Paper 2023/256 Original: eprint.iacr.org/2023/256 ↗

Traitor Tracing with N^(1/3)-size Ciphertexts and O(1)-size Keys from k-Lin

Abstract

We present a pairing-based traitor tracing scheme for $N$ users with$$ |\mathsf{pk}| = |\mathsf{ct}| = O(N^{1/3}), \quad |\mathsf{sk}| = O(1). $$This is the first pairing-based scheme to achieve ${|\mathsf{pk}|\cdot|\mathsf{sk}|\cdot|\mathsf{ct}|=o(N)}$. Our construction relies on the (bilateral) $k$-Lin assumption, and achieves private tracing and full collusion resistance. Our result simultaneously improves upon the sizes of $\mathsf{pk},\mathsf{ct}$ in Boneh–Sahai–Waters [Eurocrypt '06] and the size of $\mathsf{sk}$ in Zhandry [Crypto '20], while further eliminating the reliance on the generic group model in the latter work.