(IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 10, No. 10, 2019 353 | Page www.ijacsa.thesai.org Enhanced, Modified and Secured RSA Cryptosystem based on n Prime Numbers and Offline Storage for Medical Data Transmission via Mobile Phone Achi Harrisson Thiziers 1* , Haba Cisse Théodore 2 , Jérémie T. Zoueu 3 , Babri Michel 4 Instrumentation, Imaging and Spectroscopy Laboratory (L2IS) Institut National Polytechnique-Houphouët Boigny (INP-HB) DFR-GEE, Yamoussoukro, Côte d‘Ivoire 1,2,3 Computer Science and Telecoms Networks Laboratory (LARIT) INP-HB Abidjan, Côte d‘Ivoire 4 Abstract—The transmission of medical data by mobile telephony is an innovation that constitutes the m-health or more generally e-health. This telemedicine handles personal data of patients who deserve to be protected when they are transmitted via the operator or private network, so that malicious people do not have access to them. This is where cryptography comes in to secure the medical data transmitted, while preserving their confidentiality, integrity and authenticity. In this field of personal data security, public key cryptography or asymmetric cryptography is becoming increasingly prevalent, as it provides a public key to encrypt the transmitted message and a second private key, linked to the first by formal mathematics, that only the final recipient has to decrypt the message. The RSA algorithm of River and Shamir provides this asymmetric cryptography based on a public key and a private key, on two prime numbers. However, the factorization of these two prime numbers to give the variable N of RSA can be discovered by a hacker and thus make the security of medical data vulnerable. In this article, we propose a more secured RSA algorithm with n primes and offline storage of the essential parameters of the RSA algorithm. We performed a triple encryption-decryption with these n prime numbers, which made it more difficult to break the factorization of the variable N. Thus, the key generation time is longer than that of traditional RSA. Keywords—e-Health; medical data transmission; asymmetric cryptography; RSA algorithm; first numbers I. INTRODUCTION Transmitting medical data via interconnection technologies such as mobile telephony is an operation that requires the highest level of security, in order to preserve their private and personal nature. This subject, as well as the algorithm of River and Shamir [1], have been the topic of several studies in the literature and continue to fascinate many researchers. D. Sathya and al. [2] worked on a secure remote monitoring system, combining a symmetric algorithm and attribute-based encryption, to secure data transmission and the medical sensor network access control system. J. Heurix and al. [3] have worked on storage that preserves privacy and access to medical data through pseudonymization and encryption. Mohammed L. and al. [4] worked on remote supervision of e-health that preserves privacy, through a process of prior patient approval, before any transmission to the Health Centre. M. Milutinovic and al. [5] spoke about the management of privacy-preserving data in an e-health system, developing a protocol based on new e-health architecture. We note from these works that data encryption aims to make medical data inaccessible to unauthorized persons. Thus, the confidentiality, integrity and availability of this data are preserved [6]. There are two main types of cryptography. Symmetric key cryptography, with a unique public key that is shared between the sender who sends the encrypted message and the receiver who receives it and decrypts the full text. Among the symmetric algorithms are DES, 3DES, AES, IDEA, and BLOWFISH [7]. We also have asymmetric cryptography with two distinct keys: a public key that the sender uses to encrypt his message and another private key mathematically linked to the first that is used to decrypt the original message. We can mention here the RSA algorithm which factors two prime numbers to give a large integer number ‗N‘ [8]. The simple principle that drives RSA is to be able to perform easy mathematical calculations, but whose reverse operation is difficult, in the absence of additional information, according to M. A. Islam and al. [9]. In general, RSA uses two primes ''p'' and ''q'' to obtain the factorization of the large integer ''N''. The attack on RSA can occur at this level, when the hacker succeeds in discovering the factorization of the large number ''N'', thus preventing the generation of the private key from the public key. Our contribution, in this article, is an amelioration of the security of RSA, by accentuating key generation time, during the factorization of the large number N. We used, like M. A. Islam, four prime numbers, instead of two, in the original RSA model; this makes the factorization more robust with a large number of the exponent used for encryption. Instead of the double encryption-decryption he performed, we made a triple encryption-decryption to make RSA even stronger, therefore more secured than the original RSA of Shamir and MSRSA from Muhammad. To speed up encryption-decryption, we stored offline the essential key generation and factorization parameters. The first part of this article, constituted by the introduction, is followed by the second part which relates the state of the art, *Corresponding Author