Elliptic Curve Scalar Conversion for Parallel Fixed-Base Comb
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing cryptographic algorithms, such as Elliptic Curve Digital Signature Algorithm (ECDSA) and Elliptic-Curve Diffie-Hellman (ECDH) signatures, face challenges in achieving fast and stable operations due to the need for variable-length scalar values during encryption processes, which complicates the use of the fixed-base comb method for parallel scalar multiplication.
Innovation Solution
The proposed solution involves determining a window size for parallel scalar multiplication, generating encryption keys using binary number-based value conversion methods like signed digit representation and scalar blinding to ensure the number of bits aligns with the window size, allowing for parallel scalar multiplication operations on elliptic curves.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If variable-length scalar values are used during encryption processes, then the encryption can accommodate different key lengths and maintain flexibility, but the fixed-base comb method cannot be directly applied for parallel scalar multiplication, reducing computational speed
Solution Approach 1:
The variable-length scalar value is segmented into multiple fixed-size segments (e.g., 4-bit or 8-bit windows) that can be processed in parallel. Each segment is handled as a separate entity, allowing the fixed-base comb method to operate on standardized units while maintaining support for variable overall key lengths.
Solution Approach 2:
The scalar value parameters are transformed by padding with leading zeros or adjusting the representation format to fit fixed window sizes. This parameter transformation enables the use of fixed-base comb methodology while preserving the original variable-length capability through controlled modification of the scalar representation.
2Adaptability or versatility
If the bit length of operand is changed to variable bit length to accommodate different encryption keys, then the encryption system becomes more versatile, but the parallel processing capability of fixed-base comb method is compromised
Solution Approach 1:
The operand is divided into fixed-size segments (windows) regardless of the total variable length. Each segment is processed independently in parallel using the fixed-base comb method, while the overall variable-length capability is maintained through the combination of these fixed segments.
Solution Approach 2:
The variable-length operand is pre-processed by padding or restructuring into fixed-size segments before applying the parallel fixed-base comb method. This preliminary transformation enables efficient parallel processing while preserving the ability to handle variable-length inputs through the initial preparation step.
3Speed
If fixed-base comb method is used for parallel scalar multiplication, then the encryption operation speed increases, but the operand must be converted to fixed bit length, adding preprocessing complexity
Solution Approach 1:
The scalar value parameters are transformed by padding with leading zeros or adjusting the representation format to fit fixed window sizes. This parameter transformation enables the use of fixed-base comb methodology while preserving the original variable-length capability through controlled modification of the scalar representation.
Data Source
AI summary
An elliptic curve encryption method includes determining a window size indicating a number of groups for performing scalar multiplication in parallel, generating, based on a first encryption key, a second encryption key, the generating the second encryption key including changing a value of the first encryption key, the first encryption key being a random number, generating a third encryption key based on the second encryption key, the generating the third encryption key including changing a total number of bits of the second encryption key to be a multiple of the window size by applying a binary number-based value conversion method, and performing, in parallel, a scalar multiplication operation with the third encryption key and a vector on an elliptic curve based on the window size, wherein the second encryption key has a value conforming to the binary number-based value conversion method.