Short cycles in repeated exponentiation modulo a prime
نویسندگان
چکیده
Given a prime p, we consider the dynamical system generated by repeated exponentiations modulo p, that is, by the map u 7→ fg(u), where fg(u) ≡ gu (mod p) and 0 6 fg(u) 6 p − 1. This map is in particular used in a number of constructions of cryptographically secure pseudorandom generators. We obtain nontrivial upper bounds on the number of fixed points and short cycles in the above dynamical system.
منابع مشابه
# a 66 Integers 13 ( 2013 ) Cycles in Repeated Exponentiation Modulo
We consider a dynamical system generated by exponentiation modulo r, that is, by the map u !→ fq(u), where fq(u) ≡ qu (mod r) and 0 ≤ fg(u) ≤ r− 1. The number of cycles is estimated from above in the case when r = pn with a prime integer p and gcd(q, p) = 1. Also a more general class of functions is considered.
متن کاملAn Efficient Discrete Log Pseudo Random Generator
The exponentiation function in a finite field of order p (a prime number) is believed to be a one-way function. It is well known that O(log log p) bits are simultaneously hard for this function. We consider a special case of this problem, the discrete logarithm with short exponents, which is also believed to be hard to compute. Under this intractibility assumption we show that discrete exponent...
متن کاملA Novel Modular Multiplication Algorithm and its Application to RSA Decryption
The services such as electronic commerce, internet privacy, authentication, confidentiality, data integrity and non repudiation are presented by public key cryptosystems. The most popular of public key cryptosystems is RSA cryptosystem. RSA is widely used for digital signature and digital envelope, which provide privacy and authentication. The basic operation of RSA cryptosystem is modular expo...
متن کاملA new class of scalable parallel pseudorandom number generators based on Pohlig-Hellman exponentiation ciphers
We propose a new class of pseudorandom number generators based on Pohlig-Hellman exponentiation ciphers. The method generates uniform pseudorandom streams by encrypting simple sequences of short integer messages into ciphertexts by exponentiation modulo prime numbers. The advantages of the method are: the method is trivially parallelizable by parameterization with each pseudorandom number gener...
متن کاملA fast and exible software library for large integer arithmetic
An ANSI C library of subroutines for multiprecision operations on unsigned integers is presented, that is both fast and exible. Usability and applicability of such a library are shown to depend both on the basic design decisions as well as on the library's actual functionality. Basic design decisions are the choice of programming language, the representation of multiprecision integers, error ha...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Des. Codes Cryptography
دوره 56 شماره
صفحات -
تاریخ انتشار 2010