andr3/ComputerSecurity
Archived
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases 2 Wiki Activity

Fix small errors
All checks were successful
continuous-integration/drone/push Build is passing
Details

Browse Source
This commit is contained in:
Andre Henriques 2023-11-14 17:45:23 +00:00
parent 3ba9a63d96
commit bbe07d7a4b
1 changed files with 7 additions and 3 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

10
cw/cw.tex
View File

@ -116,7 +116,7 @@
I used factorization to obtain the private key. After obtaining the private key, I can decrypt the cipher text and obtain "handlebars'' I used factorization to obtain the private key. After obtaining the private key, I can decrypt the cipher text and obtain "handlebars''
\subsection*{3.3} \subsection*{3.3}
I used the general number sieve to factorize\cite{cadonfs} to factorize the public modulus and obtained: I used the general number sieve\cite{cadonfs} to factorize the public modulus and obtained:
$$p=112546167358047505471958486197519319605436748416824057782825895564365669780011$$ $$p=112546167358047505471958486197519319605436748416824057782825895564365669780011$$
and and
$$q=65802972772386034028625679514602920156340140357656235951559577501150333990623$$ $$q=65802972772386034028625679514602920156340140357656235951559577501150333990623$$
@ -253,9 +253,9 @@
which means that which means that
$$(((m^{r_{a\text{ alice}}})^{r_{a\text{ bob}}})^{r_{b\text{ alice}}})^{r_{b\text{ bob}}} = m (\text{mod } p)$$ $$(((m^{r_{a1}})^{r_{b1}})^{r_{a2}})^{r_{b2}} = m (\text{mod } p)$$
in this case, $r_a$ from Alice cancels $r_b$ from Alice, and $r_a$ from Bob cancels $r_b$ from Bob. in this case, $r_{a1}$ from Alice cancels $r_{a2}$ from Alice, and $r_{b1}$ from Bob cancels $r_{b2}$ from Bob.
\subsubsection*{6.3.2} \subsubsection*{6.3.2}
To send an encrypted message using this system between 2 people, i.e. Alice and Bob: To send an encrypted message using this system between 2 people, i.e. Alice and Bob:
@ -303,9 +303,13 @@
$$=\frac{\sqrt{92699}}{9427678922^{\frac{1}{4}}}\approx0.977094\approx0.98$$ $$=\frac{\sqrt{92699}}{9427678922^{\frac{1}{4}}}\approx0.977094\approx0.98$$
The Hadamard ration for the private bias is $0.98$
$$H(U)=(\frac{det(L)}{\|u1\|\times\|u2\|})^\frac{1}{n}=(\frac{92699}{\sqrt{u1_1^2 + u1_2^2}\times\sqrt{u2_1^2 + u2_2^2}})^\frac{1}{2}=$$ $$H(U)=(\frac{det(L)}{\|u1\|\times\|u2\|})^\frac{1}{n}=(\frac{92699}{\sqrt{u1_1^2 + u1_2^2}\times\sqrt{u2_1^2 + u2_2^2}})^\frac{1}{2}=$$
$$=\frac{\sqrt{92699}}{243990681350077^{\frac{1}{4}}}\approx0.0770361\approx0.077$$ $$=\frac{\sqrt{92699}}{243990681350077^{\frac{1}{4}}}\approx0.0770361\approx0.077$$
The Hadamard ration for the public bias is $0.077$
B: B:
$$w = (30548, 6642)$$ $$w = (30548, 6642)$$
$$\begin{cases} $$\begin{cases}