Elliptic Curve Authentication for Low Complexity Devices
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Solution Overview
Problem
Existing cryptographic mechanisms, such as the RSA Public Key Cryptosystem, are not suitable for low complexity devices like RFID tags and smart cards due to their limited processing power and memory, making it difficult to authenticate products in supply chains effectively.
Innovation Solution
Implementing Elliptic Curve Cryptography within a well-defined elliptic curve E over a finite field F, which reduces the computational requirements and logic gates needed for authentication, allowing for zero-knowledge proof systems that can be used in limited processing power applications like RFID tags and smart cards.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If RSA Public Key Cryptosystem is used for authentication, then security is improved, but device complexity and processing requirements increase
Solution Approach 1:
The patent changes the cryptographic parameters from RSA to Elliptic Curve Cryptography (ECC), specifically using secp256k1 curve parameters. This parameter change maintains security equivalence while reducing computational complexity and memory requirements, making it suitable for low-complexity devices like RFID tags and smart cards.
Solution Approach 2:
The patent extracts and implements only the essential authentication functionality using ECC, removing the heavy computational overhead of RSA. By using pre-defined curves and optimized arithmetic operations, it extracts the core security function while eliminating unnecessary complexity for devices with limited processing power.
2Reliability
If RSA Public Key Cryptosystem is used for authentication, then security is improved, but memory requirements increase
Solution Approach 1:
The patent changes cryptographic parameters from RSA to ECC, which requires smaller key sizes for equivalent security. The use of secp256k1 curve with 256-bit keys reduces memory requirements compared to RSA keys that would require 2048 bits or more for comparable security levels.
3Reliability
If challenge-response authentication is implemented in low complexity devices, then authentication capability is improved, but computational complexity increases
Solution Approach 1:
The patent changes the computational parameters by using ECC operations instead of RSA operations. The challenge-response mechanism uses elliptic curve point multiplication and verification, which require fewer computational steps and less processing power while maintaining the same authentication capability.
Data Source
AI summary
A method and apparatus to authenticate limited processing-power systems (LPPS) using elliptic cryptography within a well known elliptic curve E, over a well known finite field F ((E(F)). The apparatus comprises a random number generator to choose a random value b, of a similar order of magnitude to the order of E(F). The apparatus further comprises a challenge calculator to calculate a value C=bP and send the challenge to the LPPS, where P is a point on the elliptic curve E(F) which was used as a basis for generating a private key, a, for the LPPS. The apparatus further comprising an RFID reader to receive a challenge response, R=aC=abP from the LPPS, and a crypto calculator to calculate bQ, based on a public key, Q, of the LPPS. The apparatus further comprising a comparison logic to authenticate the LPPS if bQ=aC=abP.