MET CS690 - Cryptography: Authentication,Integrity & Security

This assignment delves into cryptographic mechanisms for authentication and data integrity, analyzing the security of secret key-based authentication schemes. It examines the vulnerabilities of using a single secret key versus individual secret keys among parties like Alice, Bob, and Carol, concluding that a seemingly more complex setup isn't necessarily more secure. The discussion extends to random choice protocols and the limitations of RSA in signing messages larger than the modulus n. Furthermore, it elaborates on the use of Hash functions and digital signatures, including public and private keys, to ensure message authenticity and reliability, detailing the encryption and decryption processes with mathematical examples. The assignment references several academic sources to support its analysis and explanations of cryptographic principles and algorithms.

Question One
This new approach is not any more secure than the first game plan. Alice should know Carol's
secret key with a specific end goal to confirm Carol's response to a test from Alice. Additionally,
she would require Bob's secret key to check Bob's solution to her difficulties. (Any of the three
has to know the others secret keys for confirming responses to any difficulties). In this way, Bob
could at present mimic Carol to Alice since he would know Carol's secret key so as to have the
capacity to answer Carol's difficulties. Consequently, while it is a more intricate setup, it is not
any more secure than having them all utilization a similar secret key over the long haul
(Dhivakar, 2015.
We can conclude that the new technique that is sort is better than the old method in terms of
security i.e. initially they were all using the same secret key but are now using different secret
keys. In this approach, a random choice protocol is utilized in the following manner. “Alice
generates random bitstring KA, publishes h (KA). Bob generates random bitstring BA, publishes
h (BA). Colleen generates random bitstring KC, publishes h (KC). After all hashes revealed, A,
B and C reveal KA, BA and KC. The random bitstring is R = KA XOR BA XOR KC. Assuming
h is a one-way hash function, no one can cheat, since the hashes were already revealed. Each
player has to choose their contribution to the random string without knowing the other values
that will be XOR'd with it.” (Fadhil & Younis, 2015).
Question Two
The most appropriate solution is No. Review that RSA confines the message to be marked to be
littler than n. On the off chance that m is bigger than n, at that point message m and message (m
mod-n) would have a similar signature. So it is anything but difficult to create distinctive
messages that have a similar signature. “RSA restricts the message to be signed to the process of
smaller than e If, is larger than n then the message m and message m mod n has the same
signature” (Garg, 2016).
(i) So it is easy to generate the differ message as the same signature
(ii) By using the toitent function 9(n)=(p1 — 1Xql — I) for performing the I(n)and
exponent dvalue
(iii) Where 9(n1) is divisible by 4n1)
Therefore cl e=1 (mod 9(n1)) then will perform the st 1 (mod 41))
Since common value of (pl — 1) and (q1 —1) are present in the factor of n1 — 1 =12, 1— qW
0+00— O. Therefore (pl — 1) and (q1 —1) have only very small common factors.
The sender creates an encryption of the message, attaches the encrypted message, and embeds it
in a file. After embedding the message, the sender sends over the file to the recipient. Once the
recipient receives the data, and the message is decrypted, and the process of determining the
authenticity and reliability of the message begins (Lachance, 2015).
To measure the reliability of the message, the digital signature has to match the identity of the
sender. A mathematical function known as the Hash function best explains this procedure.
During the process of data transmission, the Hash function breaks the data into smaller functions

with a fixed number of bits.
These smaller bits represent the actual data sent, and after this process, the function will develop
a unique data basing on the contents of the file. The formula the function uses in authenticating
the message is message digest/digital message, and the results must match the original message a
sender sent (Liu, Guo, & Lin, 2014).
The message created by the Hash function is permanent, and there is no way a person can reverse
it, since it is mathematical generated. After creating the message, the process of encryption
begins. In this process, a person has to produce his own unique digital identity. He has a pair of
keys, known as the public and the private keys.
The individual has an access to the private key, while the society has an access to the public key.
The purpose of these keys is to change data to a format the human eye cannot understand, and
then back to a form that a human being can understand. After creating the message, the sender
must encrypt the message using a private key.
This facilitates the embedation of the digital message into a file, which is then dispatched to the
recipient. The recipient views the message by use of a public key that associates itself with the
sender’s private key. This process is called decryption, and it establishes the authenticity of the
digital signature (Pei & Li, 2013).
To demonstrate this process, scientists must understand that the public and the private keys have
two parts; the first part is unique to each key, while the second part is identifiable by both keys.
Take an example of the numbers p and q, and make an assumption that “p” is Z and “q” is W.
The codes p and q are unique and only identified by the specific private and public code, and
therefore a common identifier “n” is encrypted (Saranya, 2016).
To get the value of n, we multiply values of p, by values of q, that is Z*W and the value is ZW.
For any encryption to occur, a researcher must get the value of totient value of n, and the formula
is, (p-1) multiplied by (q-1). Totient ZW= (Z-1) multiplied by (W-1) and it equals to (Z-1) (W-
1).
After this stage, a researcher must choose another number and equate it to value “e”. The
number must be between 1 and n, and a coprime of n. Therefore i’ll take the value of e as M. By
using the formula of (e*x-1) mod totient n = 0. Let us equate the results of this function as R.
Therefore the values will be, p is Z, q is W, n is ZW, e is M and d is R. You have to note that Z,
W ZW, M and R are real numbers. By in scripting all this values together, the public key is, the
value of e, which is M and the value of n which is ZW. The private key amounts to the value of d
which is R and the value of n which is ZW.

References
Dhivakar, A. (2015). A multi-level security in cloud computing: Image sequencing and RSA
algorithm.
Fadhil, H. M., & Younis, M. I. (2015). A Multithreading Implementation of RSA Algorithm on
Multicore and GPU: Parallel Processing. Saarbrücken: LAP LAMBERT Academic
Publishing.
Garg, S. (2016). A Review on RSA Encryption Algorithm. International Journal Of
Engineering And Computer Science. doi:10.18535/ijecs/v5i7.07
Lachance, D. (2015). Cryptography Fundamentals: Defining the RSA Algorithm.
Liu, C., Guo, Y., & Lin, J. (2014). Security analysis of RSA cryptosystem algorithm and it’s
properties. doi:10.1063/1.4897774
PEI, D., & LI, X. (2013). Further study on algebraic structure of RSA algorithm. Journal of
Computer Applications, 33(11), 3244-3246. doi:10.3724/sp.j.1087.2013.03244
Saranya, R. (2016). Image Encryption using RSA Algorithm with Biometric
Recognition. International Journal Of Engineering And Computer Science.
doi:10.18535/ijecs/v5i11.78