Group Signature Mechanism Reducing Computational Complexity
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Solution Overview
Problem
Existing group signature mechanisms are complex and resource-intensive, making them unsuitable for low-power communication devices, particularly in the context of the Internet of Things (IoT), where they are needed for secure and anonymous authentication.
Innovation Solution
A new group signature mechanism that eliminates non-interactive proof of knowledge, reducing complexity and requiring only an interactive proof, which can be implemented using a modified certificate and masking process, resulting in significantly smaller signatures and reduced computational requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If standard group signature mechanisms are used, then security and anonymity are guaranteed, but computational complexity and resource consumption increase significantly
Solution Approach 1:
The patent extracts and removes the non-interactive proof of knowledge component from the group signature mechanism. By eliminating this complex cryptographic proof while retaining the essential anonymity and authentication functions through modified certificate structures, the patent reduces computational complexity without sacrificing security guarantees.
Solution Approach 2:
The patent modifies the certificate structure parameters by changing how the signer's secret is incorporated (raising to power u) and introducing new randomness elements (t). These parameter changes in the cryptographic construction enable the removal of the non-interactive proof while maintaining the mathematical properties required for security and anonymity.
2Reliability
If non-interactive proof of knowledge is included, then signature validity is strongly guaranteed, but signature size and computational cost increase
Solution Approach 1:
The patent removes the non-interactive proof of knowledge from the signature structure, directly reducing signature size. The interactive proof that remains during setup is sufficient to guarantee validity without requiring the additional non-interactive proof components in the final signature.
Solution Approach 2:
The patent performs the proof of knowledge verification in advance during the interactive setup phase between the signer and group manager. This preliminary action ensures signature validity is established before the signature is created, eliminating the need for redundant non-interactive proofs in the final signature structure.
3Reliability
If bilinear pairing operations are used, then cryptographic security is enhanced, but energy consumption and processing time increase
Solution Approach 1:
The patent changes the cryptographic operation parameters by modifying the certificate construction to use exponentiation operations instead of requiring bilinear pairings for signature verification. This parameter change in the mathematical operations reduces energy consumption while maintaining the security properties through the modified certificate structure with randomness masking.
Data Source
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AI summary
The invention relates to a cryptographic method for the signature of a message m by a user device (2-NO) on behalf of a group (G-U) managed by a group manager (3), which has a secret key generated from two variates x and y, said group having a public key formed from a plurality of elements comprising an element g and an element gz pertaining to a cyclic group G1 of order p, p being a whole prime number and z a variate, and an element h, an element hx, an element h1/z and an element hy/z pertaining to a cyclic group G2 of order p, said signature method comprising: a step of receiving, after having proved to the group manager knowledge of a secret u selected by the user device, a certificate C provided by the group manager, comprising an element S1=gr, an element S2= gr(x+y.u) and an element S3=gz.r where r is a variate selected by the group manager for said user device; and a step of generating a group signature for the message m, on the basis of the certificate provided by the group manager, a variate t generated by the user device, and the secret u, said generated group signature comprising an element T1=S1t, an element T2=(S2.S1u.m)t and an element T3= S3ut.