Post-Quantum Verification of Fujisaki-Okamoto

Ehsan Ebrahimi, Dominique Unruh

Attila Pereszlényi

Tsuchiya Yui, Toi Tomita, Junji Shikata

Lewis Glabush, Kathrin Hövelmanns, Douglas Stebila

Practical deployments of key encapsulation mechanisms (KEMs) may entail large servers each using their public keys to communicate with potentially millions of clients simultaneously. While the standard IND-CCA security definition for KEMs considers only a single challenge public key and single challenge ciphertext, it can be relevant to consider multi-target scenarios where the adversary aims to break one of many challenge ciphertexts, for one of many challenge public keys. Many post-quantum KEMs have been built by applying the Fujisaki-Okamoto (FO) transform to a public key encryption (PKE) scheme. Although the FO transform incurs only a few bits of security loss for the standard, single-challenge IND-CCA property, this does not hold in the multi-target setting. Attacks have been identified against standards-track FO-based KEMs with 128-bit message spaces (FrodoKEM-640 and HQC-128) which become feasible if the adversary is given many challenge ciphertexts (say, 2^64). These attacks exploit the deterministic encryption induced by the FO transform which allows the IND-CCA experiment to be reduced to a search problem on the message space, which in some cases may not be large enough to avoid collisions between pre-computation and challenge values. A cost effective way to amplify the hardness of this search problem is to add a random but public salt during encapsulation. While revised versions of FrodoKEM and HQC have used salts, there has been no proof showing that salting provides multi-ciphertext security. In this work, we formally analyze a salted variant of the Fujisaki-Okamoto transform, in the classical and quantum random oracle model (ROM); for the classical ROM, we show that multi-target IND-CCA security of the resulting KEM tightly reduces to the multi-target IND-CPA security of the underlying PKE. Our results imply that, for FrodoKEM and HQC at the 128-bit security level, replacing the FO transform with the salted variant can recover 62 bits of multi-target security, at the cost of a very small overhead increase.

Craig S. Lent

Yang Lu, Jiguo Li, Junmo Xiao

The Fujisaki-Okamoto (FO) conversion is a generic conversion to enhance a public key encryption scheme with security of one-way against chosen plaintext attacks (OW-CPA) to security of indistinguishable against adaptive chosen ciphertext attacks (IND-CCA) in the random oracle model. Existing works have shown that the FO conversion also can generically upgrade the security of the identity-based encryption (IBE) schemes or certificateless public key encryption (CL-PKE) schemes. However, it is still unknown if the same holds for certificate-based encryption (CBE) schemes. In this paper, we investigate the generic security of the CBE scheme obtained by applying the FO conversion to an arbitrary underlying OW-CBE-CPA secure CBE scheme and confirm that the FO conversion can generically convert any OW-CBE-CPA secure CBE into an IND-CBE-CCA secure CBE. We also note that the straightforward application of the FO conversion only leads to a CBE scheme with a loose reduction. To solve this problem, we propose an enhanced FO conversion which just introduces minor extra computation overhead, but results in considerably more efficient security reduction.