Secret Key Agreement Using Matrix Transcripts on Public Channels
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Solution Overview
Problem
Existing key agreement protocols in cryptography rely on unproven computational hardness assumptions, leading to potential security vulnerabilities and high computational complexity, and quantum key agreement requires additional infrastructure and is not suitable for long distances.
Innovation Solution
A system and method using multi-dimensional matrices and local random numbers to establish a secure communication agreement between initiating and responding units, ensuring confidentiality, integrity, and authenticity without revealing the secret key to unauthorized parties, based on proven computational hardness.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If proven secret key agreement is achieved using certain hardness assumptions (e.g., Diffie-Hellman, RSA, Elliptic curve cryptography), then security is improved, but computational complexity increases and security remains based on unproven assumptions
Solution Approach 1:
The patent replaces traditional cryptographic mechanisms (Diffie-Hellman exponentiation, RSA modular exponentiation, Elliptic curve point multiplication) with a fundamentally different approach based on polynomial ring arithmetic and secret sharing. Instead of relying on the hardness of discrete logarithm or integer factorization problems, the system uses algebraic operations in polynomial rings Zq[x]/(x^n-1) where security is derived from the hardness of solving specific algebraic equations, thereby substituting one computational hardness assumption with another that offers proven security guarantees under defined conditions
Solution Approach 2:
The patent changes the fundamental parameters and mathematical structures used in key agreement. Rather than working with large prime numbers and modular arithmetic (RSA) or elliptic curve points (ECC), the system uses polynomial coefficients in finite fields and operates in the ring Zq[x]/(x^n-1). This parameter transformation allows the system to achieve security based on different computational hardness assumptions that can be proven under specific conditions, reducing reliance on unproven conjectures
2Reliability
If unproven computational hardness assumptions are used (e.g., discrete logarithm problem, integer factorization), then key agreement is achieved, but security may be compromised if assumptions are false
Solution Approach 1:
The patent implements security cushioning by using information-theoretic security mechanisms and secret sharing protocols that provide guaranteed security bounds. The system uses polynomial secret sharing where the secret is divided into shares distributed among parties, and any subset of shares below a threshold provides no information about the secret. This beforehand cushioning ensures that even if computational assumptions are broken, the security guarantee remains intact through mathematical proofs of unconditional security for the secret sharing component
Solution Approach 2:
The patent introduces polynomial rings and secret sharing as intermediary mechanisms between the communicating parties. Instead of directly exchanging cryptographic keys based on unproven assumptions, the system uses polynomial evaluations and secret sharing protocols as intermediaries. These intermediaries provide a layer of proven security that mediates the key agreement process, allowing the system to achieve security guarantees that are not dependent solely on unproven computational hardness assumptions
Data Source
AI summary
A system and method for establishing a secure communication agreement between an initiating unit 102 and a responding unit 104 through a channel 106 are provided. The method includes generating, using first set of local random numbers, multi-dimensional matrices by an initiating unit. The method includes computing a transcript by the initiating unit based on multi-dimensional matrices and communicating to the responding unit. The method includes determining response by selecting a subset of the transcript to communicate response to the initiating unit. The method includes iteratively generating, communicating a subsequent transcript and waiting for a subsequent response from the responding unit for one or more times. The method includes computing a secret key as a function of the first set of local random numbers, the second set of local numbers, the subsequent transcripts, the subsequent responses at each iteration, and the indices of the selected subset J.