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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 =.
This was designed by the National Security Agency (NSA) to be part of the Digital Signature Algorithm. Cryptographic weaknesses were discovered in SHA-1, and the standard was no longer approved for most cryptographic uses after 2010. SHA-2: A family of two similar hash functions, with different block sizes, known as SHA-256 and SHA-512. They ...
E.g., an attacker who wants to know the decryption of a ciphertext c ≡ m e (mod n) may ask the holder of the private key d to decrypt an unsuspicious-looking ciphertext c′ ≡ cr e (mod n) for some value r chosen by the attacker. Because of the multiplicative property, c ' is the encryption of mr (mod n).
SHA-2 (Secure Hash Algorithm 2) is a set of cryptographic hash functions designed by the United States National Security Agency (NSA) and first published in 2001. [3] [4] They are built using the Merkle–Damgård construction, from a one-way compression function itself built using the Davies–Meyer structure from a specialized block cipher.
It defines the Digital Signature Algorithm, contains a definition of RSA signatures based on the definitions contained within PKCS #1 version 2.1 and in American National Standard X9.31 with some additional requirements, and contains a definition of the Elliptic Curve Digital Signature Algorithm based on the definition provided by American ...
Hash-based signature schemes use one-time signature schemes as their building block. A given one-time signing key can only be used to sign a single message securely. Indeed, signatures reveal part of the signing key. The security of (hash-based) one-time signature schemes relies exclusively on the security of an underlying hash function.
The Cryptographic Message Syntax (CMS) is the IETF's standard for cryptographically protected messages. It can be used by cryptographic schemes and protocols to digitally sign, digest, authenticate or encrypt any form of digital data.
Threshold versions of encryption or signature schemes can be built for many asymmetric cryptographic schemes. The natural goal of such schemes is to be as secure as the original scheme. Such threshold versions have been defined by the above and by the following: [7] Damgård–Jurik cryptosystem [8] [9] DSA [10] [11] ElGamal