Download Basics of Contemporary Cryptography for IT Practitioners by Boris Ryabko PDF

By Boris Ryabko

The purpose of this publication is to supply a complete creation to cryptography with out utilizing advanced mathematical buildings. the subjects are conveyed in a sort that in simple terms calls for a easy wisdom of arithmetic, however the tools are defined in adequate element to allow their machine implementation.

The e-book describes the most ideas and amenities of latest cryptography, proving key effects alongside the best way. The contents of the 1st 5 chapters can be utilized for one-semester path.

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1 -a3y. 7) is the solution of Eq. (3,l). 6) exist. Proof. 6)). 6) exist. 1). We can see that all numbers from 1 to k m are contained in the table. 3) that the table contains all numbers from 1 to p . e. 6) always has a solution. 1 Numbers of the form im - j . iJ. j-+ 1 2 0 1 m 2m m- l 2m- 1 m- 2 2m- 2 km- 1 km- 2 ... k km ... 2 ... m-1 ... 1 ... ... m+l ... 1 Find the solution of the equation 2” mod 23 = 9 with the aid of baby-step giant-step algorithm. Choose m and k. Let m = 6, k = 4. 3) is fulfilled.

Taking into account Eq. 23) and then Eqs. 18)) we may continue x 4 = m ( c ~ d ~ c s mod d ~ )( ~ - 1 )mod - m(cAdA mod ( P - l ) ) ( c E d E mod ( P - 1 ) ) mod = ml'l mod which proves the first statement of the proposition. = 24 Basics of Contemporary Cryptography f o r IT Practitioners The proof of the second statement is based on the assumption that for an adversary trying to recover m, there is no strategy more effective than the following. 22). But to implement this strategy the adversary has to solve discrete logarithm problem which is impossible if p is large.

We can see that the time of exponentiation grows linearly as the length of numbers ( n ) increases but the time of solving the inverse problem grows exponentially or (for the index calculus algorithm) subexponentially. The issue of the existence of faster algorithms for computing discrete logarithms, as well as for solving other inverse problems in cryptography, remains an open question. 2 35 The Baby-step Giant-step Algorithm In the unclassified literature this method was first described by Daniel Shanks (see [Knuth (1973)l); references thereto have been known since 1973.

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