1. What are the categories of modern cryptographic techniques?
Modern cryptographic techniques can be categorized into asymmetric and symmetric key cryptosystems. Asymmetric key cryptosystems, such as RSA cryptography, rely on the use of a third party, Certificate Authority (CA), for key distribution. Symmetric key cryptosystems, on the other hand, face the challenge of secure key distribution due to eavesdropping during key sharing. In symmetric-key systems, n*(n-1)/2 keys are required for n users, while in asymmetric key systems, a single key pair is used for encryption and decryption. Both types of cryptographic techniques aim to provide data confidentiality, integrity, and authenticity.
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2. What are the limitations of the ESRKGS, MRSA, and RSA algorithms in terms of encryption, decryption time, and key generation?
The limitations of the ESRKGS, MRSA, and RSA algorithms are as follows: 1. ESRKGS has a higher encryption and decryption time compared to the original RSA algorithm due to its character-by-character encryption and looping process. 2. MRSA has a high key generation time due to the exponentiation and modulation operations, and it is vulnerable to double encryption attacks and generating alternative private key exponents. 3. RSA's security is based on the assumption of the difficulty of integer factorization, which can be compromised by quantum computers. Additionally, RSA's encryption and decryption keys are dependent on the common modulus, making it easier to unlock the system. Furthermore, RSA's cipher text size is doubled compared to other algorithms, which is a major concern in data transmission.
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3. What is the proposed Hidden Real Modulus RSA (HRM-RSA) Algorithm?
The proposed Hidden Real Modulus RSA (HRM-RSA) Algorithm is a cryptographic method that introduces a new security parameter called public mask modulus M to hide a real modulus n from the public. Unlike traditional RSA and related works that use a common real modulus for encryption and decryption, HRM-RSA keeps the real modulus n private for decryption and uses a public mask modulus M for encryption. This approach enhances security by making it difficult for attackers to exploit the limitations of existing algorithms, such as D-Wave quantum computer attacks and Shor's integer factorization algorithm. The key generation process in HRM-RSA involves generating two large prime numbers, computing the hidden real modulus n, calculating Euler's O(n), generating the encryption exponent e, computing the decryption exponent d, and generating a large random number m. The public mask modulus M is then computed by multiplying n and m. The encryption step involves encrypting the plain text T using the public key components e and M, while the decryption step involves decrypting the false cipher text C using the private key components d and n. The HRM-RSA algorithm provides enhanced security by challenging cryptanalysts to design cryptanalysis algorithms to unlock it, making it a promising approach in the field of cryptography.
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4. How does HRM-RSA encryption and decryption process prove to be inverses?
In the HRM-RSA algorithm, the encryption and decryption processes are proven to be inverses of each other using the second version of Euler's theorem. The theorem states that if n = p*q, a<n, and k is an integer, then a k*O(n) + 1 = a (mod n), where O(n) is the totient function. Additionally, the congruence of modular properties is used, where a kr mod n = (a k mod n) r mod n. By assuming the plain text T1 delivered to Bob from Alice is equal to the plaintext T sent by Alice as encrypted cipher text C, we can prove this using the formula C = T e mod M, where M = n*m. By applying the congruence of modular properties, T1 = (T e d mod n) where n|M and n<M, we can see that the fields size is n. This demonstrates that the encryption and decryption processes are inverses of each other in the HRM-RSA algorithm.
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