On the distribution of the power generator
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Publication:2723530
DOI10.1090/S0025-5718-00-01283-7zbMath1029.11042OpenAlexW2014937115MaRDI QIDQ2723530
John B. Friedlander, Igor E. Shparlinski
Publication date: 5 July 2001
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0025-5718-00-01283-7
Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Estimates on exponential sums (11L07) Cryptography (94A60) Exponential sums (11T23) Pseudo-random numbers; Monte Carlo methods (11K45)
Related Items (17)
On the cycle structure of repeated exponentiation modulo a prime ⋮ Character sums with exponential functions ⋮ Optimal strong primes ⋮ On the power generator and its multivariate analogue ⋮ Exponential sums of nonlinear congruential pseudorandom number generators with Rédei functions ⋮ On the uniformity of distribution of the RSA pairs ⋮ Period of the power generator and small values of Carmichael’s function ⋮ On the elliptic curve endomorphism generator ⋮ Mordell’s exponential sum estimate revisited ⋮ Distribution of exponential functions with \(k\)-full exponent modulo a prime ⋮ On the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators ⋮ Multivariate permutation polynomial systems and nonlinear pseudorandom number generators ⋮ Character sums with exponential functions over smooth numbers ⋮ Random Generators and Normal Numbers ⋮ On the average distribution of inversive pseudorandom numbers ⋮ On the distribution of the Diffie-Hellman pairs ⋮ Exponential sums with Dickson polynomials
Cites Work
- Analysis of iterated modular exponentiation: The orbits of \(x^\alpha \mod N\)
- On the multidimensional distribution of inversive congruential pseudorandom numbers in parts of the period
- On the distribution of pseudorandom numbers and vectors generated by inversive methods
- Stronger security proofs for RSA and Rabin bits.
- On the distribution of inversive congruential pseudorandom numbers in parts of the period
- Period of the power generator and small values of Carmichael’s function
- A Simple Unpredictable Pseudo-Random Number Generator
- Quasi-Monte Carlo methods and pseudo-random numbers
- On Certain Exponential Sums and the Distribution of Diffie-Hellman Triples
- Character sums with exponential functions
- Properties of the x/sup 2/ mod N pseudorandom number generator
- On the statistical properties of Diffie-Hellman distributions
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