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codes/classical/properties/block/copyright/frameproof.yml

@@ -13,18 +13,18 @@ introduced: '\cite{doi:10.1007/3-540-44750-4_36,doi:10.1109/18.705568}'
 description: |
   A block code designed to prevent a group of users from being able to collude to frame another user outside of the group for creating an unauthorized copy of data.
   Even further, the group of users cannot frame a separate user even if they know the unique codeword of the separate user \cite{doi:10.1007/3-540-44750-4_36}.
-  Frameproof codes help to provide software protection from the illegal distribution and copying of computer software and copyrighted materials. These codes help protect products of distributors as well as other naive users from being framed of illegal activity \cite{doi:10.1007/3-540-44750-4_36}.
+  Frameproof codes help to provide software protection from the illegal distribution and copying of computer software and copyrighted materials. These codes help protect products of distributors as well as other naive users from being framed for illegal activity \cite{doi:10.1007/3-540-44750-4_36}.
 
   Separating codes are equivalent to codes with the secure frameproof property. A \(c\)\textit{-separating} code has the property that, for any two disjoint sets that each contain at most \(c\) code words, there is at least one position where the set of symbols of each set are disjoint \cite{doi:10.1007/s10623-021-00988-z}.
 
   Let us define \(\Gamma = \{w^{(1)}, \dots, w^{(n)}\} \subseteq \{(0,1)\}^{l}\) as an ( \(l,n\) )-code.
   Each codeword \(w^{(i)}\) correlates to a user \(u_i\).
   Let \(C\) be a group of users.
   A bit in position \(i\) is undetectable for the group \(C\) when the words assigned to the users in the group match at the the same position \(i\).
-  The feasible set of the group \(C\), denoted \(F(C;\Gamma)\) or \(F(C)\), for some user \(u \in C\) contains all of the codewords that match the groups set of undetectable bits.
+  The feasible set of the group \(C\), denoted \(F(C;\Gamma)\) or \(F(C)\), for some user \(u \in C\) contains all of the codewords that match the group's set of undetectable bits.
   Finally, if every subset \(S \subset \Gamma\) of size at most \(c\) satisfies \(F(S)\cap\Gamma = S\), then \(\Gamma\) is a \(c\)\textit{-frameproof} code \cite{doi:10.1007/3-540-44750-4_36}.
 
-  Any \(c\)-frameproof code must have at least length \(c\) \cite{doi:10.1007/3-540-44750-4_36}.
+  Any \(c\)-frameproof code must be of length at least \(c\) \cite{doi:10.1007/3-540-44750-4_36}.
   A length-\(l\) \(q\)-ary \(c\)-frameproof code has at most \(tq^{\lceil l/c \rceil} + O(q^{\lceil l/c \rceil - 1})\) codewords, where \(t\) is an integer between \(1\) and \(c\), and \(t \equiv 1\) modulo \(c\) \cite{doi:10.1137/S0895480101384633}.
 
 
@@ -44,7 +44,7 @@ relations:
   cousins:
     - code_id: traceability
       detail: 'Frameproof codes fingerprint digital data and also they help prevent copyrighted information from unauthorized use \cite{arXiv:1411.5782}.
-      Codes with traceability also deter users from unauthorized copying or sharing of digital materials by being able to trace source of leaks, which also helps to ensure that an innocent user is not framed for the unauthorized activity \cite{doi:10.1109/18.841169}.'
+      Codes with traceability also deter users from unauthorized copying or sharing of digital materials by being able to trace sources of leaks, which also helps to ensure that an innocent user is not framed for the unauthorized activity \cite{doi:10.1109/18.841169}.'
     - code_id: evaluation
       detail: 'Asymptotic bounds on frameproof codes can be formulated using evaluation AG codes \cite{doi:10.1109/TIT.2002.804111,arXiv:1010.5764}.
       A sufficient condition for an evaluation AG code to be frameproof can be recast as an instance of the Riemann-Roch equation \cite[Sec. 15.8.2]{doi:10.1201/9781315147901}.'

codes/classical/properties/block/copyright/traceability.yml

@@ -6,16 +6,14 @@
 
 code_id: traceability
 
-name: 'Traceability Codes'
+name: 'Traceability code'
 introduced: '\cite{doi:10.1109/18.841169}'
 
 description: |
-  A code that protects materials that have be copyrighted by providing the ability to trace potential leaks via combinatorial properties \cite{doi:10.1109/18.841169}.
+  A code that protects copyrighted materials by providing the ability to trace potential leaks via combinatorial properties \cite{doi:10.1109/18.841169}.
   The code also aids in helping to ensure that an innocent party cannot be framed for the pirated information \cite{doi:10.1109/18.915661}.
-  Having this ability will help to identify and disable pirates \cite{doi:10.1109/18.841169}.
 
-  Codes with strong traceability traces at least one member of a group that has constructed a pirate decoder \cite{doi:10.1109/18.915661}.
-  A pirate decoder is a generic pirate decryption process \cite{doi:10.1109/18.841169}.
+  Codes with strong traceability trace at least one member of a group that has constructed a pirate decoder (i.e., a generic pirate decryption process \cite{doi:10.1109/18.841169}).
   A code with weak traceability has the ability to ensure that no group is able to frame another user \cite{doi:10.1109/18.915661}.
 
 
@@ -28,8 +26,8 @@ features:
     A secret resilient scheme using a hash function has the personal keys of the users consisting of \(O(k \log(n/p))\) decryption keys, which is the amount of decryptions needed to reveal the information.
     The amount of data redundancy overhead is about \(O(k^{2} \log(n/p))\) \cite{doi:10.1109/18.841169}.
 
-    A threshold (secret) scheme using a hash function that is successful against pirates which decrypt with probability \(> q\), has the personal keys of the users consisting of \((4k/3q)\log(n/p)\) decryption keys (note that this is the same as in the secret resilient schreme above).
-    These types of schemes only need order \(O(1)\) decryption operation performed by users to decrypt the information successfully.
+    A threshold (secret) scheme using a hash function that is successful against pirates which decrypt with probability \(> q\), has the personal keys of the users consisting of \((4k/3q)\log(n/p)\) decryption keys (note that this is the same as in the secret resilient scheme above).
+    These types of schemes only need order \(O(1)\) decryption operations performed by users to decrypt the information successfully.
     Finally, the amount of data redundancy overhead is 4k encrypted keys which is a large improvement compared to the above \cite{doi:10.1109/18.841169}.
 
   decoders: