# Traceability code[1]

## Description

An IPP code with which it is possible to detect a parent of a given pirated descendent by finding the closest codeword to that descendant.

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 [1]). A code with weak traceability has the ability to ensure that no group is able to frame another user [2].

## Rate

Suppose \(n\) is the number of users, \(k\) is the number of users known by the pirates, and \(p\) is the probability that the pirates cannot be traced. An open (public) resilient scheme using a hash function has the personal keys of the users consisting of \(O(k^{2}\log n)\) decryption keys, which is the amount of decryptions needed to reveal the information. The amount of data redundancy overhead is about \(O(k^{4}\log n)\) [1].

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 \(O(k^{2} \log(n/p))\) [1].

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, a large improvement compared to the above [1].

## Realizations

## Notes

## Parent

- Identifiable parent property (IPP) code — Traceability codes allow for detection of parents of pirated descendant copies by only determining the closest codeword to the descendant; see [2; Lemma 1.3].

## Cousin

- Galois-field \(q\)-ary code — A \(q\)-ary code with distance \(d \geq n(1-1/t^2)\) has the \(t\)-traceability property [2; Thm. 4.3].

## References

## Page edit log

- Raley Roberts (2024-03-15) — most recent
- Victor V. Albert (2024-03-15)

## Cite as:

“Traceability code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/traceability