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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 .
For large RSA key sizes (in excess of 1024 bits), no efficient method for solving this problem is known; if an efficient method is ever developed, it would threaten the current or eventual security of RSA-based cryptosystems—both for public-key encryption and digital signatures. More specifically, the RSA problem is to efficiently compute P ...
The Digital Signature Algorithm (DSA) is a public-key cryptosystem and Federal Information Processing Standard for digital signatures, based on the mathematical concept of modular exponentiation and the discrete logarithm problem. In a public-key cryptosystem, a pair of private and public keys are created: data encrypted with either key can ...
The first widely marketed software package to offer digital signature was Lotus Notes 1.0, released in 1989, which used the RSA algorithm. [26] Other digital signature schemes were soon developed after RSA, the earliest being Lamport signatures, [27] Merkle signatures (also known as "Merkle trees" or simply "Hash trees"), [28] and Rabin ...
The signature schemes are actually signatures with appendix, which means that rather than signing some input data directly, a hash function is used first to produce an intermediary representation of the data, and then the result of the hash is signed. This technique is almost always used with RSA because the amount of data that can be directly ...
The two best-known types of public key cryptography are digital signature and public-key encryption: In a digital signature system, a sender can use a private key together with a message to create a signature. Anyone with the corresponding public key can verify whether the signature matches the message, but a forger who does not know the ...
In cryptography, the strong RSA assumption states that the RSA problem is intractable even when the solver is allowed to choose the public exponent e (for e ≥ 3). More specifically, given a modulus N of unknown factorization, and a ciphertext C , it is infeasible to find any pair ( M , e ) such that C ≡ M e mod N .
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 ...