Titlebook: Cryptographic Applications of Analytic Number Theory; Complexity Lower Bou Igor Shparlinski Book 2003 Springer Basel AG 2003 Cryptography.D

兴奋过度

Polynomials and Recurrence SequencesHere we collect some lemmas we will need later.

诽谤

Exponential SumsAbstract.We need some bounds of exponential sums as well.

甜瓜

Distribution and DiscrepancyHere we collect some results about the distribution properties of various sequences. Some of them are quite generic, while the others are rather specialised and tailored to our applications.

TRACE

Arithmetic FunctionsWe use the well-know estimates.see Theorem 5.1 and Theorem 5.2 of Chapter 1 of [468]. Also, from the inequality v(m)!≤m, we derive.The above bounds are tight. Thus although sometimes the values of Τ(m) are rather big, “on average”, much stronger bounds hold. Namely, for any X≥2.see Theorems 5.3 and 5.4 of Chapter 1 of [468].

mechanical

remission

典型

Platelet

Approximation of the Discrete Logarithm by Real PolynomialsHere we consider some questions about approximation of the discrete logarithm by real and even complex polynomials. Unfortunately our results are weaker than those in our previous settings.

heterodox

下垂

Polynomial Approximation and Arithmetic Complexity of the Diffie-Hellman Secret Keyol, is based on the still unproved assumption that recovering the value of the Diffie-Hellman secret key . from the known values of g.and g.is essentially equivalent to the discrete logarithm problem and therefore is hard. Here we show that even computation of . from g.cannot be realized by a polynomial of low degree.