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from-0-to-crypto-by-projects/episode-2-proof-demonstration/index.html

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 A secure hash algorithm is an hash algorithm so that for any function hash that transform the original (plaintext) value $ hased = H(plain) $ there does not exist a function $ rev(hashed) $ so that $ rev(hashed) = plain $.
-1 - Analysis under mathematical thinking The reverse engineering of the hash of vigenere cisco has permitted to deduct the method taken by this algorithm."><meta itemprop=datePublished content="2024-10-13T01:25:30+02:00"><meta itemprop=dateModified content="2024-10-13T01:25:30+02:00"><meta itemprop=wordCount content="185"><meta itemprop=image content="https://gogo2464.github.io/gogo-s-blog-cpe/"><meta name=twitter:card content="summary_large_image"><meta name=twitter:image content="https://gogo2464.github.io/gogo-s-blog-cpe/"><meta name=twitter:title content="Episode 2: Reversing cryptography algorithm made to be unreversables (checksum). Method by mathematical proof: disproof"><meta name=twitter:description content="I - Identify According to the documentation and as it is mentionned that type 7 is an hashing algorithm.
+1 - Analysis under mathematical thinking The reverse engineering of the hash of vigenere cisco has permitted to deduct the method taken by this algorithm."><meta itemprop=datePublished content="2024-10-13T01:25:30+02:00"><meta itemprop=dateModified content="2024-10-13T01:25:30+02:00"><meta itemprop=wordCount content="182"><meta itemprop=image content="https://gogo2464.github.io/gogo-s-blog-cpe/"><meta name=twitter:card content="summary_large_image"><meta name=twitter:image content="https://gogo2464.github.io/gogo-s-blog-cpe/"><meta name=twitter:title content="Episode 2: Reversing cryptography algorithm made to be unreversables (checksum). Method by mathematical proof: disproof"><meta name=twitter:description content="I - Identify According to the documentation and as it is mentionned that type 7 is an hashing algorithm.
 A secure hash algorithm is an hash algorithm so that for any function hash that transform the original (plaintext) value $ hased = H(plain) $ there does not exist a function $ rev(hashed) $ so that $ rev(hashed) = plain $.
 1 - Analysis under mathematical thinking The reverse engineering of the hash of vigenere cisco has permitted to deduct the method taken by this algorithm."><meta property="article:published_time" content="2024-10-13 01:25:30 +0200 +0200"><link rel=stylesheet href=https://cdn.jsdelivr.net/npm/[email protected]/dist/katex.min.css integrity=sha384-nB0miv6/jRmo5UMMR1wu3Gz6NLsoTkbqJghGIsx//Rlm+ZU03BU6SQNC66uf4l5+ crossorigin=anonymous><script defer src=https://cdn.jsdelivr.net/npm/[email protected]/dist/katex.min.js integrity=sha384-7zkQWkzuo3B5mTepMUcHkMB5jZaolc2xDwL6VFqjFALcbeS9Ggm/Yr2r3Dy4lfFg crossorigin=anonymous></script><script defer src=https://cdn.jsdelivr.net/npm/[email protected]/dist/contrib/auto-render.min.js integrity=sha384-43gviWU0YVjaDtb/GhzOouOXtZMP/7XUzwPTstBeZFe/+rCMvRwr4yROQP43s0Xk crossorigin=anonymous onload='renderMathInElement(document.body,{delimiters:[{left:"$$",right:"$$",display:!0},{left:"\\[",right:"\\]",display:!0},{left:"$",right:"$",display:!1},{left:"\\(",right:"\\)",display:!1}]})'></script></head><body><script defer src=https://cdn.jsdelivr.net/npm/[email protected]/dist/katex.min.js></script><script defer src=https://cdn.jsdelivr.net/npm/[email protected]/dist/contrib/auto-render.min.js onload=renderMathInElement(document.body)></script><div class=container><header class=header><span class=header__inner><a href=/gogo-s-blog-cpe style=text-decoration:none><div class=logo><span class=logo__mark>></span>
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-</span><span class="theme-toggle not-selectable"><svg class="theme-toggler" width="24" height="24" viewBox="0 0 48 48" fill="none"><path d="M22 41c10.4934.0 19-8.5066 19-19C41 11.5066 32.4934 3 22 3 11.5066 3 3 11.5066 3 22s8.5066 19 19 19zM7 22C7 13.7157 13.7157 7 22 7V37C13.7157 37 7 30.2843 7 22z"/></svg></span></span></span></header><div class=content><main class=post><div class=post-info></p></div><article><h2 class=post-title><a href=https://gogo2464.github.io/gogo-s-blog-cpe/from-0-to-crypto-by-projects/episode-2-proof-demonstration/>Episode 2: Reversing cryptography algorithm made to be unreversables (checksum). Method by mathematical proof: disproof</a></h2><div class=post-content><h2 id=i---identify>I - Identify</h2><p>According to the documentation and as it is mentionned that type 7 is an hashing algorithm.</p><p>A secure hash algorithm is an hash algorithm so that for any function hash that transform the original (plaintext) value $ hased = H(plain) $ there does not exist a function $ rev(hashed) $ so that $ rev(hashed) = plain $.</p><h2 id=1---analysis-under-mathematical-thinking>1 - Analysis under mathematical thinking</h2><p>The reverse engineering of the hash of vigenere cisco has permitted to deduct the method taken by this algorithm.</p><p>We could then guess that the researchers thanks then that:</p><p><img alt=image src=/gogo-s-blog-cpe/from-0-to-crypto-by-projects/episode-2-proof-demonstration/theory-behind-type7-hash.png></p><p>The question is to proove that there exists a function $ rev(hashed) $ so that $ \forall plain [rev(H(plain)) = plain] $ then $ \forall x [x = H(plain)]$</p><p>We intuitevely see points to split the issue into easier pieces:</p><ul><li>the algorithm threat data block by blocks with blocks of two opcodes (numbers between 0 and 256) knowns bigram.</li></ul><p>The algorith treat bigrams as following:</p><ul><li>the two opcodes are both xored to the hardcoded password.</li></ul><p>We now have the mathematical proof (demonstration) that the algorithm is vulnerable:</p><p><a href=/gogo-s-blog-cpe/from-0-to-crypto-by-projects/episode-2-proof-demonstration/latex-reverse-type7.pdf>Download the pdf</a></p></div></article><hr><div class=post-info></div></main></div><footer class=footer><div class=footer__inner><ul class=icons><li><a href=https://gogo2464.github.io/gogo-s-blog-cpe/posts/index.xml target=_blank title=rss class="icon fa-solid fa-rss"></a></li></ul></div><div class=footer__inner><span>&copy;2024</span>&nbsp;
+</span><span class="theme-toggle not-selectable"><svg class="theme-toggler" width="24" height="24" viewBox="0 0 48 48" fill="none"><path d="M22 41c10.4934.0 19-8.5066 19-19C41 11.5066 32.4934 3 22 3 11.5066 3 3 11.5066 3 22s8.5066 19 19 19zM7 22C7 13.7157 13.7157 7 22 7V37C13.7157 37 7 30.2843 7 22z"/></svg></span></span></span></header><div class=content><main class=post><div class=post-info></p></div><article><h2 class=post-title><a href=https://gogo2464.github.io/gogo-s-blog-cpe/from-0-to-crypto-by-projects/episode-2-proof-demonstration/>Episode 2: Reversing cryptography algorithm made to be unreversables (checksum). Method by mathematical proof: disproof</a></h2><div class=post-content><h2 id=i---identify>I - Identify</h2><p>According to the documentation and as it is mentionned that type 7 is an hashing algorithm.</p><p>A secure hash algorithm is an hash algorithm so that for any function hash that transform the original (plaintext) value $ hased = H(plain) $ there does not exist a function $ rev(hashed) $ so that $ rev(hashed) = plain $.</p><h2 id=1---analysis-under-mathematical-thinking>1 - Analysis under mathematical thinking</h2><p>The reverse engineering of the hash of vigenere cisco has permitted to deduct the method taken by this algorithm.</p><p>We could then guess that the researchers thanks then that:</p><p><img alt=image src=/gogo-s-blog-cpe/from-0-to-crypto-by-projects/episode-2-proof-demonstration/theory-behind-type7-hash.png></p><p>The question is to proove that there exists a function $ rev(hashed) $ so that $ \forall plain [rev(H(plain)) = plain] $ then $ \forall x [x = H(plain)]$</p><p>We intuitevely see points to split the issue into easier pieces:</p><ul><li>the algorithm threat data block by blocks with blocks of two opcodes (numbers between 0 and 256) knowns bigram.</li></ul><p>The algorith treat bigrams as following:</p><ul><li>the two opcodes are both xored to the hardcoded password.</li></ul><p>We now have the mathematical proof (demonstration) that the algorithm is vulnerable:</p><p><img alt=pdf src=/gogo-s-blog-cpe/from-0-to-crypto-by-projects/episode-2-proof-demonstration/latex-reverse-type7.pdf></p></div></article><hr><div class=post-info></div></main></div><footer class=footer><div class=footer__inner><ul class=icons><li><a href=https://gogo2464.github.io/gogo-s-blog-cpe/posts/index.xml target=_blank title=rss class="icon fa-solid fa-rss"></a></li></ul></div><div class=footer__inner><span>&copy;2024</span>&nbsp;
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