Richelot Isogeny Cryptography for Faster SETA Decryption
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
The SETA encryption scheme requires significant time for decryption due to its reliance on the cryptoanalysis method described in Non-Patent Literature 2.
Innovation Solution
A cryptographic system utilizing a Richelot isogeny sequence φs with an abelian surface A0 as the starting point and A s as the public key, employing an encryption device to compute an abelian surface A m by encoding a plaintext m and a decryption device to compute a Richelot isogeny φ m based on the secret key φ s, reducing the prime number p to ⅓.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the SETA encryption scheme uses the cryptoanalysis method for decryption, then security is maintained, but decryption time becomes excessively long
Solution Approach 1:
The patent changes the fundamental parameters of the cryptographic system by transitioning from elliptic curves to abelian surfaces and from ordinary isogenies to Richelot isogenies. This parameter change enables a new decryption approach that computes Richelot isogenies directly rather than using time-consuming cryptoanalysis methods, thereby reducing decryption time while maintaining security based on the hardness of the basic isogeny problem.
2Loss of time
If the prime number p is reduced to 1/3, then decryption time is reduced, but the complexity of the isogeny computation increases
Solution Approach 1:
The patent substitutes the traditional decryption mechanism (cryptoanalysis method) with a new mechanism based on Richelot isogeny computation. Although Richelot isogenies are more complex than ordinary isogenies, the substitution enables direct computation that is still faster than the cryptoanalysis approach, especially when the prime number p is reduced to 1/3, achieving the desired balance between complexity and decryption speed.
Data Source
AI summary
A cryptographic system (1) performs a cryptographic process in which a Richelot isogeny sequence φs whose starting point is an abelian surface A0 and whose end point is an abelian surface As is a secret key and the abelian surface As is a public key. An encryption device (28) computes an abelian surface Am by transitioning the abelian surface As, which is the public key, by a Richelot isogeny sequence φm generated by encoding a plaintext m, and sets the abelian surface Am as a ciphertext. A decryption device (30) computes a Richelot isogeny φm whose starting point is the abelian surface As, which is the public key, and whose end point is the abelian surface Am, which is the ciphertext, based on the Richelot isogeny sequence φs, which is the secret key.