Cryptographic Signature Integrity via Spatial Redundancy
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
The Crystals-Dilithium encryption algorithm is vulnerable to Rowhammer attacks, which can leak sensitive private keys, and existing defense mechanisms like temporal redundancy introduce significant performance overhead.
Innovation Solution
Implementing spatial redundancy by generating and storing multiple copies of cryptographic secrets before signature generation and comparing them post-generation to detect any manipulation, reducing the likelihood of successful attacks while minimizing memory and performance overhead.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If temporal redundancy is used to defend against Rowhammer attacks by re-executing signature generation, then security against fault attacks is improved, but performance overhead increases by more than 100%
Solution Approach 1:
The patent creates redundant copies of cryptographic secrets (specifically the polynomial s1 and seed rho) and stores them in separate memory locations. Before signature generation, the system retrieves these secrets from multiple locations and verifies they match. This copying approach provides fault detection capability with minimal performance overhead compared to temporal redundancy, as it avoids re-executing the entire signature generation process.
2Reliability
If Verify-after-Sign is implemented to verify signature integrity, then fault tolerance against Rowhammer attacks is improved, but performance overhead increases by 30%
Solution Approach 1:
The patent performs verification of cryptographic secret integrity before the signature generation process begins. Specifically, it retrieves redundant copies of the secrets, compares them to ensure they match, and only proceeds with signature generation if verification succeeds. This preliminary action prevents faulty signatures from being generated in the first place, eliminating the need for post-generation verification and reducing overall performance overhead.
3Reliability
If multiple redundant copies of cryptographic secrets are stored in memory, then detection probability of Rowhammer attacks is improved, but memory overhead increases
Solution Approach 1:
The patent applies redundancy selectively to specific cryptographic secrets that are most vulnerable to Rowhammer attacks, namely the polynomial s1 and seed rho used in the Dilithium signing process. Rather than redundantly storing all cryptographic data, it focuses redundancy on these critical elements. The redundant copies are stored in physically separate memory locations to maximize protection against localized faults, balancing detection probability with memory overhead.
Data Source
AI summary
Various examples relate to an apparatus, device, method, and computer program for determining an integrity of a generated cryptographic signature. The apparatus is to generate, before generating the cryptographic signature, redundancy information of at least one cryptographic secret being used for generating the cryptographic signature, generate the cryptographic signature using the at least one cryptographic secret, compare, after generating the cryptographic signature, the redundancy information and the at least one cryptographic secret to determine whether the redundancy information matches the at least one cryptographic secret, and use the cryptographic signature if the redundancy information matches the at least one cryptographic secret.

