How is Blakley's Secret Sharing Scheme perfect?












2














Currently, I am trying to understand Blakley's secret sharing scheme. However, there seem to be multiple descriptions of it, which are very different from another, but everyone states that the scheme would be perfectly secure.



From my understanding it works like this:




  • a point $S$ in $t$-dimensional space is created with one coordinate being secret and the others randomly selected


  • $n$ hyperplanes through the point $S$ are created and distributed

  • to reconstruct the secret, $t$ hyperplanes are required, which will intersect at the point $S$.


However, from my understanding, if someone would possess one or more hyperplanes, they would know that $S$ lies somewhere on that hyperplane (or the intersection of multiple hyperplanes)



So my question is;




  • how is Blakley's scheme considered perfectly secure when an insider knows that the secret lies on his plane?






secret-sharing







share|improve this question









New contributor




Ceriath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
















  • 2




    If I give you a line, can you find my secret point on it?
    – kelalaka
    yesterday










  • since a line is infinite, i can't. But from my understanding perfect means, that no information at all is revealed about the secret, while in this case it would reveal that it is somewhere on that line
    – Ceriath
    yesterday






  • 1




    OK, better formulation: If I give you a line, can you find the x-coordinate of my secret point on it?
    – SEJPM♦
    yesterday










  • Defn: A secret sharing scheme is called perfect if the probability of deception has the same value for all illegal constellations of participants. and see page 21
    – kelalaka
    yesterday


















2














Currently, I am trying to understand Blakley's secret sharing scheme. However, there seem to be multiple descriptions of it, which are very different from another, but everyone states that the scheme would be perfectly secure.



From my understanding it works like this:




  • a point $S$ in $t$-dimensional space is created with one coordinate being secret and the others randomly selected


  • $n$ hyperplanes through the point $S$ are created and distributed

  • to reconstruct the secret, $t$ hyperplanes are required, which will intersect at the point $S$.


However, from my understanding, if someone would possess one or more hyperplanes, they would know that $S$ lies somewhere on that hyperplane (or the intersection of multiple hyperplanes)



So my question is;




  • how is Blakley's scheme considered perfectly secure when an insider knows that the secret lies on his plane?






secret-sharing







share|improve this question









New contributor




Ceriath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
















  • 2




    If I give you a line, can you find my secret point on it?
    – kelalaka
    yesterday










  • since a line is infinite, i can't. But from my understanding perfect means, that no information at all is revealed about the secret, while in this case it would reveal that it is somewhere on that line
    – Ceriath
    yesterday






  • 1




    OK, better formulation: If I give you a line, can you find the x-coordinate of my secret point on it?
    – SEJPM♦
    yesterday










  • Defn: A secret sharing scheme is called perfect if the probability of deception has the same value for all illegal constellations of participants. and see page 21
    – kelalaka
    yesterday
















2












2








2







Currently, I am trying to understand Blakley's secret sharing scheme. However, there seem to be multiple descriptions of it, which are very different from another, but everyone states that the scheme would be perfectly secure.



From my understanding it works like this:




  • a point $S$ in $t$-dimensional space is created with one coordinate being secret and the others randomly selected


  • $n$ hyperplanes through the point $S$ are created and distributed

  • to reconstruct the secret, $t$ hyperplanes are required, which will intersect at the point $S$.


However, from my understanding, if someone would possess one or more hyperplanes, they would know that $S$ lies somewhere on that hyperplane (or the intersection of multiple hyperplanes)



So my question is;




  • how is Blakley's scheme considered perfectly secure when an insider knows that the secret lies on his plane?






secret-sharing







share|improve this question









New contributor




Ceriath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











Currently, I am trying to understand Blakley's secret sharing scheme. However, there seem to be multiple descriptions of it, which are very different from another, but everyone states that the scheme would be perfectly secure.



From my understanding it works like this:




  • a point $S$ in $t$-dimensional space is created with one coordinate being secret and the others randomly selected


  • $n$ hyperplanes through the point $S$ are created and distributed

  • to reconstruct the secret, $t$ hyperplanes are required, which will intersect at the point $S$.


However, from my understanding, if someone would possess one or more hyperplanes, they would know that $S$ lies somewhere on that hyperplane (or the intersection of multiple hyperplanes)



So my question is;




  • how is Blakley's scheme considered perfectly secure when an insider knows that the secret lies on his plane?






secret-sharing




secret-sharing






share|improve this question









New contributor




Ceriath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|improve this question









New contributor




Ceriath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|improve this question




share|improve this question








edited yesterday









kelalaka

5,97022041




5,97022041






New contributor




Ceriath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked yesterday









CeriathCeriath

314




314




New contributor




Ceriath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Ceriath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Ceriath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.








  • 2




    If I give you a line, can you find my secret point on it?
    – kelalaka
    yesterday










  • since a line is infinite, i can't. But from my understanding perfect means, that no information at all is revealed about the secret, while in this case it would reveal that it is somewhere on that line
    – Ceriath
    yesterday






  • 1




    OK, better formulation: If I give you a line, can you find the x-coordinate of my secret point on it?
    – SEJPM♦
    yesterday










  • Defn: A secret sharing scheme is called perfect if the probability of deception has the same value for all illegal constellations of participants. and see page 21
    – kelalaka
    yesterday
















  • 2




    If I give you a line, can you find my secret point on it?
    – kelalaka
    yesterday










  • since a line is infinite, i can't. But from my understanding perfect means, that no information at all is revealed about the secret, while in this case it would reveal that it is somewhere on that line
    – Ceriath
    yesterday






  • 1




    OK, better formulation: If I give you a line, can you find the x-coordinate of my secret point on it?
    – SEJPM♦
    yesterday










  • Defn: A secret sharing scheme is called perfect if the probability of deception has the same value for all illegal constellations of participants. and see page 21
    – kelalaka
    yesterday










2




2




If I give you a line, can you find my secret point on it?
– kelalaka
yesterday




If I give you a line, can you find my secret point on it?
– kelalaka
yesterday












since a line is infinite, i can't. But from my understanding perfect means, that no information at all is revealed about the secret, while in this case it would reveal that it is somewhere on that line
– Ceriath
yesterday




since a line is infinite, i can't. But from my understanding perfect means, that no information at all is revealed about the secret, while in this case it would reveal that it is somewhere on that line
– Ceriath
yesterday




1




1




OK, better formulation: If I give you a line, can you find the x-coordinate of my secret point on it?
– SEJPM♦
yesterday




OK, better formulation: If I give you a line, can you find the x-coordinate of my secret point on it?
– SEJPM♦
yesterday












Defn: A secret sharing scheme is called perfect if the probability of deception has the same value for all illegal constellations of participants. and see page 21
– kelalaka
yesterday






Defn: A secret sharing scheme is called perfect if the probability of deception has the same value for all illegal constellations of participants. and see page 21
– kelalaka
yesterday












1 Answer
1






active

oldest

votes


















2














Okay so SEJPM's comment just gave me an answer or better made me realize my flaw:



Since the secret is only one coordinate (e.g. $x$) the information that the secret is on a specific infinite line is as much information as having none at all, since guessing $x$ of a point on $y = 5*x$ is worth as much as guessing $x$ of a point on $y = z * x$



The information would only be revealed if the secret would be the entire point, not just one coordinate.






share|improve this answer










New contributor




Ceriath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.


















  • And you can use the link I provided to make it more formal. as $r leq (t-1)$
    – kelalaka
    yesterday











Your Answer





StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");

StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "281"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});

function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});


}
});






Ceriath is a new contributor. Be nice, and check out our Code of Conduct.










draft saved

draft discarded


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fcrypto.stackexchange.com%2fquestions%2f66337%2fhow-is-blakleys-secret-sharing-scheme-perfect%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown

























1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









2














Okay so SEJPM's comment just gave me an answer or better made me realize my flaw:



Since the secret is only one coordinate (e.g. $x$) the information that the secret is on a specific infinite line is as much information as having none at all, since guessing $x$ of a point on $y = 5*x$ is worth as much as guessing $x$ of a point on $y = z * x$



The information would only be revealed if the secret would be the entire point, not just one coordinate.






share|improve this answer










New contributor




Ceriath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.


















  • And you can use the link I provided to make it more formal. as $r leq (t-1)$
    – kelalaka
    yesterday
















2














Okay so SEJPM's comment just gave me an answer or better made me realize my flaw:



Since the secret is only one coordinate (e.g. $x$) the information that the secret is on a specific infinite line is as much information as having none at all, since guessing $x$ of a point on $y = 5*x$ is worth as much as guessing $x$ of a point on $y = z * x$



The information would only be revealed if the secret would be the entire point, not just one coordinate.






share|improve this answer










New contributor




Ceriath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.


















  • And you can use the link I provided to make it more formal. as $r leq (t-1)$
    – kelalaka
    yesterday














2












2








2






Okay so SEJPM's comment just gave me an answer or better made me realize my flaw:



Since the secret is only one coordinate (e.g. $x$) the information that the secret is on a specific infinite line is as much information as having none at all, since guessing $x$ of a point on $y = 5*x$ is worth as much as guessing $x$ of a point on $y = z * x$



The information would only be revealed if the secret would be the entire point, not just one coordinate.






share|improve this answer










New contributor




Ceriath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









Okay so SEJPM's comment just gave me an answer or better made me realize my flaw:



Since the secret is only one coordinate (e.g. $x$) the information that the secret is on a specific infinite line is as much information as having none at all, since guessing $x$ of a point on $y = 5*x$ is worth as much as guessing $x$ of a point on $y = z * x$



The information would only be revealed if the secret would be the entire point, not just one coordinate.







share|improve this answer










New contributor




Ceriath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|improve this answer



share|improve this answer








edited yesterday









kelalaka

5,97022041




5,97022041






New contributor




Ceriath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









answered yesterday









CeriathCeriath

314




314




New contributor




Ceriath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Ceriath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Ceriath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.












  • And you can use the link I provided to make it more formal. as $r leq (t-1)$
    – kelalaka
    yesterday


















  • And you can use the link I provided to make it more formal. as $r leq (t-1)$
    – kelalaka
    yesterday
















And you can use the link I provided to make it more formal. as $r leq (t-1)$
– kelalaka
yesterday




And you can use the link I provided to make it more formal. as $r leq (t-1)$
– kelalaka
yesterday










Ceriath is a new contributor. Be nice, and check out our Code of Conduct.










draft saved

draft discarded


















Ceriath is a new contributor. Be nice, and check out our Code of Conduct.













Ceriath is a new contributor. Be nice, and check out our Code of Conduct.












Ceriath is a new contributor. Be nice, and check out our Code of Conduct.
















Thanks for contributing an answer to Cryptography Stack Exchange!


  • Please be sure to answer the question. Provide details and share your research!

But avoid …



  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.


Use MathJax to format equations. MathJax reference.


To learn more, see our tips on writing great answers.





Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


Please pay close attention to the following guidance:


  • Please be sure to answer the question. Provide details and share your research!

But avoid …



  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fcrypto.stackexchange.com%2fquestions%2f66337%2fhow-is-blakleys-secret-sharing-scheme-perfect%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







-

Popular posts from this blog

An IMO inspired problem

Image
14 4 This problem from IMO 1988 is said to be one of the most elegant ones in functional equations. Problem : The function $f$ is defined on the set of all positive integers as follows: begin{align} f(1) = 1, f(3) &= 3, f(2n) = f(n), \ f(4n+1) &= 2f(2n+1) - f(n), \ f(4n+3) &= 3 f(2n+1) - 2f(n) end{align} Find the number of $n$ with $f(n) = n, 1 leq n leq 1988$. The main idea towards the solution is realizing that these conditions stand for the fact that $f(n)$ just reverses the digits in the binary representation of the number $n$. So, essentially the solution is finding the number of binary pallindromes $leq 1988_{10}$. My question is the following : How to reformulate the problem so that $f(n)$ reverses the digits of $n$ in its ternary representation. Or even better, can we reformulate it for a
Read more

Management

Image
Management From Wikipedia, the free encyclopedia Jump to navigation Jump to search "Manager" redirects here. For other uses, see Management (disambiguation) and Manager (disambiguation). An organization chart for the United States Coast Guard shows the hierarchy of managerial roles in that organization. Business administration Management of a business Accounting Management accounting Financial accounting Financial audit Business entities Cooperative Corporation Limited liability company Partnership Sole proprietorship State-owned enterprise Corporate governance Annual general meeting Board of directors Supervisory board Advisory board Audit committee Corporate law Commercial law Constitutional documents Contract Corporate crime Corporate liability Insolvency law International trade law Mergers and acquisitions Economics Commodity Pu
Read more

Has there ever been an instance of an active nuclear power plant within or near a war zone?

Image
36 3 The question Has there ever been a military combat going on around an active (running or in outage but not decommissioned) commercial nuclear power plant? Or dangerously near it? If yes, how did the plant and its personnel fare in such situation? Why I ask Let's assume for the scope of this question modern commercial nuclear power plants (CANDU, PWR, BWR of generation II plus all of gen III and newer) are usually reasonably safe to operate given that the engineering has been done right and there is a whole cohort of very well trained personnel on-site at all times, well rested and with considerable resources on their hands. Things hard to get with an armed conflict like the recent Syrian war raging around. I can't seem to find any reference or a comprehensive article about this, hence this question.
Read more