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The cryptography that protects our privacy and security online relies on the fact that even the strongest computers will take essentially forever to do certain tasks, like factoring prime numbers and finding discrete logarithms which are important for RSA encryption , Diffie-Hellman key exchanges , and elliptic curve encryption. But what happens when those problems – and the cryptography they underpin – are no longer infeasible for computers to solve? Will our online defenses collapse? Not if Deirdre Connolly can help it. As a cutting-edge thinker in post-quantum cryptography, Connolly is making sure that the next giant leap forward in computing – quantum machines that use principles of subatomic mechanics to ignore some constraints of classical mathematics and solve complex problems much faster – don’t reduce our digital walls to rubble. Connolly joins EFF’s Cindy Cohn and Jason Kelley to discuss not only how post-quantum cryptography can shore up those existing walls but also help us find entirely new methods of protecting our information.   In this episode you’ll learn about:   Why we’re not yet sure exactly what quantum computing can do yet, and that’s exactly why we need to think about post-quantum cryptography now   What a “Harvest Now, Decrypt Later” attack is, and what’s happening today to defend against it How cryptographic collaboration, competition, and community are key to exploring a variety of paths to post-quantum resilience Why preparing for post-quantum cryptography is and isn’t like fixing the Y2K bug H ow the best impact that end users can hope for from post-quantum cryptography is no visible impact at all Don’t worry—you won’t have to know, or learn, any math for this episode!   Deidre Connolly is a research and applied cryptographer at Sandbox AQ with particular expertise in post-quantum encryption. She also co-hosts the “ Security Cryptography Whatever ” podcast about modern computer security and cryptography, with a focus on engineering and real-world experiences. Earlier, she was an engineer at the Zcash Foundation – a nonprofit that builds financial privacy infrastructure for the public good – as well as at Brightcove , Akamai , and HubSpot .  

We propose a general method for studying properties of quantum channels acting on an n-partite system, whose action is invariant under permutations of the subsystems. Our main result is that, in order to prove that a certain property holds for any arbitrary input, it is sufficient to consider the special case where the input is a particular de Finetti-type state, i.e., a state which consists of n identical and independent copies of an (unknown) state on a single subsystem. A similar statement holds for more general channels which are covariant with respect to the action of an arbitrary finite or locally compact group. Our technique can be applied to the analysis of information-theoretic problems. For example, in quantum cryptography, we get a simple proof for the fact that security of a discrete-variable quantum key distribution protocol against collective attacks implies security of the protocol against the most general attacks. The resulting security bounds are tighter than previously known bounds obtained by proofs relying on the exponential de Finetti theorem [Renner, Nature Physics 3,645(2007)].

Description: Abstract The rapid evolution of cyber threats, coupled with the advent of quantum computing, necessitates a fundamental rethinking of web security architectures. This dissertation introduces Darkelf Browser, a pioneering high-security web browser explicitly designed for users operating in high-threat environments such as investigative journalists, political dissidents, security researchers, and penetration testers. Traditional browsers, even those emphasizing privacy like Tor, are increasingly vulnerable to sophisticated attacks, forensic recovery, and quantum cryptographic breaking. Darkelf integrates lattice-based post-quantum cryptography—specifically, Kyber768 and Kyber1024 algorithms—into core communication protocols to ensure resilience against quantum adversaries. Its architecture emphasizes ephemeral memory-resident session keys, preventing forensic recovery of session data. The browser employs a supervised machine learning pipeline utilizing the RandomForestClassifier to detect malicious JavaScript in real time, safeguarding users from drive-by malware and script-based exploits. Complementing cryptography and threat detection are robust anti-forensic strategies, including encrypted RAM logs, runtime detection of debugging and forensic tools, disabling system swap files, and storing cryptographic keys exclusively in volatile memory (e.g., TPM hardware or in-memory regions). These features collectively create a hardened, stealthy, and adaptive browser framework. This work critically compares Darkelf's capabilities with legacy anonymity systems like Tor, emphasizing improvements in quantum resilience, forensic resistance, and usability in high-risk contexts. Ethical considerations surrounding dual-use technologies are discussed, and the entire project is released under an LGPL license, promoting transparency and responsible deployment. License: GNU Lesser General Public License (LGPL) 3.0

Perma.cc archive of https://csrc.nist.gov/Projects/post-quantum-cryptography/faqs created on 2022-02-26 21:38:27.285513+00:00.

Summary: An NIST guide is published aimed at IT and Security professionals Series: Privacy and Security Source: https://hackerpublicradio.org/eps/hpr4014/index.html In May of 2023 a guide was published by NIST that aimed to guide IT Professionals and Security Officers on steps to take as we move into a world where Quantum computing has made traditional cryptography and security measures obsolete. This is their take on a best practices manual, and if you are in security or are an IT professional it merits a good look. And it is only 4 pages long, so you can do it easily. Links: https://www.nccoe.nist.gov/sites/default/files/2023-04/pqc-migration-nist-sp-1800-38a-preliminary-draft.pdf

Summary: An NIST guide is published aimed at IT and Security professionals Series: Privacy and Security Source: https://hackerpublicradio.org/eps/hpr4014/index.html In May of 2023 a guide was published by NIST that aimed to guide IT Professionals and Security Officers on steps to take as we move into a world where Quantum computing has made traditional cryptography and security measures obsolete. This is their take on a best practices manual, and if you are in security or are an IT professional it merits a good look. And it is only 4 pages long, so you can do it easily. Links: https://www.nccoe.nist.gov/sites/default/files/2023-04/pqc-migration-nist-sp-1800-38a-preliminary-draft.pdf

A collection of papers written on the PQC finalists Dilithium and Falcon

Quantum computing promises unprecedented computational power but poses a grave threat to today’s encryption schemes. This chapter explains the nature of that threat, the urgency of transitioning to post‑quantum cryptography (PQC), and the global efforts underway to secure our digital future. It analyzes vulnerabilities in classical systems (RSA, ECC), surveys leading PQC approaches including lattice‑based (CRYSTALS‑Kyber, Dilithium), multivariate (Rainbow, GeMSS), code‑ and hash‑based, and isogeny‑based constructions and examines real‑world applications in blockchain, secure communications, IoT, and government adoption, highlighting implementation challenges and future research directions.

Quantum computing promises unprecedented computational power but poses a grave threat to today’s encryption schemes. This chapter explains the nature of that threat, the urgency of transitioning to post‑quantum cryptography (PQC), and the global efforts underway to secure our digital future. It analyzes vulnerabilities in classical systems (RSA, ECC), surveys leading PQC approaches including lattice‑based (CRYSTALS‑Kyber, Dilithium), multivariate (Rainbow, GeMSS), code‑ and hash‑based, and isogeny‑based constructions and examines real‑world applications in blockchain, secure communications, IoT, and government adoption, highlighting implementation challenges and future research directions.

Quantum computing promises unprecedented computational power but poses a grave threat to today’s encryption schemes. This chapter explains the nature of that threat, the urgency of transitioning to post‑quantum cryptography (PQC), and the global efforts underway to secure our digital future. It analyzes vulnerabilities in classical systems (RSA, ECC), surveys leading PQC approaches including lattice‑based (CRYSTALS‑Kyber, Dilithium), multivariate (Rainbow, GeMSS), code‑ and hash‑based, and isogeny‑based constructions and examines real‑world applications in blockchain, secure communications, IoT, and government adoption, highlighting implementation challenges and future research directions.

There are countless post-quantum buzzwords to list: lattices, codes, multivariate polynomial systems, supersingular elliptic curve isogenies. We cannot possibly explain in one hour what each of those mean, but we will do our best to give the audience an idea about why elliptic curves and isogenies are awesome for building strong cryptosystems. It is the year 2019 and apparently quantum supremacy is finally upon us [1,2]. Surely, classical cryptography is broken? How are we going to protect our personal communication from eagerly snooping governments now? And more importantly, who will make sure my online banking stays secure? The obvious sarcasm aside, we should strive for secure post-quantum cryptography in case push comes to shove. Post-quantum cryptography is currently divided into several factions. On the one side there are the lattice- and code-based system loyalists. Other groups hope that multivariate polynomials will be the answer to all of our prayers. And finally, somewhere over there we have elliptic curve isogeny cryptography. Unfortunately, these fancy terms "supersingular", "elliptic curve", "isogeny" are bound to sound magical to the untrained ear. Our goal is to shed some light on this proposed type of post-quantum cryptography and bring basic understanding of these mythical isogenies to the masses. We will explain how elliptic curve isogenies work and how to build secure key exchange and signature algorithms from them. We aim for our explanations to be understandable by a broad audience without previous knowledge of the subject. [1] https://www.quantamagazine.org/john-preskill-explains-quantum-supremacy-20191002/ [2] https://www.nature.com/articles/d41586-019-02936-3 Source: https://media.ccc.de/v/36c3-10543-post-quantum_isogeny_cryptography Uploader: tubeup.py

By resorting to basic features of topological knot theory we propose a (classical) cryptographic protocol based on the `difficulty' of decomposing complex knots generated as connected sums of prime knots and their mutants. The scheme combines an asymmetric public key protocol with symmetric private ones and is intrinsecally secure against quantum eavesdropper attacks.

Perma.cc archive of https://csrc.nist.gov/projects/post-quantum-cryptography created on 2021-12-28 18:29:56+00:00.

Shor's quantum factoring algorithm and a few other efficient quantum algorithms break many classical crypto-systems. In response, people proposed post-quantum cryptography based on computational problems that are believed hard even for quantum computers. However, security of these schemes against \emph{quantum} attacks is elusive. This is because existing security analysis (almost) only deals with classical attackers and arguing security in the presence of quantum adversaries is challenging due to unique quantum features such as no-cloning. This work proposes a general framework to study which classical security proofs can be restored in the quantum setting. Basically, we split a security proof into (a sequence of) classical security reductions, and investigate what security reductions are "quantum-friendly". We characterize sufficient conditions such that a classical reduction can be "lifted" to the quantum setting. We then apply our lifting theorems to post-quantum signature schemes. We are able to show that the classical generic construction of hash-tree based signatures from one-way functions and and a more efficient variant proposed in~\cite{BDH11} carry over to the quantum setting. Namely, assuming existence of (classical) one-way functions that are resistant to efficient quantum inversion algorithms, there exists a quantum-secure signature scheme. We note that the scheme in~\cite{BDH11} is a promising (post-quantum) candidate to be implemented in practice and our result further justifies it. Finally we demonstrate the generality of our framework by showing that several existing works (Full-Domain hash in the quantum random-oracle model~\cite{Zha12ibe} and the simple hybrid arguments framework in~\cite{HSS11}) can be reformulated under our unified framework.

Perma.cc archive of https://www.muckrock.com/foi/united-states-of-america-10/nsa-nist-and-post-quantum-cryptography-126349/ created on 2022-04-09 14:57:37.319719+00:00.

Perma.cc archive of https://csrc.nist.gov/projects/post-quantum-cryptography/selected-algorithms-2022 created on 2022-07-07 16:08:57.157699+00:00.

We introduce the concept of cryptographic reduction, in analogy with a similar concept in computational complexity theory. In this framework, class $A$ of crypto-protocols reduces to protocol class $B$ in a scenario $X$, if for every instance $a$ of $A$, there is an instance $b$ of $B$ and a secure transformation $X$ that reproduces $a$ given $b$, such that the security of $b$ guarantees the security of $a$. Here we employ this reductive framework to study the relationship between security in quantum key distribution (QKD) and quantum secure direct communication (QSDC). We show that replacing the streaming of independent qubits in a QKD scheme by block encoding and transmission (permuting the order of particles block by block) of qubits, we can construct a QSDC scheme. This forms the basis for the \textit{block reduction} from a QSDC class of protocols to a QKD class of protocols, whereby if the latter is secure, then so is the former. Conversely, given a secure QSDC protocol, we can of course construct a secure QKD scheme by transmitting a random key as the direct message. Then the QKD class of protocols is secure, assuming the security of the QSDC class which it is built from. We refer to this method of deduction of security for this class of QKD protocols, as \textit{key reduction}. Finally, we propose an orthogonal-state-based deterministic key distribution (KD) protocol which is secure in some local post-quantum theories. Its security arises neither from geographic splitting of a code state nor from Heisenberg uncertainty, but from post-measurement disturbance.

We consider the distinguishability of Gaussian states from the view point of continuous-variable quantum cryptography using post-selection. Specifically, we use the probability of error to distinguish between two pure coherent (squeezed) states and two particular mixed symmetric coherent (squeezed) states where each mixed state is an incoherent mixture of two pure coherent (squeezed) states with equal and opposite displacements in the conjugate quadrature. We show that the two mixed symmetric Gaussian states (where the various components have the same real part) never give an eavesdropper more information than the two pure Gaussian states. Furthermore, when considering the distinguishability of squeezed states, we show that varying the amount of squeezing leads to a "squeezing" and "anti-squeezing" of the net information rates.

Perma.cc archive of https://csrc.nist.gov/projects/post-quantum-cryptography created on 2022-02-03 12:40:01.990253+00:00.

Perma.cc archive of https://csrc.nist.gov/Projects/post-quantum-cryptography/faqs created on 2022-04-04 20:41:41.399539+00:00.

Perma.cc archive of https://csrc.nist.gov/projects/post-quantum-cryptography/ created on 2022-04-04 20:32:13.273737+00:00.

Quantum Thursday conference 2020

Perma.cc archive of https://en.wikipedia.org/wiki/Post-quantum_cryptography created on 2022-01-20 22:31:11.904457+00:00.

Perma.cc archive of https://csrc.nist.gov/projects/post-quantum-cryptography created on 2022-02-16 02:23:00.803720+00:00.

Here we show that, if we insert context dependent unitary evolutions (which can be achieved via post selection) into spatial (i.e., normal) Bell-CHSH test, then it is possible to violate space-time Bell-CHSH inequality maximally (i.e., up to $4$). However this does not contradict Tsirelson quantum bound ($2\sqrt{2}$), as the latter has been derived without taking into consideration context dependent unitary evolutions and/or post selection. As an important application, this leads to a more efficient quantum key distribution protocol.

We derive a bound for the security of QKD with finite resources under one-way post-processing, based on a definition of security that is composable and has an operational meaning. While our proof relies on the assumption of collective attacks, unconditional security follows immediately for standard protocols like Bennett-Brassard 1984 and six-states. For single-qubit implementations of such protocols, we find that the secret key rate becomes positive when at least N\sim 10^5 signals are exchanged and processed. For any other discrete-variable protocol, unconditional security can be obtained using the exponential de Finetti theorem, but the additional overhead leads to very pessimistic estimates.

We derive a bound for the security of QKD with finite resources under one-way post-processing, based on a definition of security that is composable and has an operational meaning. While our proof relies on the assumption of collective attacks, unconditional security follows immediately for standard protocols like Bennett-Brassard 1984 and six-states. For single-qubit implementations of such protocols, we find that the secret key rate becomes positive when at least N\sim 10^5 signals are exchanged and processed. For any other discrete-variable protocol, unconditional security can be obtained using the exponential de Finetti theorem, but the additional overhead leads to very pessimistic estimates.

Currently there is an active Post-Quantum Cryptography (PQC) solutions search, which attempts to find cryptographic protocols resistant to attacks by means of for instance Shor’s polynomial time algorithm for numerical field problems like integer factorization (IFP) or the discrete logarithm (DLP). The use of non-commutative or non-associative structures are, among others, valid choices for these kinds of protocols. In our case, we focus on a permutation subgroup of high order and belonging to the symmetric group S381. Using adequate one-way functions (OWF), we derived a Diffie-Hellman key exchange and an ElGamal ciphering procedure that only relies on combinatorial operations. Both OWF pose hard search problems which are assumed as not belonging to BQP time-complexity class. Obvious advantages of present protocols are their conceptual simplicity, fast throughput implementations, high cryptanalytic security and no need for arithmetic operations and therefore extended precision libraries. Such features make them suitable for low performance and low power consumption platforms like smart cards, USB-keys and cellphones.

Currently there is an active Post-Quantum Cryptography (PQC) solutions search, which attempts to find cryptographic protocols resistant to attacks by means of for instance Shor’s polynomial time algorithm for numerical field problems like integer factorization (IFP) or the discrete logarithm (DLP). The use of non-commutative or non-associative structures are, among others, valid choices for these kinds of protocols. In our case, we focus on a permutation subgroup of high order and belonging to the symmetric group S381. Using adequate one-way functions (OWF), we derived a Diffie-Hellman key exchange and an ElGamal ciphering procedure that only relies on combinatorial operations. Both OWF pose hard search problems which are assumed as not belonging to BQP time-complexity class. Obvious advantages of present protocols are their conceptual simplicity, fast throughput implementations, high cryptanalytic security and no need for arithmetic operations and therefore extended precision libraries. Such features make them suitable for low performance and low power consumption platforms like smart cards, USB-keys and cellphones.