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RSASSA-PSS is a digital signature algorithm that is part of the RSA family of cryptographic algorithms. It stands for RSA Probabilistic Signature Scheme with Appendix. The algorithm is designed to provide a high level of security and is widely used in various applications, including secure communications, digital certificates, and software signing.

RSASSA-PSS is based on the RSA algorithm, which relies on the mathematical difficulty of factoring large integers. The PSS (Probabilistic Signature Scheme) component adds a layer of randomness to the signature process, making it more resistant to certain types of attacks. The "with Appendix" part refers to the way the signature is appended to the message, rather than being integrated into it.

The RSASSA-PSS algorithm works by first hashing the message to be signed, then applying a mask generation function to the hash, and finally combining the masked hash with a random salt value. The resulting value is then encrypted using the RSA private key to produce the signature. The signature can be verified by decrypting it with the corresponding RSA public key and checking the resulting value against the original hash.

RSASSA-PSS is considered secure against a wide range of attacks, including chosen-message attacks and adaptive chosen-ciphertext attacks. However, like all cryptographic algorithms, it is subject to ongoing analysis and improvement. The algorithm is standardized by the International Organization for Standardization (ISO) and the International Electrotechnical Commission (IEC) in the ISO/IEC 9796-2 standard.