CCA2-Secure Unidirectional Proxy Re-encryption from Cryptographic Group Actions

Proxy re-encryption (PRE) allows a semi-trusted party (called a proxy) to transform ciphertexts under one user's public key into ciphertexts under another user's public key, without revealing any information about the underlying messages or the secret keys. On the other hand, post-quantum cryptography (PQC) is one of the most active areas, and in particular, many lattice-based PRE schemes have been proposed so far in the area of PQC. However, there is no post-quantum PRE satisfying security against adaptive chosen ciphertext attacks ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="sans-serif">C</mml:mi> <mml:mi mathvariant="sans-serif">C</mml:mi> <mml:mi mathvariant="sans-serif">A</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> security), while <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="sans-serif">C</mml:mi> <mml:mi mathvariant="sans-serif">C</mml:mi> <mml:mi mathvariant="sans-serif">A</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> security is one of the most desirable security notions for PRE. In this paper, we propose a group-action-based PRE scheme that achieves <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="sans-serif">C</mml:mi> <mml:mi mathvariant="sans-serif">C</mml:mi> <mml:mi mathvariant="sans-serif">A</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> security for the first time. We give security proofs for our PRE in the random oracle model (ROM) and the quantum random oracle model (QROM). In particular, we can obtain the CSIDH-instantiation of this PRE scheme as the first post-quantum PRE. Our result contributes to the developments of post-quantum cryptography, and shows further potential of isogeny-based cryptography.