A Note on Quantum Security for Post-Quantum Cryptography

S. Yu. Mikhnevich, P. I. Hladun

The process of selecting post-quantum cryptography algorithms for standardization based on parameters proposed by the National Institute of Standards and Technology (NIST) is described. The resistance of post-quantum cryptography algorithms to attacks by classical and quantum computers is assessed, taking into account their specific features. The different numbers of operations for attacks by quantum and classical computers are substantiated. The parallelization potential of post-quantum cryptography algorithms is analyzed. It is noted that, despite the proposed use of quantum computers, the primary goal of cryptography is the application of algorithms based on problems that are not reducible to problems of P-class complexity.

Syed Ismail Abdul Lathif, Priya Saxena, Priyanshi Singh

Sam Buxbaum, Mohammad Mahmoody

In classical cryptography, one-way functions (OWFs) play a central role as the minimal primitive that (almost) all primitives imply. The situation is more complicated in quantum cryptography, in which honest parties and adversaries can use quantum computation and communication, and it is known that analogues of OWFs in the quantum setting might not be minimal. In this work we ask whether OWFs are minimal for the intermediate setting of post-quantum cryptography, in which the protocols are classical while they shall resist quantum adversaries. We show that for a wide range of natural settings, if a primitive Q implies OWFs, then so does its (uniformly or non-uniformly secure) post-quantum analogue. In particular, we show that if a primitive Q implies any other primitive P that has a 2-message security game (e.g., OWFs) through a black-box classical security reduction R, then one can always (efficiently) turn any polynomial-size quantum adversary breaking P into a polynomial-size quantum adversary breaking Q. Note that this result holds even if the implementation of P using that of Q is arbitrarily non-black-box. We also prove extensions of this result for when the reduction R anticipates its oracle adversary to be deterministic, whenever either of the following conditions hold: (1) the adversary needs to win the security game of Q only with non-negligible probability (e.g., Q is collision-resistant hashing) or (2) that either of P and Q have “falsifiable” security games (this is the case when P is OWFs). Our work leaves open answering our main question when Q implies OWFs through a non-black-box security reduction, or when P uses a more complicated security game than a two-message one.

Seung Min Kim, Sung Hee Lim, So-Hee Kim +1 more

Quan Thoi Minh Nguyen

Post-quantum cryptography is inevitable. National Institute of Standards and Technology (NIST) starts standardizing quantum-resistant public-key cryptography (aka post-quantum cryptography). The reason is that investment in quantum computing is blooming which poses significant threats to our currently deployed cryptographic algorithms. As a security engineer, to prepare for the apocalypse in advance, I've been watching the development of quantum computers and post-quantum cryptography closely. Never mind, I simply made up an excuse to study these fascinating scientific fields. However, they are extremely hard to understand, at least to an amateur like me. This article shares with you my notes with the hope that you will have an intuitive understanding of the beautiful and mind-blowing quantum algorithms and post-quantum cryptography. Update: Multivariate signature scheme Rainbow is broken by Ward Beullens. Supersingular Isogeny Diffie-Hellman protocol (SIDH) is broken by Wouter Castryck and Thomas Decru