Modified RSA Encryption Algorithm (MREA)

TLDR: This scheme presents a new cryptography algorithm based on additive homomorphic properties called Modified RSA Encryption Algorithm (MREA), which is secure as compared to RSA as it is based on the factoring problem as well as decisional composite residuosity assumptions which is the intractability hypothesis.

Abstract: In asymmetric key cryptography, also called Public Key cryptography, two different keys (which forms a key pair) are used. One key is used for encryption & only the other corresponding key must be used for decryption. No other key can decrypt the message, not even the original (i.e. the first) key used for encryption. The beauty of this scheme is that every communicating party needs just a key pair for communicating with any number of other communicating parties. Once some one obtains a key pair, he /she can communicate with any one else. RSA is a well known public-key cryptography algorithm. It is the first algorithm known to be suitable for signing as well as encryption, and was one of the first great advances in public key cryptography. The security of the RSA cryptosystem is based on two mathematical problems: the problem of factoring large numbers know mathematical attack and the problem of trying all possible private keys know brute force attack. So to improve the security, this scheme presents a new cryptography algorithm based on additive homomorphic properties called Modified RSA Encryption Algorithm (MREA). MREA is secure as compared to RSA as it is based on the factoring problem as well as decisional composite residuosity assumptions which is the intractability hypothesis. The scheme is an additive homomorphic cryptosystem, this means that, given only the public-key and the encryption of m1 and m2, one can compute the encryption of m1 + m2. This scheme also presents comparison between RSA and MREA cryptosystems in terms of security and performance.