Post-Quantum Decryption Using Randomized Polynomial Segmentation
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Solution Overview
Problem
Existing post-quantum cryptographic algorithms are vulnerable to side channel attacks, and the current methods to protect against these attacks significantly increase implementation time and complexity.
Innovation Solution
A method for decrypting secrets encrypted by an asymmetric cryptographic key encapsulation mechanism using Quasi-Cyclic Moderate-Density Parity-Check corrector codes, which involves generating random integers and applying specific operations to sparse polynomials to form a modified private key, thereby decrypting the syndrome polynomial and deducing the shared secret.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If masking techniques are applied to each elementary operation to protect against side channel attacks, then security against side channel attacks is improved, but implementation time increases significantly (15 to 30 times longer)
Solution Approach 1:
The decryption process is segmented into five distinct operations (O1-O5) applied to different polynomials (h1, h2, S, e1, e2). Each operation uses random integers to modify the representation of intermediate values, isolating side channel leakage to individual operations rather than exposing the entire computation chain to attacks.
Solution Approach 2:
Random integers serve as intermediaries that transform the representation of polynomials during computation. These random values act as masks that prevent direct observation of secret-dependent intermediate values, while still allowing the cryptographic computation to proceed correctly through the structured operations.
2Reliability
If masking techniques are applied to protect against side channel attacks, then security is improved, but the complexity of the decryption process increases
Solution Approach 1:
The complex decryption process is divided into five manageable operations, each with a specific function and input/output. This segmentation makes the overall complex process more controllable and easier to implement securely, as each operation can be independently analyzed and protected.
Solution Approach 2:
The patent changes the parameters of the polynomial representations by introducing random integers that modify the exponents and coefficients. This parameter transformation approach maintains the mathematical structure needed for decryption while obscuring the actual secret values from side channel observers.
3Productivity
If standard decryption methods are used, then implementation is simpler and faster, but the system becomes vulnerable to side channel attacks
Solution Approach 1:
The patent applies preliminary protective actions by introducing randomizing operations before the actual decryption computation. Operations O1-O3 modify the representation of input polynomials (h1, h2, S) using random integers, preventing side channel attacks from directly observing the secret-dependent computation in its vulnerable standard form.
Solution Approach 2:
The decryption process becomes dynamic by incorporating random integers that change the representation of polynomials during computation. This dynamic transformation allows the system to adapt its computational path based on random values, making side channel analysis significantly more difficult while maintaining decryption functionality.
Data Source
AI summary
The present invention relates to a method for decrypting a secret encrypted by a QC-MDPC mechanism, the decryption method being implemented by the receiver (14) and comprising the reception of a syndrome polynomial derived from the secret, the generation of random integers, the application of respective operations on the first and second sparse polynomials of the private key, the application of a third operation on the syndrome polynomial, the search for modified error polynomials such as the linear combination of modified error polynomials gives the modified syndrome polynomial, and the deduction of the shared secret by application of a respective operation on the first and second modified error polynomials, the five operations depending on the generated random integers and keeping the weight of the polynomial on which the operation is applied.