Search results
Results from the WOW.Com Content Network
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. Whether it is as difficult as the factoring problem is an open question. [3] There are no published methods to defeat the system if a large enough key is used.
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 ...
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.
RSA Laboratories stated: "Now that the industry has a considerably more advanced understanding of the cryptanalytic strength of common symmetric-key and public-key algorithms, these challenges are no longer active." [6] When the challenge ended in 2007, only RSA-576 and RSA-640 had been factored from the 2001 challenge numbers. [7]
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields.ECC allows smaller keys to provide equivalent security, compared to cryptosystems based on modular exponentiation in Galois fields, such as the RSA cryptosystem and ElGamal cryptosystem.
For example, RSA relies on the assertion that factoring large numbers is hard. A weaker notion of security, defined by Aaron D. Wyner, established a now-flourishing area of research that is known as physical layer encryption. [4] It exploits the physical wireless channel for its security by communications, signal processing, and coding techniques.
FIPS PUB 112 Password Usage 1985, defines 10 factors to be considered in access control systems that are based on passwords FIPS PUB 113 Computer Data Authentication 1985, specifies a Data Authentication Algorithm (DAA) based on DES , adopted by the Department of Treasury and the banking community to protect electronic fund transfers.
Clifford Christopher Cocks CB FRS [2] (born 28 December 1950) is a British mathematician and cryptographer.In the early 1970s, while working at the United Kingdom Government Communications Headquarters (GCHQ), he developed an early public-key cryptography (PKC) system.