A new post-quantum multivariate polynomial public key encapsulation algorithm

Kuang, Randy; Perepechaenko, Maria; Barbeau, Michel

doi:10.1007/s11128-022-03712-5

Cited by 18 publications

(24 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These algorithms can be used for authentication and key establishment. Moreover, novel PQC algorithms such as MPPK/DS and MPPK can be used to pre-share a secret key k [31,32].…”

Section: Initial Set Up Proceduresmentioning

confidence: 99%

Quantum encryption of superposition states with quantum permutation pad in IBM quantum computers

Perepechaenko

Kuang

2023

EPJ Quantum Technol.

Self Cite

View full text Add to dashboard Cite

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 quantum 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.

show abstract

“…These algorithms can be used for authentication and key establishment. Moreover, novel PQC algorithms such as MPPK/DS and MPPK can be used to pre-share a secret key k [31,32].…”

Section: Initial Set Up Proceduresmentioning

confidence: 99%

Quantum encryption of superposition states with quantum permutation pad in IBM quantum computers

Perepechaenko

Kuang

2023

EPJ Quantum Technol.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In MPPK/DS 1 , the security parameters are the generalized safe prime , with and an odd prime q , a positive integer n , representing the order of message variable in the base multivariate polynomial , and a positive integer representing the order of univariate polynomials and . Variable is associated with the secret, while variables represent noise.…”

Section: Mppk/ds Optimizationmentioning

confidence: 99%

“…Kuang, Perepechaenko, and Barbeau recently proposed a novel post-quantum cryptographic algorithm for key encapsulation based on multivariate polynomial multiplication for the key construction and division for the secret extraction 1 . This mechanism is called Multivariate Polynomial Public Key or MPPK.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimization of the multivariate polynomial public key for quantum safe digital signature

Kuang¹,

Perepechaenko²

2023

Sci Rep

Self Cite

View full text Add to dashboard Cite

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. These polynomials are then used to produce two multivariate product polynomials, while excluding the constant term and highest order term with respect to the message variable. The excluded terms are used to create two noise functions. Then four produced polynomials, masked with two randomly chosen even numbers over the ring, form the Public Key. The two univariate polynomials and two randomly chosen numbers, behaving as an encryption key to obscure public polynomials, form the Private Key. The verification equation is derived from multiplying all of the original polynomials together. MPPK/DS uses a special safe prime to prevent private key recovery attacks over the ring, forcing adversaries to solve for private values over a sub-prime field and lift the solutions to the original ring. Lifting entire solutions from the sub-prime field to the ring is designed to be difficult based on security requirements. This paper intends to optimize MPPK/DS to reduce the signature size by a fifth. We added extra two private elements to further increase the complexity of the private key recovery attack. However, we show in our newly identified optimal attack that these extra private elements do not have any effect on the complexity of the private recovery attack due to the intrinsic feature of MPPK/DS. The optimal key-recovery attack reduces to a Modular Diophantine Equation Problem or MDEP with more than one unknown variables for a single equation. MDEP is a well-known NP-complete problem, producing a set with many equally-likely solutions, so the attacker would have to make a decision to choose the correct solution from the entire list. By purposely choosing the field size and the order of the univariate polynomials, we can achieve the desired security level. We also identified a new deterministic attack on the coefficients of two univariate private polynomials using intercepted signatures, which forms a overdetermined set of homogeneous cubic equations. To the best of our knowledge, the solution to such a problem is to brute force search all unknown variables and verify the obtained solutions. With those optimizations, MPPK/DS can offer extra security of 384 bit entropy at 128 bit field with a public key size being 256 bytes and signature size 128 or 256 bytes using SHA256 or SHA512 as the hash function respectively.

show abstract

“…These algorithms can be used for authentication and key establishment. Moreover, novel PQC algorithms such as MPPK/DS and MPPK can be used to pre-share a secret key k [29,30].…”

Section: Initial Set Up Proceduresmentioning

confidence: 99%

Quantum Encryption of superposition states with Quantum Permutation Pad in IBM Quantum Computers

Perepechaenko¹,

Kuang²

2023

Preprint

View full text Add to dashboard Cite

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 quantum 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.

show abstract

A new post-quantum multivariate polynomial public key encapsulation algorithm

Cited by 18 publications

References 43 publications

Quantum encryption of superposition states with quantum permutation pad in IBM quantum computers

Quantum encryption of superposition states with quantum permutation pad in IBM quantum computers

Optimization of the multivariate polynomial public key for quantum safe digital signature

Quantum Encryption of superposition states with Quantum Permutation Pad in IBM Quantum Computers

Contact Info

Product

Resources

About