Cryptosystems - Science topic

сложность выполнения задачи факторизации N^0.5 Эта задача не может относиться к класс NP-полных. Количество операций растет как полином в степени 0.5. Сложность обусловлена размером чисел, но не более.

I need codes to encrypt and decode images in Matlab for the following algorithms.

AES, with key 128 bit

AES, with key 256 bit

RSA, with key 1024 bit

RSA, with key 2048 bit

hello.

please see the book an introduction to mathematical Cryptography by Jeffrey Hoffstein Jill Pipher Joseph H. Silverman , and see chapter 6, Babai’s algorithm page 379.

Want the encryption and decryption time complexity when used by pallier cryptosystem

TLS in your browser is built on authentication (at least of the server), every time you log in with a password to a web service or locally it is authentication of the client as well. Every time you use password and a second factor like a one-time device that puts in a few numbers to report to a server or a ubkey authentication using a public key from a USB. These are all authentication used all the time...on the web, locally, and to apps on your phone. Authentication is teh key to having an account in anything related to computing and connecting to the right servers!!!

A brief introduction to cryptography from the IBM website may also help you to understand: https://www.ibm.com/support/knowledgecenter/en/SSB23S_1.1.0.14/gtps7/seccon.html

This website will generate keys online:

They are incomparable: PKI can be used to certify public keys constructed by users where private keys are only at users. IBE is based on private keys constructed by an authority (outside the user's private space, assumed to be trusted). Certificate based systems   and certificate based encryption  attempt to combine the two: you get the IBE key and use a certificate based on it for a private key and use both keys to encrypt. The main thing to remember is that to embed a solution in your system you have to know what "trust assumption" is made in the system ad who is trusted and who is not and hw private you want your secrets to be.

Dear Lakshmi, there is no way the minimum distance could be so high. Use the Plotkin bound to see how small the rate would be ( asymptotically zero). The dimension of the code one half I can believe. Not the minimum weight.

In the public key technology area: Factoring and Discrete Log are broken by Quantum algorithms, so other techniques are needed like Lattice-based methods (these are non classical but more recent like NTRU, and others LWE, and so on). Recently, an attempt to develop quantum algorithms against lattices was published briefly (but it had some flaw, and it is not clear it is correctable-- it is a reminder though that all we know about quantum resistance is that we do not know such algorithms that are efficient; any day such algorithms can be found).

For signature schemes, post-quant. method include the one-way hash based (variants of Merkle).

In symmetric key cryptography, searching a list in quantum is square-root(N) rather than n, and therefore the measure is to double the key length as was done to AES (starting with 128 already factored in quantum search) and so on.

Newbie question/remark: AES( which is a private key crypto) is not dependent on the prime factorization problem, so the big push of Shor's algorithm is not relevant on AES. Right?

I like ECC. But I need to know more about it. What is said about it here is absolutely true.

Everything depends on how you modify your algorithm ,CPU clock cycles to perform it , iteration process capacity of a processor for the running operation.Compare to the previous & the modified one.You'll understand. Better to apply on raw code.You can get the result in per/sec then convert it to j/s.In your needed result must have to know how many works the algorithm will perform in per second. - Thanks.

ECC requires shorter key to achieve security as compared to RSA, and that the mathematical operation involved in ECC is scalar multiplication while RSA uses exponentiation.  Because of these, computational complexity involved in ECC is much less as compared to other asymmetric cryptosystems.  

This enables much faster encryption, decryption and signature verification.  Also it saves bandwidh and memory space.  

Hence ECC is best suited for devices which have limited storage and computational power (like smart cards).  Also it is suited for web-browsers, which use a number of encryption sessions.

So your observation about ECC is right.

Regards.