Quantum-Resistant Key Agreement and Key Encapsulation

We explore quantum-resistant key establishment and hybrid encryption. We
nd that while the discrete logarithm problem is e ciently solved by a quantum
computer using Shor's algorithm, some instances are insecure even using classical
computers. The discrete logarithm problem based on a symmetric group Sn is e -
ciently solved in polynomial time.
We design a PUF-based 4-round group key establishment protocol, adjusting
the model to include a physical channel capable of PUF transmission, and modify
adversarial capabilities with respect to the PUFs. The result is a novel group key establishment
protocol which avoids computational hardness assumptions and achieves
key secrecy.
We contribute a hybrid encryption scheme by combining a key encapsulation
mechanism (KEM) with a symmetric key encryption scheme by using two hash
functions. We require only one-way security in the quantum random oracle model
(QROM) of the KEM and one-time security of the symmetric encryption scheme in
the QROM. We show that this hybrid scheme is IND-CCA secure in the QROM.
We rely on a powerful theorem by Unruh that provides an upper bound on indistinguishability between the output of a random oracle and a random string, when
the oracle can be accessed in quantum superposition. Our result contributes to the
available IND-CCA secure encryption schemes in a setting where quantum computers
are under adversarial control.
Finally, we develop a framework and describe biometric visual cryptographic
schemes generically under our framework. We formalize several security notions and
de nitions including sheet indistinguishability, perfect indistinguishability, index recovery,
perfect index privacy, and perfect resistance against false authentication. We
also propose new and generic strategies for attacking e-BVC schemes such as new
distinguishing attack, new index recovery, and new authentication attack. Our quantitative
analysis veri es the practical impact of our framework and o ers concrete
upper bounds on the security of e-BVC.