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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.
Since public-key algorithms tend to be much slower than symmetric-key algorithms, modern systems such as TLS and SSH use a combination of the two: one party receives the other's public key, and encrypts a small piece of data (either a symmetric key or some data used to generate it). The remainder of the conversation uses a (typically faster ...
G (key-generator) gives the key k on input 1 n, where n is the security parameter. S (signing) outputs a tag t on the key k and the input string x. V (verifying) outputs accepted or rejected on inputs: the key k, the string x and the tag t. S and V must satisfy the following: Pr [ k ← G(1 n), V( k, x, S(k, x) ) = accepted] = 1. [5]
If, however, the receiver wants to search for a specific record in the database, this becomes very difficult. There are some Public Key encryption schemes that allow keyword search, [1] [2] [3] however these schemes all require search time linear in the database size. If the database entries were encrypted with a deterministic scheme and sorted ...
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.
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.
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 =.
The vulnerability arises from an approach to RSA key generation used in vulnerable versions of the software library RSALib provided by Infineon Technologies and incorporated into many smart cards, Trusted Platform Modules (TPM), and Hardware Security Modules (HSM), including YubiKey 4 tokens when used to generate RSA keys on-chip for OpenPGP or ...