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**2019/636**

**Title:**

Broadcast and Trace with N^epsilon Ciphertext Size from Standard Assumptions

**Authors:**
Rishab Goyal, Willy Quach, Brent Waters, Daniel Wichs

**Abstract:**

We construct a broadcast and trace scheme (also known as trace and revoke or broadcast, trace and revoke) with N users, where the ciphertext size can be made as low as O(N^\epsilon), for any arbitrarily small constant \epsilon>0. This improves on the prior best construction of broadcast and trace under standard assumptions by Boneh and Waters (CCS `06), which had ciphertext size $O(N^{1/2})$. While that construction relied on bilinear maps, ours uses a combination of the learning with errors (LWE) assumption and bilinear maps. Recall that, in both broadcast encryption and traitor-tracing schemes, there is a collection of $N$ users, each of which gets a different secret key $\textrm{sk}_i$. In broadcast encryption, it is possible to create ciphertexts targeted to a subset $S \subseteq [N]$ of the users such that only those users can decrypt it correctly. In a traitor tracing scheme, if a subset of users gets together and creates a decoder box $D$ that is capable of decrypting ciphertexts, then it is possible to trace at least one of the users responsible for creating $D$. A broadcast and trace scheme intertwines the two properties, in a way that results in more than just their union. In particular, it ensures that if a decoder $D$ is able to decrypt ciphertexts targeted toward a set $S$ of users, then it should be possible to trace one of the users in the set $S$ responsible for creating $D$, even if other users outside of $S$ also participated. As of recently, we have essentially optimal broadcast encryption (Boneh, Gentry, Waters CRYPTO `

05) under bilinear maps and traitor tracing (Goyal, Koppula, Waters STOC `18) under LWE, where the ciphertext size is at most poly-logarithmic in N. The main contribution of our paper is to carefully combine LWE and bilinear-map based components, and get them to interact with each other, to achieve broadcast and trace.

**ePrint:**
https://eprint.iacr.org/2019/636

**Talk: **https://www.youtube.com/watch?v=g8uQqHx_H1o

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