Forty years of attacks on the RSA cryptosystem: A brief survey

RSA public key cryptosystem is the de-facto standard use in worldwide technologies as a strong encryption/decryption and digital signature scheme. RSA successfully defended forty years of attack since invention. In this study we survey, its past, present advancements and upcoming challenges that needs concrete analysis and as a counter measure against possible threats according to underlying algebraic structure. Past studies shows us some attacks on RSA by inspecting flaws on relax model using weak public/private keys, integer factorization problem, and some specific low parameter selection attacks. Such flaws can not hamper the security of RSA cryptosystem by at large, but can explore possible vulnerabilities for more deep understanding about underlying mathematics and improper parameter selection. We describe a brief survey of past findings and detail description about specific attacks. A comprehensive survey of known attacks on RSA cryptosystem shows us that a well implemented algorithm is unbreakable and it survived against a number of cryptanalytic attacks since last forty years.