Isogeny-Based Key Distribution for Quantum-Resistant Multicast
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Solution Overview
Problem
The existing dynamic multicast key distribution (DMKD) protocols are not quantum-resistant, particularly due to their reliance on Diffie-Hellman key exchange, which may not guarantee security with the advent of quantum computers, and proposed quantum-resistant methods using key encapsulation mechanisms incur additional communication costs.
Innovation Solution
A key distribution system employing isogeny cryptography between terminal devices, utilizing an isogeny calculating unit to calculate public values based on torsion subgroups of elliptic curves, and a distributing unit to share these values among terminal devices via a key distribution server, enabling a quantum-resistant multi-party key exchange with reduced communication rounds.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a key encapsulation mechanism is used to achieve quantum-resistant key distribution, then security against quantum computers is improved, but communication cost increases due to requiring an extra communication round
Solution Approach 1:
The patent changes the cryptographic parameter from traditional Diffie-Hellman or key encapsulation mechanisms to isogeny-based cryptography. This parameter change enables quantum resistance while reducing communication rounds to 2, resolving the contradiction between security and communication cost.
Solution Approach 2:
The patent substitutes the cryptographic mechanism from classical algebraic problems (Diffie-Hellman) or key encapsulation to isogeny-based mathematical problems. This substitution achieves quantum resistance without the communication overhead of key encapsulation mechanisms.
2Loss of time
If the Diffie-Hellman key exchange is used in DMKD protocol, then communication cost is reduced, but quantum security is compromised
Solution Approach 1:
The patent changes the cryptographic parameter from Diffie-Hellman to isogeny-based cryptography, maintaining efficient communication while achieving quantum security. The isogeny-based key exchange requires only 2 communication rounds and provides resistance against quantum computer attacks.
Solution Approach 2:
The patent substitutes the Diffie-Hellman key exchange mechanism with an isogeny-based key exchange mechanism. This substitution replaces the classical mathematical foundation with one that is quantum-resistant, achieving both low communication cost and quantum security.
3Reliability
If isogeny cryptography is used for multi-party key exchange, then quantum resistance is achieved with low communication cost, but system complexity increases due to torsion subgroup calculations
Solution Approach 1:
The patent segments the key exchange process into distinct phases: setup phase (generating public parameters including torsion subgroups), key exchange phase (computing isogenies and sharing public values), and key derivation phase (computing the shared session key). This segmentation manages complexity by organizing operations into manageable, reusable components.
Solution Approach 2:
The patent performs preliminary actions by pre-computing and publishing public parameters including torsion subgroups and their bases before the actual key exchange. This preliminary setup reduces the computational complexity during the key exchange phase, as participants can reuse these pre-computed values.
Data Source
AI summary
With respect to a key distribution system including N terminal devices Ui and a key distribution server used for exchanging a session key, the key distribution system includes an isogeny calculating unit configured to calculate a first public value using a basis of a first torsion subgroup of a predetermined elliptic curve at an odd-numbered terminal device Ui and calculate a second public value using a basis of a second torsion subgroup of the predetermined elliptic curve at an even-numbered terminal device Ui, when N is an even number, a distributing unit configured to distribute the first public value calculated at the odd-numbered terminal device Ui to a terminal device Ui−1 and a terminal device Ui+1, and distribute the second public value calculated at the even-numbered terminal device Ui to a terminal device Ui−1 and a terminal device Ui+1, from the key distribution server, a key generating unit configured to use second public values distributed by the distributing unit to generate the session key at the odd-numbered terminal device Ui, and use first public values distributed by the distributing unit to generate the session key at the even-numbered terminal device Ui, wherein the isogeny calculating unit calculates the first public value using the basis of the first torsion subgroup and the second public value using the basis of the second torsion subgroup at a predetermined terminal device UI among the terminal devices Ui, when N is an odd number.