont think there is any standard code table available though, there are  some predefined guidelines such as, in English text, the frequency of occurrence of 'e' is highest. Vowels will be more frequent then consonants. So should be assigned with less numbers of bits.  Z, X will have minimum frequency and will fall towards the end of the symbol table etc.  When the text size is high, the variable length codes will provide high compression rate and a small symbol table can be accommodated without consuming much space (in comparison to the space we gained through the coding scheme). For image/ video compression, redundancy is even higher incomprehension to text . I presume LZW will be preferable for this case.

Most LSB based techniques can be steganalyzed using generalized chi-squared attack, RS- Steganalysis, Sample pair analysis, Weighted Stego, AUMP and with rich feature classifier. Please visit: dde.binghamton.edu and visit the Downloads section for many important and useful information on steganography and steganalysis

Depending on what you want to achieve with an efficient hardware architecture in terms of resource utilization, speed, power, etc., you should first divide and conquer the whole crypto algorithm into the sub-modules and write HDL code for each sub-module. As far as I know, there is no existing library in VHDL which supports crypto primitives (possible sub-modules). You may check OpenCores http://opencores.org/ website where you can find some HDL code that may help you. I highly suggest you to read these papers [1,2] in which they show you an efficient way to implement a crypto algorithm in FPGA. 

[1] At, Nuray, et al. "A Low-Area Unified Hardware Architecture for the AES and the Cryptographic Hash Function Grøstl." IACR Cryptology ePrint Archive 2012 (2012): 535. https://eprint.iacr.org/2012/535.pdf

[2] At, Nuray, et al. "Compact Hardware Implementations of ChaCha, BLAKE, Threefish, and Skein on FPGA," in IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 61, no. 2, pp. 485-498, Feb. 2014.

A better, and free solution is using Apache PDFbox: (https://pdfbox.apache.org/) You can use this together with BouncyCastle crypto library (https://www.bouncycastle.org/) to get assistance with cryptographic manipulations.

You're right Dr Yung. group signatures are perfectly suited for this purposeو but privacy level is not adjustable.

Tracing part is implemented in some protocols that have used ring signatures, such as "Efficient and Spontaneous Privacy-Preserving Protocol for Secure Vehicular Communications" by Hu Xiong et al. It's using trusted party private key. 

good luck

Thank you Dr Paillier and Dr Yung.

You're right Dr Yung, this method can be useful. but there is one small problem that should be considered before implementation. there are many clients and the CA should verify the received signatures from clients in a short period of time. So, matching the keys used in signatures increases the processing time in verification step (Depending on the number of received messages ).

"Why is it so? How to prove it?"

If encryption were linear, by taking two plaintexts A and B as well as their ciphertexts E(A) and E(B), you would get E(A + B) = E(A) + E(B). Of course, the meaning of "+" can vary. Are we talking GF(2)-linearity (XOR), addition modulo 2^128, truncated addition of words, ...?

This cannot be true with AES (or any other secure blockcipher), because otherwise you would get the key trivially with just 1 plaintext-ciphertext pair, encrypting 0 would always give 0, etc.

If you take the risk and opt for end-to-end-encryption in order to save your ciphertext data in a cloud, I strongly recommend that you scrutinize your exerted crypto suite for undeliberate and especially deliberate security leaks. It is commonly known that crook intelligencies embed weaknesses in crypto suites to reveal private data for their own purposes.

I don't know what you mean "best" but one of the most elegant and simplest I've seen is this: Tung Chou and Claudio Orlandi: "The Simplest Protocol for Oblivious Transfer"

The implementation is far too simple to discuss it.

A S-box random generated is dangereous. because it may contain weaknesses. Then a differential or linear cryptanalysis can be used to find session keys. See analysis of old encryption systems (DES for example). The construction of S-boxes for AES is based on the algebraic structure: GF(2^8). Here equivalence means a choice of a polynomial generator. There is somewhere a (public) paper with all these polynomial, but I have not its coordinates in this moment.

Please let me intimate two approaches to you!

Start with a solid book like Katz Lindel (new version) then go to papers like Shoup, Pointcheval, etc.

It would be great to work together or with other researchers who have desire to work together.

Yes you can. The poly must be irreducible. Any irreducible poly can be used. After changing it you have to change MDS matrix.

There has to be a way. Let's say that, in a non-mechanical encryption algorithm, we use a product rather than an XOR operation (using whole numbers). Multiply the plaintext by a secret number (or secret string of numbers, one per plaintext character). The product is the ciphertext.

In the decryption step, we use division. If the divisor is secret (or the stream of divisors is secret), the dividend is the ciphertext, and the reconstructed plaintext is the quotient. If the secret divisor (or divisor string) is correct, identical to the secret number(s) used in the multiplication step previously, and if the ciphertext was unchanged in transit, the quotient in the decryption step will result in whole numbers always, and must correspond to the original plaintext values. 

By the way, I have done this, and it does work.

Is this not possible with gears too? With unequal size gears, the cipher would have more potential values than the plaintext. But if the ciphertext received is identical to the transmitted string, and the gear ratios used in decryption are the same as those used in encryption, then the decryption should reconstruct the plaintext.

This type of cipher creates longer ciphertext than plaintext. So you might say "not fair," because the enigma machine only used the letters of the Roman alphabet in the ciphertext. It didn't have a large number of extra characters. So I'll respond that this would be a "more modern" enigma machine.

Cramer Damgard Schoonmakers Crypto 94 proceedings, or DeSantis, Di Crescenzo, Persiano and Yung FOCS 94 deal with the or proofs etc. that may be useful (can be viewed as extending the so called sigma-protocols techniques).

Steganography is the practice of concealing a file, message, image, or video within another file, message, image, or video. In contrast with this in Cryptograpy a file, message, image, or video is keyed transformed in order to hide information.

Steganography requires a carrier/payload in order to carry Obfuscated information.

Because of this Steganographed payload size is way larger then the Obfuscated information.

But in Cryptography sizes are same for Encrypted Data(Payload) and Data that has being encrypted.

Thus in a network scenario where bandwidth efficiency is an important stack holder, Cryptography is definitely is a winner because of its smaller Payload overheads. 

Data (size x) --->   Steganography ---> Steganographed data (size y)

observation:  x << y

Data (size x) --->   Cryptography ---> Encrypted data (size y)

observation:  x = y

hi

pleasesee

SEAL developped in 1993 by IBM (Don Coppersmith) and RC4 (1987 - Ron Rivest)) from RSA Security are very known streamciphers which are not based on LFSRs.

Pls go through Page nos 6,7,8 on below link for details on how to construct 16x16 MDS involution matrix

What about Pollard's Rho method and its parallelized?  it may be more efficient and fast.

Generally,once a cryptographic approach meets a PQC requirement, I think that will be fine. Or new PQC-Post Quantum Cryptographic approaches are welcomed.

Dear Neetesh,

  Try this. This may facilitate your research. all the best

 In choosing plain text attack, after receiving the cipher text of a message, you need some of the plain text of the same encrypted message that was received. and then using a technique, depending of the cryptosystem, to match the cipher text with its identical plain text to get the part of key which help to find the hole key or break the algorithm.

in choosing cipher text attack, the cryptanalysis depend only on the cipher text of the received message to recover the key or break the algorithm by using for example statistical tests.

Simple example, to attack a message that encrypted using simple substitution .

The letter frequency of encrypted message is calculated. And depending on the previous information about English letters, letter E is high frequency. So the letter with most frequency with replace with letter E as plain text and so on.

By Asymptotic I mean the Asymptotic complexity or Theta notation, tight bound, for the rate of growth of the function.

I am taking your suggestions.

I think you used the floating point arithmetic for your DWT transform. Then in this case, even if you didn't carry out any encryption, the inverse transform will not got the exactly image back. But only guarantees that the information loss is invisible to our eyes (you may check it by calculate the PSNR). When you embed the encryption to part of the transform coefficients, then the encrypted result may suffer other arithmetic problems, for example, the ciphertext is out the range of the original data.

I hope this may help you

Finally i developed RS steganalysis code by myself with the help of 

Thanks

(Combining methods are always being asked in conjunction with crypto, typically: encryption, compression, error correction, etc.)

You can combine in many ways, take Gunter's two ways and you can also iterate.

However, the more you combine the more you pay in performance, of course! (and this was noted above). So combination is often not practical.

Also, if your cipher is good why embed the message in a file first and then encrypt it rather then encrypting the message directly? It is a technique but does it make sense (ciphertext entropy will always reveal it is an encryption, and will defeat the basic trait of stego.)?

The main advantage of stego is its subliminal nature (hiding without being noticed), thus "encryption then stego" has some meaning (if your stego is broken [say by file dif] your message is still protected), while encrypting after stego has less use.

How can you compare different functions? For each function there is a protocol, and one should not compare apples to oranges!

ZK password proof is for user authentication (this user knows the password without revealing it) suitable for user auth. to a server.

Key exchange is for the two parties to share a key privately for whatever they want to use it for, and they better authenticate themselves to prevent Man-in-the-Middle attacks.

Hi,

In the website of Prof. Jessica Fridich you can fin some useful tools:

With best regards,

David

Dear Amal,

Salam,

In the attached file, the formulas precisely prove why Pr[ no E3] >=1/2. E3 is an event based on which the adversary A guesses the bit b'. If the attack applied by A is succeeded, its advantage is not negligible, means that 

Since the guess of b' is made according to the event E3 (described in the previous pages of the attached file), we can use of Total Probability Theorem to write

Since the value of the term "Pr[b=b'|no E3]" is between 0 and 1, then

Pr[b=b'|no E3]Pr[no E3] =< Pr[no E3]

Thus, we can write the equation (2) as

Pr[b=b'] =< Pr[b=b'|E3]Pr[E3] + Pr[no E3]      (3)

besides, when the event E3 is occurred, the adversary A have to guess b' completely random which its probability is 1/2. Thus, Pr[b=b'|E3] = 1/2. Now, we can rewrite the equation (3) as

Pr[b=b'] =< 1/2Pr[E3] + Pr[no E3]        (4)

if we replace Pr[E3] by "1-Pr[no E3]", we have

Pr[b=b'] =< 1/2 - 1/2Pr[no E3] + Pr[no E3] = 1/2 + 1/2Pr[no E3]

Eventually, we find 

Pr[b=b'] =< 1/2 + 1/2Pr[no E3]     (5)

The above equation can be written as 

On the other hand, we can consider the equation (2) by the second term "Pr[b=b'|no E3]Pr[no E3]". This term is an probability function which is between 0 and 1. Thus we can rewrite the equation (2) as  

Pr[b=b'] >= Pr[b=b'|E3]Pr[E3]         (7)

as mentioned above, Pr[b=b'|E3] = 1/2. Thus thus we can rewrite the equation (7) as

Pr[b=b'] >= 1/2Pr[E3]         (8)

if we replace Pr[E3] by "1-Pr[no E3]", we have

Pr[b=b'] >= 1/2 - 1/2Pr[no E3]      (9)

The above equation can be written as 

From the equations (6) and (10) we have 

By combining the equations (1) and (11) we have 

As our goal was to find a lower bound for Pr[no E3], we obtain from the equation (12) that 

epsilon =< 1/2Pr[no E3] 

and then 

that is the end of our proof to find a lower bound for Pr[no E3].

I just want to say that the Ruben Arias answer is a good example of a good professor which can do real knowledge to students.

To the question: read the chapter 3 of the book: Hyperelliptic curve  encryption theory

Dear Ighoroje,

You are right, but I am not totally agree. Homomorphic encryption guarantees you that the operations you perform on the ciphetext domanin are equivalent to operations in the plaintext domain. This is very useful when you store your data on non-trusted cloud servers, since you can ask the server to compute your encrypted data without decrypting it. Nevertheless, I am not sure in this case you are, in strict sense, perfoming prediction on encrypted data. In the end, if I am not wrong, you have to use the secret key in order to get the result of the computation you have perfomed in the ciphertext domain.

Regarding privacy, I think that in the current technology state maybe it is better to go for techniques as k-anonymity, l-diversity or statistical disclosure of information (SDC). Of course, in the next future FHE can and should be an option (which is clearly pinpointed in the paper you mention, but even further highlighted in the papers of Raluca Popa: http://web.mit.edu/ralucap/www/mylar.pdf). Recently I have read this very interesting manuscript:

In any case, if you are interested on working with the encrypted data, you could use the set of tools in NIST randomness test package (http://csrc.nist.gov/groups/ST/toolkit/rng/index.html), the Diehard suite (http://www.stat.fsu.edu/pub/diehard/), but also tools for generating markov models from time series (http://vserver1.cscs.lsa.umich.edu/~crshalizi/CSSR/ ) and those for string comparison (http://cran.r-project.org/web/packages/stringdist/stringdist.pdf).

With best regards,

David

I think you will need to change your solvent system from CH3CN, it is hopeful that it is trying to crystallize but it is not giving you decent shape or size crystals. You could try a mixture of solvents, what about BuCN or maybe THF? It looks like if its only going into CH3CN hot then its not too soluble in that so its coming out rather qickly on cooling, you could try and slow down the cooling rate maybe suspend flask in a water bath and slowly reduce the temperature of the bath, sometimes I leave it on a warm hot plate stirrer and switch off the stirrer. The other thing you could try is varying the shape of the flask, NMR tubes are particularly good at affording crystals. There is no simple answer to your question but good luck with it.

G(n) is a DiGraph with vertex set S={1,2,…,n} and arc set A=SxS, i.e., for every ordered (x,y) in SxS, there is an arc xy (directed edge from x to y; when x=y the arc is a cycle). Is there a Euler circuit C of G(n) such that for each ordered pair (x,y) there is a directed path from x to y with length 2 in C?

IBE is affected by key escrow problem, and based on cryptographic primitives making it less performant than other encryption schemes.

i suggest you to read "multiparty computation with low communication, computation, and interaction via threshold FHE" and "on-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption". It concludes re-linearization, dimension modulus reduction and bootstrapping techniques used in LWE.

First, asymmetric cryptography takes two forms: authentication and confidentiality

For message confidentiality, the message is encrypted with the receiver's public key and only the authentic receiver who has the corresponding private key can successfully decrypt it.

For message authentication, it is the other way around, encryption is done with the sender's private key and any receiver who holds the corresponding public key can decrypt the message. A successful decryption indicates that this message is from the claimed sender.

The choice over public or private key cryptography would depend highly on the exact place of non-interactive application you have in mind and how would (or did) you implement it.

For example, suppose you would like to control the access of you application that only you would like to use. You may prefer a symmetric cryptography (private key) to achieve this (although a conventional method is to use a digest function like MD5).

But, if you would like to selectively lock a specific functionality of an application that you would like to distribute (to customers), you may want to create a configuration file and encrypt it. If this is done with a symmetric key, then one way or another, the application must include the symmetric key along with it to decrypt the config. file for use - a simple reverse engineering attempt can locate the key within the application.

The solution thus lies in public key cryptography. You can encrypt your config. file in your own system with your private key, then store the public key along with the application to decrypt it for its use. You can encode the config. file to include the MAC address of the system or the disk ID for an integrity check for the machine it is entitled to operate in. This is what I did for my ERP application, it works just fine.

As far as I know, there's no universal automatic cryptanalysis tool to tell you "how secure this algorithm is". Especially, you have mentioned several types of cipher: AES/DES (Block), RSA(Public Key) and RC4(stream). Blowfish is also a block cipher, but due to the key-dependent S-boxes, many attacks on block cipher may not work on Blowfish.

There's one thing that's universal---brute force attack. You don't need tools for this; just take a look at the key length, and make sure brute force search is infeasible.

http://www.cryptool.org/

You might be interested in this site, which provide several cryptanalysis in a platform. However, this is mainly for e-learning purpose; it doesn't contain much cutting edge technology.

I agree with Professor Drossos that the work of mathematicians on whole-population surveillance is dangerous. Not only does such widespread surveillance destroy the possibility of privacy and private communications, it also tends calls into question the amount oversight required to prevent misuse of garnered information by government agencies.

CoO presents an absorption band at 550cm-1 strongly overlapped with Co3O4 signals as indicated by FTIR measurement.

At this stage in the (very limited) maturity of cryptocurrencies, I usually look at exchange volume. Obviously, a CC isn't much use unless it's liquid. One thing that makes me uncomfortable about this approach is that I don't really understand why people are buying the CC they are (in the sense that every femto-satoshi exchanged has both a seller and a buyer.) Market Cap doesn't have much functional meaning, and is distorted by pre-mined CC.

The trade-volume approach leads one to think Bitcoin and probably Litecoin (about 1/4 of Btc volume) are viable, but Dogecoin is way down (usually around 1/10 of Ltc) , and past that it's all noise.

Until the regulatory environment is figured out, all CC are going to be volatile.

Since blockchains are public, there are some interesting *data* mining opportunities, though it doesn't seem like there's been much sustained or academic interest in this so far.

Who is the threat in your question? If I am reading it correctly you are excluding the trusted third party as a threat, and you are excluding any active attackers. The rough answer to your question is that if there are no threats you could send the email in clear text and be just fine. Encryption is only necessary if you are protecting yourself from something.

Alternatively, you may be viewing passive network monitors as threats. For example, systems that are scanning email for keywords at the boarder of an organization. However, most passive monitors can be easily handled by even XORing the bits, a complex security protocol is only needed in the presence of an active attack on the email in question.

Finally, if you are assuming that there are no active attackers, and you actually have a trusted third party, you would be much better served by using stenography than public/private key encryption. Passive monitors are likely looking for odd things to flag for further scrutiny, a hidden email is more likely to pass unnoticed than an encrypted one.

Maybe the following work could help you: http://lasecwww.epfl.ch/pub/lasec/doc/YV04a.pdf.

Regards,

Llanos

A systematic transformation of the latitudes and longitudes of locations on the surface of a sphere or an ellipsoid into locations on a plane

if an irreducible n-degree polynomial f(x) is not primitive, then f(x) divides x ^ k - 1 for some positive k less than 2 ^ n - 1 (over GF[2]; analogous results hold for other finite fields), so its roots do not generate the full multiplicative group of GF[2 ^ n], and the period of the LFSR is the smallest such k

we still have k divides 2 ^ n - 1, so the periodic sequences generated by f(x) partition the space into disjoint cycles

and there are cases in which all irreducible f(x) are primitive (3, 7, 31, other mersenne primes), but that is a rare situation

there are lots of other algebraic things to consider for other prime bases

you may use a complex Permutation Generator,

Check this Sameer: http://textmechanic.com/Permutation-Generator.html

First thing to realize: a double-DES algorithm wiht two different keys has a keyspace of 2^112 bits. A brute force approach takes effort O(2^112) which is currently not feasible.

Second: the Meet-in-the-Middle attack allows you to decrease this effort to about O(2^57), which IS feasible.

How does it work?

Suppose you have two pairs of plaintext and cyphertext, namely, (P1, C1) and (P2, C2).

You want to find keys K1, K2 such that:

Enc(K2, Enc(K1,Pi)) = Ci, i = 1,2. In schematic form, this is

P -----> X, by function Enc(K1,.)

X -----> C, by function Enc(K2,.)

But you also know that

Dec(K2, Ci) = Enc(K1, Pi)

P -----> X, by function Enc(K1,.)

X <----- C, by function Dec(K2,.)

So you can proceed by making an array of 2^56 positions with all possible encryptions P1 under the 2^56 possible values for K1.

To select which of these may be possible keys, you now decrypt C1 under all possible 2^56 and stored the corresponding values. Now, you have two ways to reach your middle point X. And since you must arrive at the same value by both directions, you now filter the lists you have to keep only those elements that appear on both.

Now, it is possible that there are several pairs of keys that handle (P1,C1). So you still likely can not make a decision on which one is the right key.

But if you join another pair (P2,C2), the number of key pairs that actually encrypt (P2,C2) as well as (P1,C1) should be much reduced. I'm not sure two plaintext/ciphertext pairs are enough to identify exactly one key, but surely every new pair will decrease the number of possible key pairs dramatically.

I had good experiences with FlexiProvider (www.flexiprovider.de) - it is suitable for JCA (Java Cryptography Architecture). Once I found a bug in an implemented algorithm, they reacted very fast!

I don't understand what you mean by "dimension zero" of a number system.

If you are looking for a "new number system" you may want to see the paper Z₂-graded Number Theory" (By Regev, Henke and myself)

where we investigate the arithmetic/algebraic properties of a number system that extends the integers (that I prefer to call the "superintegers"). I don't know if it can be any use in cryptography. The main motivation to study their arithmetic properties is that they are convenient as index sets for grading superalgebras, and for indexing characters of the symmetric group, as their arithmetic operations are related to "hook numbers" of young diagrams related to characters, so they do encode some not entirely trivial combinatorics in their arithmetics.

Are you asking for references for prototype or you need real time scenarios to know where it is used.

I have used cantor to map to a single integer and in the message part I have converted to their ascii value and mapped into co-ordinates through koblitz and perform additive cycling. Does I'm going in right direction or not???

yes hash is not the ideal choice for longer run. My previous suggestion is not against Kerckhoff's principle. Instead of using available encryption, it is suggested to write own code to understand the concepts.

Hi Rens,

You've hit on the exactly key principle behind QKD, which is that one cannot perfectly clone quantum states. This is what makes the whole process work (i.e. it is this limitation the defeats the would-be eavesdropper) but this also means traditional forwarding is impossible. Thus current QKD schemes are limited to single hop transmissions which at the moment is only feasible over ~100km.

To go further distances one would have to either use a free space uplink to a satellite, or build genuinely quantum nodes. In the literature these are called quantum repeaters, but at the moment they exist only in theory and some proof of principle experiments for some of the necessary components.

Also I should emphasise that if one wants complete security OTP is the only option. In the papers you quote the authors aren't talking about sending Gbps of key, rather they are showing you can send ~66kbps through a fibre that also has Gbps of classical communication traffic.

Hope that was useful,

Nathan