Homomorphic polynomial public key encapsulation over two hidden rings for quantum- safe key encapsulation
Abstract:
Kuang et al. recently introduced a novel quantum-safe public key scheme, called the multivariate Polynomial Public Key or MPPK. MPPK is based upon the mutual inversion relationship of multiplication and division, with the former used for key pair construction, and the latter used for decryption. For key pair construction, two solvable univariate polynomials are each multiplied by a base multivariate polynomial used for the purpose of noise injection.
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Abstract:
This paper presents the results of benchmarking the quantum-safe Multivariate Public Key Cryptosystem (MPPK) key encapsulation mechanism for quadratic solvable univariate polynomials. We used a benchmarking tool containing implementations of the four NIST Post-Quantum Cryptography (PQC) finalists: Kyber, McEliece, NTRU, and Saber. The benchmark demonstrates that the performance of MPPK is comparable with that of the four PQC algorithms, offering relatively fast key generation and small key sizes. Key encapsulation and decapsulation performance are comparable with the PQC schemes, with room for improvement.
Abstract:
Kuang, Perepechaenko, and Barbeau recently proposed a novel quantum-safe digital signature algorithm called Multivariate Polynomial Public Key or MPPK/DS. The key construction originated with two univariate polynomials and one base multivariate polynomial defined over a ring. The variable in the univariate polynomials represents a plain message. All but one variable in the multivariate polynomial refer to noise used to obscure private information.
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Abstract:
Kuang et al. introduced the new quantum-safe algorithm Multivariate Polynomial Public Key Digital Signature (MPPK DS). To create a signature, the MPPK DS scheme’s private key consists of univariate polynomials used as exponents of a secret randomly generated base. For signature verification, the verifier leverages public key multivariate polynomials and a modular arithmetic property.
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Abstract:
We propose a new quantum-safe cryptosystem called multivariate polynomial public key (MPPK). Its security stems from the hardness of finding integer solutions to multivariate equations over a prime field GF(p). Indeed, for a large prime p, solving modular Diophantine equations is an NP-complete problem.
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Abstract:
We propose a new quantum-safe digital signature algorithm called Multivariate Polynomial Public Key Digital Signature (MPPK/DS). The core of the algorithm is based on the modular arithmetic property that for a given element g, greater than equal to two, in a prime Galois field GF(p) and two multivariate polynomials P and Q, if P is equal to Q modulo p-1, then g to the power of P is equal to g to the power of Q modulo p.
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Indistinguishability and Non-deterministic Encryption of the Quantum Safe Multivariate Polynomial Public Key Cryptographic System
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Performance Analysis of the Quantum Safe Multivariate Polynomial Public Key Algorithm
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Abstract:
We present an implementation of Kuang and Bettenburg’s Quantum Permutation Pad (QPP) used to encrypt superposition states. The project was conducted on currently available IBM … Read Morequantum systems using the Qiskit development kit. This work extends previously reported implementation of QPP used to encrypt basis states and demonstrates that application of the QPP scheme is not limited to the encryption of basis states. For this implementation, a pad of 56 2-qubit Permutation matrices was used, providing 256 bits of entropy for the QPP algorithm. An image of a cat was used as the plaintext for this experiment. The plaintext was randomized using a classical XOR function prior to the state preparation procedure. To create corresponding superposition states, we applied a novel operator defined in this paper. These superposition states were then encrypted using QPP, with 2-qubit Permutation Operators, producing superposition ciphertext states. Due to the lack of a quantum channel, we omitted the transmission and executed the decryption procedure on the same IBM quantum system. If a quantum channel existed, the superposition ciphertext states could be transmitted as qubits, and be directly decrypted on a different quantum system. We provide a brief discussion of the security, although the focus of the paper remains on the implementation. Previously we have demonstrated QPP operating in both classical and quantum computers, offering an interesting opportunity to bridge the security gap between classical and quantum systems. This work broadens the applicability of QPP for the encryption of basis states as well as superposition states. We believe that quantum encryption schemes that are not limited to basis states will be integral to a secure quantum internet, to reduce vulnerabilities introduced by using two separate algorithms for secure communication between a quantum and a classical computer.
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Abstract:
We present a functioning implementation of Kuang et al.’s Quantum Permutation Pad (QPP) using the Qiskit developmental kit on the currently available International Business Machines (IBM) quantum computers. For this implementation, we use a pad with 28 2-qubit permutation gates that provides 128 bits of entropy. … Read More In this implementation, we divide the plaintext into blocks of 2-bits each. Each such block is encrypted one at a time. For any given block of plaintext, a quantum circuit is created with qubits initialized according to the given plaintext 2-bit block. The plaintext qubits are then acted on with 2-qubit permutation operators chosen from a 28- permutation QPP pad. Due to the inability to send qubits directly, the ciphertext qubits are measured and transmitted to the decrypting side over a classical channel. The decryption can be performed on either a classical or quantum computer. The decryption uses an inverse Quantum Permutation Pad with the Hermitian conjugates of the corresponding permutation gates used for the encryption. We are currently working on advancing the implementation of QPP to include additional steps for security and efficiency.
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Shannon Perfect Secrecy in a Discrete Hilbert Space
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Quantum secure lightweight cryptography with quantum permutation pad
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Quantum Safe Lightweight Cryptography with Quantum Permutation Pad
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Pseudo Quantum Random Number Generator with Quantum Permutation Pad
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Abstract:
In photonic computing, the quantum systems consist of coherent states and squeezed coherent states. Common quantum gates found in these systems are: phase shift, displacement, and squeezing gates. These gates are all unitary and reversible. Outside of quantum systems, coherent states also plays a significant role in coherent optical communications with speeds of hundreds of gigabits per second. … Read MoreSecure optical communications is generally implemented at the data layer with classical symmetric encryption such as Advanced Standard Encryption or AES. This inevitably allows any wiretapping to capture the transmitted data either in the plaintext mode or in the encrypted ciphertext mode in the optical infrastructure. The recent and rapid developments in Quantum computing further lift up the need for quantum secure communications in the optical infrastructure. This paper proposes a novel quantum encryption in the coherent optical domain utilizing a displacement operator and implementing with IQ-MZM optical modules, called Quantum Encryption in Phase Space or QEPS. The communication peers share a secret used to seed cryptographic pseudo random number generators to produce a synchronized random number at both the transmitter and receiver. The synchronized random numbers are used to establish displacement operators to encrypt the coherent states at the transmission and decrypt the cipher coherent states at the receiver. Therefore, malicious parties tapping along the fibre line would not extract the message in transit from optical domain due to a high Bit Error Rate or BER. The optimal displacement operator is split into a standard 16-QAM and a random phase shift operator to enhance the transmission security. We analysis the transmission security with the wiretap channel model for semantic security. We have simulated the QEPS encryption and decryption for two data modulation schemes: QPSK and 16-QAM over 80 km for transmission speeds of 56 Gbps for QPSK and 112 Gbps for 16-QAM.
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Quantum Public Key Distribution using Randomized Glauber States
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Security Performance of Public Key Distribution in Coherent Optical Communications Links
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Randy holds a doctorate in quantum physics. His research findings have been published in top international journals and named “Kuang’s semi-classical formalism” by NASA in 2012. With a career spanning IT, including with Nortel as senior network researcher & developer, he co-founded inBay Technologies in 2009, serving as CTO of the cybersecurity platform. As the first recipient of a patent for two-level authentication (2011), Randy is a prolific inventor, with 30+ U.S. patents in broad technology fields, such as WiMAX, optical networks, multi-factor identity authentication, transaction authorization, as well as concepts, technologies and industrial applications for quantum key distribution.
Cory brings a breadth of experience to the Quantropi team, working fractionally with multiple SaaS technology companies as CFO, and as the CFO with Celtic House Venture Partners. Prior to these roles, Cory was CFO and COO at Solink, and played a lead role in the metrics-led pivot to a direct-sales SaaS model, followed by multiple VC-backed funding rounds and their recognition as one of the fastest growing start-ups in Canada. He qualified as a CPA while serving technology, VC & PE-fund clients at Deloitte, and earned his Bachelor of Commerce at Queen’s University.
A seasoned technology executive, business builder and angel investor, Raj has held operational and advisory roles in Recognia (Trading Central), Belair Networks (Ericsson), March Networks (Infinova), Sandvine (Procera), Neurolanguage (ADEC), Bridgewater Systems (Amdocs), Vayyoo (Cafex), TenXc (CCI), 1Mobility (Qualys) and others. Having divided his time among North America, EMEA and Asia-Pac for over 20 years, Raj speaks several languages. He grew up in Asia, Europe, South America and Canada, and holds a B.Eng degree in Mechanical Engineering from the University of Ottawa. He is also a co-founder and Charter Member of the Ottawa chapter of TiE (the Indus Entrepreneur).
Before joining Quantropi, Mike was Managing Director and co-founder of Accenture Ventures, where he grew a global portfolio of strategic partnerships and 38 equity investments in emerging technology startups.
During his nearly 30 years with Accenture, he incubated and launched technology innovations for enterprises across multiple geographies and industries. Ever-passionate about bold ideas with game-changing results, he speaks frequently on the impact of emerging technology on large organizations.
With a bachelor’s degree in Electrical Engineering and Computer Science from Princeton, and a Master’s in Biomedical Engineering from Northwestern, Mike is a former member of the Board of Directors for the Accenture Foundation and Board Observer for startups Maana and Splice Machine.
Eric Chan a.k.a. EEPMON is a Crypto / Digital Artist with 15 years in the industry – and Quantropi’s Creative Emissary. His hybrid fractal/digital creations have been seen in fashion, comics to museums and has exhibited worldwide. EEPMON’s collaborations include Canada Goose, MARVEL, Snoopy, Microsoft Xbox, Canada Science & Technology Museum and was a TEDx performing artist. In 2018 he represented Canada on its first Creative Industries Trade Mission led by Canada’s Minister of Heritage and serves on the Canadian Museums Association‘s Board of Directors. At the same time, he is currently completing his Master of Information Technology – Digital Media at Carleton University.
Dat Nguyen has executive experience with top global consultancies such as IBM, Accenture, Ernst & Young (EY), and decacorn start-up Grab at C-Level roles.
During 20 years of consulting, Dat has worked with multiple companies across Canada, the USA, the Caribbean, and the Asia Pacific with CEO roles and leadership such as CEO for Accenture Vietnam, CEO of Grab Vietnam, and Partner of EY Consulting leading the technology practice (including Cybersecurity) in Indochina (Vietnam, Laos, Cambodia).
Dat is a tech entrepreneur, a co-founder, and a digital ecosystem builder. He is passionate about new and innovative technologies and is involved in multiple companies across verticals such as AI, Blockchain, Web3, Cybersecurity, InsurTech, and FinTech. Dat is currently a member of the ASIA CEO Club.
Dat earned the Executive Education at Harvard University, John F. Kennedy School, and received the Executive Certificate in Public Leadership in 2018.
Renato has 30 + years of experience as a trusted legal advisor and strategist. As an executive he has assisted numerous companies and their Boards of Directors to plot out and implement significant growth, diversification and reorganization plans in challenging circumstances. He was lead counsel on the sale of Zarlink Semiconductor’s $680 million dollar business as part of a takeover bid. At Zarlink he negotiated significant development, manufacturing, supply, distribution and IP licensing agreements with leading suppliers (eg Cisco, Nokia, Ericsson, Medtronic, Starkey, TSMC, Global Foundries, etc.). Renato has been involved in M&A, restructuring, financings and commercial contracts for dozens of companies. He also provides legal support in regards to intellectual property, securities, real estate leasing and employment law. He represents clients mostly in the SaaS, wireless, proptech, quantum, renewables, e-commerce, engineering and real estate conversion space.
James Nguyen is a Co-Founder and the CEO of Quantropi, a quantum-secure communications company established in 2018. Alongside Dr. Randy Kuang, he aims to uphold truth and trust in the digital economy on a global scale. In 2021, James was officially recognized as a recipient of Ottawa’s Top Forty Under 40 Award, and he holds a degree in Economics from Carleton University.
With a profound understanding of banking and global finance, James actively invests in and advises early-stage companies in the fields of Fintech, Graphene, and Quantum Technologies, particularly in emerging markets. Prior to his role at Quantropi, he served as the Chief Investment Officer and VP of Asia Operations for a diverse group of private and public interests involved in real estate, mining, energy storage, and manufacturing. In this capacity, he was responsible for strategy, banking, and global expansions, successfully securing substantial investments and partnerships to commercialize graphene applications across various industries.
James participates as a speaker and panelist at international conferences focused on quantum technology, cybersecurity, and investment. He also contributes to the community as a volunteer and mentor, leveraging his expertise and experiences to benefit others.