利用個人化秘密的RSA密碼學方法與系統

This patent invention creates flexibility into the RSA cryptography. The goal is achieved by allowing a user to select a personalized secret such as a password to derive an exponent that functions like a leading part of the RSA private key, and by further allowing the user to discretionarily change the selection without resorting to a regeneration of the public/private key pair. The invention also includes methods and cryptosystems of using a personalized secret and a crypto-key trio to produce and validate a digital signature. Exchanging a symmetric crypto key between two communication parties is one further application utilizing the devised techniques for the crypto-key generation, update, and validation.