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The RSA problem is defined as the task of taking e th roots modulo a composite n: recovering a value m such that c ≡ m e (mod n), where (n, e) is an RSA public key, and c is an RSA ciphertext. Currently the most promising approach to solving the RSA problem is to factor the modulus n.
The PKCS #1 standard defines the mathematical definitions and properties that RSA public and private keys must have. The traditional key pair is based on a modulus, n, that is the product of two distinct large prime numbers, p and q, such that =.
Later, the 128-bit RSA SecurID algorithm was published as part of an open source library. [4] In the RSA SecurID authentication scheme, the seed record is the secret key used to generate one-time passwords. Newer versions also feature a USB connector, which allows the token to be used as a smart card-like device for securely storing certificates.
PKCS Standards Summary; Version Name Comments PKCS #1: 2.2: RSA Cryptography Standard [1]: See RFC 8017. Defines the mathematical properties and format of RSA public and private keys (ASN.1-encoded in clear-text), and the basic algorithms and encoding/padding schemes for performing RSA encryption, decryption, and producing and verifying signatures.
The PKCS #11 standard defines a platform-independent API to cryptographic tokens, such as hardware security modules (HSM) and smart cards, and names the API itself "Cryptoki" (from "cryptographic token interface" and pronounced as "crypto-key", although "PKCS #11" is often used to refer to the API as well as the standard that defines it).
Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. [1] [2] Key pairs are generated with cryptographic algorithms based on mathematical problems termed one-way functions.
PBKDF2 is part of RSA Laboratories' Public-Key Cryptography Standards (PKCS) series, specifically PKCS #5 v2.0, also published as Internet Engineering Task Force's RFC 2898. It supersedes PBKDF1, which could only produce derived keys up to 160 bits long. [2] RFC 8018 (PKCS #5 v2.1), published in 2017, recommends PBKDF2 for password hashing.
G (key-generator) generates a public key (pk), and a corresponding private key (sk), on input 1 n, where n is the security parameter. S (signing) returns a tag, t, on the inputs: the private key (sk), and a string (x). V (verifying) outputs accepted or rejected on the inputs: the public key (pk), a string (x), and a tag (t).