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The prime numbers are kept secret. Messages can be encrypted by anyone, via the public key, but can only be decrypted by someone who knows the private key. [1] The security of RSA relies on the practical difficulty of factoring the product of two large prime numbers, the "factoring problem". Breaking RSA encryption is known as the RSA problem.
In cryptography, the RSA problem summarizes the task of performing an RSA private-key operation given only the public key. The RSA algorithm raises a message to an exponent, modulo a composite number N whose factors are not known. Thus, the task can be neatly described as finding the e th roots of an arbitrary number, modulo N.
In the RSA cryptosystem, Bob might tend to use a small value of d, rather than a large random number to improve the RSA decryption performance. However, Wiener's attack shows that choosing a small value for d will result in an insecure system in which an attacker can recover all secret information, i.e., break the RSA system.
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. Security of public-key cryptography depends on keeping the private key secret; the public key can be openly distributed without compromising security. [3]
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 RSA private key may have two representations. The first compact form is the tuple (,), where d is the private exponent. The second form has at least five terms (,,,,) , or more for multi-prime keys. Although mathematically redundant to the compact form, the additional terms allow for certain computational optimizations when using the ...
It depends on the selected cryptographic algorithm which key—public or private—is used for encrypting messages, and which for decrypting. For example, in RSA, the private key is used for decrypting messages, while in the Digital Signature Algorithm (DSA), the private key is used for authenticating them. The public key can be sent over non ...
Public-key cryptosystems use a public key for encryption and a private key for decryption. Diffie–Hellman key exchange; RSA encryption; Rabin cryptosystem; Schnorr signature; ElGamal encryption; Elliptic-curve cryptography; Lattice-based cryptography; McEliece cryptosystem; Multivariate cryptography; Isogeny-based cryptography