High Memory Masked Convolutional Codes Enable Scalable, Secure Post-quantum Cryptography with Linear-time Decryption

The increasing threat to current encryption methods drives the search for post-quantum cryptography, and a new approach utilising masked convolutional codes offers a significant step forward in securing communications against future attacks. Meir Ariel from Tel Aviv University, along with colleagues, presents a system that overcomes limitations of traditional code-based cryptography by offering both enhanced security and adaptability to messages of any length. This construction achieves a substantial improvement in cryptographic strength, exceeding the security margins of the well-established McEliece system by a factor greater than 2100, through the injection of greater randomness and the use of transformations that conceal the underlying code structure. The method also enables efficient decryption using parallel processing, positioning it as a viable candidate for practical, future-proof public-key cryptosystems.

Masked Convolutional Codes Resist Quantum Attacks

This work introduces a novel post-quantum cryptographic scheme based on high-memory masked convolutional codes, delivering enhanced security and flexibility compared to traditional code-based methods. The system efficiently encrypts messages of any length with linear-time decryption and a consistent computational cost per bit, enabling seamless scalability. Security is reinforced by injecting a high rate of random errors and introducing noise through polynomial division, effectively obscuring the underlying code structure and resisting known structural attacks. The method employs semi-invertible transformations to generate dense, random-like generator matrices, concealing algebraic properties and making the code statistically indistinguishable from a random code.

Consequently, the scheme achieves cryptanalytic security margins exceeding those of the classic McEliece system by factors greater than 2100. During decryption, the recipient processes quotients derived from masking polynomials, resulting in multiple possible values for each quotient. Determining the correct value requires further processing, creating a set of candidate solutions. These candidates are then processed simultaneously using an array of parallel Viterbi decoders. The most likely plaintext is identified by selecting the decoder that yields the codeword with the minimum Hamming weight, revealing the transformed plaintext with an appended Cyclic Redundancy Check (CRC).

The system reverses a transformation induced by a matrix to recover the original plaintext, discarding the CRC bits if the process is successful. If the initial attempt fails, the process iterates with the next most likely candidate until a valid plaintext is identified or all candidates are exhausted. The structure of the code ensures the Viterbi decoder returns the most likely information sequence. The public key remains a full-rank generator matrix through random column permutation, a nonsingular transformation, and dense masking with a low-rank matrix, effectively defeating structural attacks.

High-Memory Codes Enhance Cryptographic Security

This research presents a new post-quantum cryptosystem built upon high-memory masked convolutional codes, offering both enhanced security and greater flexibility compared to existing code-based schemes. The system supports encryption of messages of any length with efficient decryption, achieved through parallel processing, and maintains a consistent computational cost per bit. Security stems from injecting a substantial amount of randomness and introducing noise via polynomial division, effectively concealing the underlying code structure and resisting known structural attacks. The construction utilizes semi-invertible transformations to generate generator matrices that obscure algebraic properties, making the code statistically indistinguishable from a random code.

Consequently, the scheme demonstrably exceeds the security margins of the classic McEliece system by a significant factor, exceeding 2100. The design incorporates strong error-correction capabilities within the convolutional code, mitigating the risk of error propagation during decryption. Careful selection of polynomials limits the spread of errors, even at relatively high error rates, further bolstering its robustness. The system acknowledges that polynomial divisions during decryption can introduce errors, and focuses on minimizing this risk through code design and parameter selection. Future work could explore optimizations to the polynomial selection process, potentially through simulation-based testing to identify parameters that further limit error propagation. This research establishes a promising new direction in post-quantum cryptography, offering a viable candidate for secure public-key cryptosystems in the future.