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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 .
In cryptography, ciphertext or cyphertext is the result of encryption performed on plaintext using an algorithm, called a cipher. [1] Ciphertext is also known as encrypted or encoded information because it contains a form of the original plaintext that is unreadable by a human or computer without the proper cipher to decrypt it.
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.
Deterministic encryption can leak information to an eavesdropper, who may recognize known ciphertexts. For example, when an adversary learns that a given ciphertext corresponds to some interesting message, they can learn something every time that ciphertext is transmitted.
RSA (Rivest–Shamir–Adleman) is another notable public-key cryptosystem. Created in 1978, it is still used today for applications involving digital signatures. [18] Using number theory, the RSA algorithm selects two prime numbers, which help generate both the encryption and decryption keys. [19]
The RSA Secret-Key Challenge was a series of cryptographic contests organised by RSA Laboratories with the intent of helping to demonstrate the relative security of different encryption algorithms. The challenge ran from 28 January 1997 until May 2007.
First layer of the encryption: The ciphertext of the original readable message is hashed, and subsequently the symmetric keys are encrypted via the asymmetric key - e.g. deploying the algorithm RSA. In an intermediate step the ciphertext, and the hash digest of the ciphertext are combined into a capsule, and packed together.
Such a system is called (t,n)-threshold, if at least t of these parties can efficiently decrypt the ciphertext, while fewer than t have no useful information. Similarly it is possible to define a (t,n) -threshold signature scheme , where at least t parties are required for creating a signature.