منابع مشابه
Gaussian Mersenne and Eisenstein Mersenne primes
The Biquadratic Reciprocity Law is used to produce a deterministic primality test for Gaussian Mersenne norms which is analogous to the Lucas–Lehmer test for Mersenne numbers. It is shown that the proposed test could not have been obtained from the Quadratic Reciprocity Law and Proth’s Theorem. Other properties of Gaussian Mersenne norms that contribute to the search for large primes are given....
متن کاملAttacks on the AJPS Mersenne-Based Cryptosystem
Aggarwal, Joux, Prakash and Santha recently introduced a new potentially quantum-safe public-key cryptosystem, and suggested that a brute-force attack is essentially optimal against it. They consider but then dismiss both Meet-in-the-Middle attacks and LLL-based attacks. Very soon after their paper appeared, Beunardeau et al. proposed a practical LLL-based technique that seemed to significantly...
متن کاملGeneralised Mersenne Numbers Revisited
Generalised Mersenne Numbers (GMNs) were defined by Solinas in 1999 and feature in the NIST (FIPS 186-2) and SECG standards for use in elliptic curve cryptography. Their form is such that modular reduction is extremely efficient, thus making them an attractive choice for modular multiplication implementation. However, the issue of residue multiplication efficiency seems to have been overlooked....
متن کاملMersenne and Fermat Numbers
The first seventeen even perfect numbers are therefore obtained by substituting these values of ra in the expression 2n_1(2n —1). The first twelve of the Mersenne primes have been known since 1914; the twelfth, 2127 —1, was indeed found by Lucas as early as 1876, and for the next seventy-five years was the largest known prime. More details on the history of the Mersenne numbers may be found in ...
متن کاملOn Using Mersenne Primes in Designing Cryptoschemes
The paper proposes justification of using Mersenne primes in the following cryptoschemes: commutative and publickey encryption algorithms and zero-knowledge protocol. The cryptoschemes are based on computational difficulty of finding discrete logarithm in the finite fields GF (2), where s is a sufficiently large prime such that 2s−1 is also a prime, for example s = 1279, s = 2203, and s = 4253.
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ژورنال
عنوان ژورنال: Performance Practice Review
سال: 1993
ISSN: 1044-1638,2166-8205
DOI: 10.5642/perfpr.199306.02.06