Quantum-safe Encryption: A New Method to Reduce Complexity and/or Improve Security Level

TL;DR

The paper addresses secure key encapsulation in the post-quantum era by combining masking and memory-enabled, repetition-code–based error mechanisms to enlarge key entropy while keeping decoding trivial. It introduces a two-party randomness framework (Alice and Bob) where public keys are masked and columns can be privately discarded, with recovery guaranteed by a carefully structured matrix construction that preserves decodability. Key contributions include: (i) masking via random matrices to hide the underlying code, (ii) memory in the error sequence to raise attack complexity, (iii) concatenation of repetition codes of length 3 for negligible decoding cost, (iv) a two-layer verification that complicates key-validation attacks, and (v) a framework to compute security level and direct key-entropy, yielding significantly larger keys at lower computational cost compared to certain post-quantum baselines. Together, these ideas propose a scalable, quantum-resistant PKI primitive with practical key sizes and favorable resource usage, suitable for public-key infrastructure in a post-quantum world.

Abstract

This work presents some novel techniques to enhance an encryption scheme motivated by classical McEliece cryptosystem. Contributions include: (1) using masking matrices to hide sensitive data, (2) allowing both legitimate parties to incorporate randomness in the public key without sharing any additional public information, (3) using concatenation of a repetition code for error correction, permitting key recovery with a negligible decoding complexity, (4) making attacks more difficult by increasing the complexity in verifying a given key candidate has resulted in the actual key, (5) introducing memory in the error sequence such that: (i) error vector is composed of a random number of erroneous bits, (ii) errors can be all corrected when used in conjunction with concatenation of a repetition code of length 3. Proposed techniques allow generating significantly larger keys, at the same time, with a much lower complexity, as compared to known post-quantum key generation techniques relying on randomization.

Figures (19)

• Figure 1: Matrix $\mathbf{A}$ composed of a unitary matrix in the upper left corner, and random rows and columns in $\mathbf{S}$, $\mathbf{R}$ and $\mathbf{Q}$ (used by Alice to recover the key).
• Figure 2: Structure of matrix $\mathbf{B}$ used in generating the public key.
• Figure 3: A decomposition of matrix $\mathbf{B}$.
• Figure 4: Structure of matrix $\mathbf{A}\mathbf{B}$ formed implicitly, as the first step in recovering the key, by Alice (also see Fig. \ref{['FNSet1']}).
• Figure 5: ${\mathbf P}={\mathbf B}{\mathbf G}$ is the public key, ${\mathbf e}$ is the error vector following state diagram in Fig. \ref{['FigS']}, ${\mathbf M}$ is the masking matrix and $\hat{\mathbf e}$ is the error vector capturing the effect of virtual errors due to ${\mathbf M}$. To add further confusion, Bob removes $\mathsf{p}$ randomly selected columns from ${\mathbf P}$ to generate $\hat{\mathbf P}$ which is then multiplied by a shortened data vector $\hat{\mathbf d}$ of length $\mathsf{d-p}$.

Theorems & Definitions (10)

• Theorem 1
• proof
• Theorem 2
• proof
• Theorem 3
• proof
• Theorem 4
• proof
• Theorem 5
• proof