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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.
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.
It provides the basic definitions of and recommendations for implementing the RSA algorithm for public-key cryptography. It defines the mathematical properties of public and private keys, primitive operations for encryption and signatures, secure cryptographic schemes, and related ASN.1 syntax representations. The current version is 2.2 (2012 ...
PKCS #7 files may be stored both as raw DER format or as PEM format. PEM format is the same as DER format but wrapped inside Base64 encoding and sandwiched in between ‑‑‑‑‑BEGIN PKCS7‑‑‑‑‑ and ‑‑‑‑‑END PKCS7‑‑‑‑‑. Windows uses the .p7b file name extension [6] for both these encodings.
More specifically, the RSA problem is to efficiently compute P given an RSA public key (N, e) and a ciphertext C ≡ P e (mod N). The structure of the RSA public key requires that N be a large semiprime (i.e., a product of two large prime numbers), that 2 < e < N, that e be coprime to φ(N), and that 0 ≤ C < N.
PKCS #8 is one of the family of standards called Public-Key Cryptography Standards (PKCS) created by RSA Laboratories. The latest version, 1.2, is available as RFC 5208. [1] The PKCS #8 private key may be encrypted with a passphrase using one of the PKCS #5 standards defined in RFC 2898, [2] which supports multiple encryption schemes.
The public key in the RSA system is a tuple of integers (,), where N is the product of two primes p and q.The secret key is given by an integer d satisfying (() ()); equivalently, the secret key may be given by () and () if the Chinese remainder theorem is used to improve the speed of decryption, see CRT-RSA.
The message is encrypted using a public key, and the corresponding private key is shared among the participating parties. With a threshold cryptosystem, in order to decrypt an encrypted message or to sign a message, several parties (more than some threshold number) must cooperate in the decryption or signature protocol.