MHB A question on cryptography....

  • Thread starter Thread starter chisigma
  • Start date Start date
  • Tags Tags
    Cryptography
AI Thread Summary
The discussion centers on the security implications of a proposed cryptographic system that uses a sequence of keys for encoding messages. It highlights that while the initial method may seem secure, sharing key information (like the sum of two keys) could compromise the system's integrity, particularly in relation to the One-Time Pad. The conversation emphasizes the importance of using truly random keys and the risks associated with reusing keys for multiple plaintexts, which can lead to vulnerabilities. The consensus is that communicating key information alongside ciphertext is generally inadvisable and can weaken security. Overall, the proposed method raises significant concerns regarding its effectiveness in maintaining cryptographic security.
chisigma
Gold Member
MHB
Messages
1,627
Reaction score
0
The recent case 'datagate' suggests me to prose to You a question I didn.t resolve completely. Let's suppose that we have a plaintext $p_{n}$ and we code it with a key $k_{n}$ generating a chipertext...

$\displaystyle c_{n} = p_{n} + k_{n}\ (1)$

... where the sum is modulo some 'large number' N. It is well known that the (1) is 'theoretically secure' if and only if...

a) the sequence $k_{n}$ is 'absolutely random'...

b) the sequence $k_{n}$ is to be use only for a single message...

It is also well known that this solution has many pratical problems, mainly the necessity to have a large number of sequence $k_{n}$ only for have a secure communication between two persons. An idea to overcome that drawback may be to use a $k_{n,m}$ for the message m and a $k_{n,m+1}$ for the message m+1 and in the message m to communicate...

$\displaystyle c_{n,m} = p_{n,m} + k_{n,m},\ h_{n,m}= k_{n,m} + k_{n,m+1}\ (2)$

What is Your opinion regarding the security of this type of cryptosystem?...

Kind regards

$\chi$ $\sigma$
 
Mathematics news on Phys.org
I should think communicating $h_{n,m}= k_{n,m} + k_{n,m+1}$ would greatly compromise the security of the so-called One-Time Pad, as you've described it. Naturally, for a single transmission, your proposal will have the same level of security as a one-time pad normally does. However, the additional information could be decoded once several messages have been transmitted in this way, in order to figure out what the next $k$ will be.

In general, communicating much of any key information along with the ciphertext is a bad idea.
 
May be that for the readers and for me is useful to remember some basic concept. A ciphertext $\displaystyle c_{n}$ is given by...

$\displaystyle c_{n}= p_{n} + k_{n}\ \text{mod}\ N\ (1)$

... i.e. the sum modulo N of a plaintext and a key. The main difference between a plaintext and a key is that the key is 'random' and a plaintext isn't random. Why the use of the same key to code two different plaintexts is 'a bad choice'?...

Let's suppose that the two plaintexts are monday and friday. In that case with a systematic search i find, sooner or later, the key that produces the playntext monday produces the plaintext friday and both the ciphertexts are brooken. Completely different is the situation if the same key is used to code a plaintext and another key. In that case monday produces something like jaab?+ and friday something like \gw>o@ and it's impossible to extablishes which plaintext is 'more probable'...

Am I right?...

Kind regards

$\chi$ $\sigma$
 
Last edited:
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

Similar threads

Replies
1
Views
2K
Replies
2
Views
1K
Replies
15
Views
2K
Replies
5
Views
2K
Replies
9
Views
5K
Replies
1
Views
12K
Replies
7
Views
3K
Back
Top