# Burmester-Desmedt-Bd-Key-Agreement-Protocols

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How to find such values \$x\$. Well, if \$\$p is small, you can simply test the different options (as I did in this case). However, if \$p\$ is large, you can find such values efficiently with Euclid`s advanced algorithm The key gene process includes participants t {displaystyle t}. Participants in u {displaystyle u_i} organize a “ring” so that u t + 1 = u 1 {displaystyle u_ {t+1} =u_1}. We now see that \$7 4 = \$28 and \$28 = 6 (bmod 11)\$, or \$6/4 = \$7\$. And yes, if \$p\$prim and if what you divide by is not zero, it turns out that such a division is clearly defined; There will always be exactly a number between \$0 and \$p-\$1 that meets these criteria. Mike Burmester, Yvo Desmedt A secure and scalable group key exchange system. — Department of Computer Science, Florida State University, Tallahassee. — www.cs.fsu.edu/~burmeste/ipl-final.pdf K i = β i − 1 t r i x i t − 1 x i + 1 t − 2.

. . x i + t − 3 2 x i + t − 2 1 = A i − 1 ( A i − 1 x i ) ( A i − 1 x i x i + 1 ). . . ( A i − 1 x i x i + 1 x i + t − 2 ) = A i − 1 A i A i + 1. . . A i − 2 = A 0 A 1. .

. A i − 1 = α r 0 r 1 + r 1 r 2 +. . . + r t − 1 r t = K {displaystyle K_i = beta_{i-1}^{t r_i} x_i^{t-1} x_{i+1}^{t-2}. x_{i+t-3}^2 x_{i+t-2}^1 = A_{i-1} (A_{i-1} x_i) (A_{i-1} x_i x_{i+1}). (A_{i-1} x_i x_{i+1} x_{i+t-2}) = A_{i-1} A_i A_{i+1}. A_{i-2} = A_0 A_1. A_{i-1} = alpha^{r_0 r_1 + r_1 r_2 +. + r_{t-1} r_t} = K ,!} Wir definieren \$x = 6/4 (bmod 11)\$ als diesen Wert, so dass \$x times 4 = 6 (bmod 11)\$. Der resultierende Schlüssel wird in einer Form dargestellt: K = α r 0 r 1 + r 1 r 2 +.

. . + r t − 1 r t ( m o d p ) {displaystyle K = alpha^{r_0 r_1 + r_1 r_2 +. + r_{t-1} r_t} (mod,p) ,!} Colin Boyd, Anish Mathuria Protocols for Authentication and Key Establishment. — Springer Science & Business Media, 2013. – С. 214 – 216. – ISBN 5-09-002630-0. This protocol is an extension of the Diffie Hellman key agreement protocol. It allows the creation of a common secret key for a large number of (predefined) participants. The protocol uses a cyclic function for data encryption. The public parameters are determined: p {displaystyle p} – a prime number, the calculation module.

α {displaystyle alpha } is a generator of the cyclic group. All this work will be modulo the premium \$p \$ (which is 11 in your example of toys); In this area, addition, subtraction and multiplication are done in the usual way (unless you make a module \$p\$ at the end); However, the distribution is defined differently. Each participant generates a random number: r i i ∈ R 1 , p − 1 ̄ → S K {displaystyle r_i in R, overline{1, p-1} to SK , ! } and the secret guard. . . .