RSA

RSA is an asymmetric cryptographic algorithm based on prime factorisation, widely used for encryption and digital signatures in PKI.

RSA is an asymmetric cryptographic algorithm, one of the earliest practical public-key systems, published in 1977 by Rivest, Shamir and Adleman. It relies on the mathematical difficulty of factoring large numbers that are the product of two large primes: the public key contains that product (the modulus) and an exponent, while the private key contains the prime factors, making it computationally infeasible to derive the private key from the public one; the reverse - deriving the public key from the private key - is straightforward.

RSA can both encrypt/decrypt and sign/verify, which is why it underpins much of PKI: certificates (X.509) commonly carry RSA public keys, and the matching private key - the signature creation data - signs a document's hash rather than the document itself. In practice RSA is rarely used to encrypt bulk data directly: because RSA operations are relatively slow, it typically encrypts only a symmetric key that then encrypts the actual data, a technique known as hybrid encryption; newer protocols such as TLS 1.3 have dropped RSA key transport entirely in favour of other key-exchange methods, though RSA certificates remain widely used for authentication. For qualified signatures and seals, RSA key pairs must be produced by trustworthy key generation and held on a certified QSCD: a QSCD may be built on a general-purpose HSM, but it has to be certified against the Annex II requirements of eIDAS (Regulation (EU) 910/2014), so the private key never exists unprotected outside that hardware. Which standards that certification runs against depends on who holds the key: Commission Implementing Decision (EU) 2016/650 lists them for a device the signatory keeps (ISO/IEC 15408 and 18045, plus the EN 419211 protection profiles), while for remote signing, where the provider manages the key, Article 1(2) of that Decision instead requires a process with comparable security levels that is notified to the Commission. See QSCD for that route.