Asymmetric cryptography (public key / private key)

Asymmetric cryptography relies on a mathematically linked pair of keys: the private key (secret, preserved in an HSM or QSCD) and the public key (freely distributed in a certificate). To sign a document, the signer calculates the fingerprint of the document and encrypts it with their private key; anyone can verify the signature by decrypting this fingerprint with the public key and comparing it to the hash of the original document. The dominant algorithms are RSA (2048–4096 bit keys) and ECC (P-256, P-384 curves). RSA 2048 bits is recommended until 2030 by NIST; ECC P-256 offers equivalent security level with 10× shorter keys (performance gain on HSM). Resistance to quantum computers is assured by post-quantum algorithms CRYSTALS-Dilithium and CRYSTALS-Kyber, currently being standardized by NIST.