A New Look-Up Table Approach for High-Speed Finite Field Multiplication

2011 ◽  
Author(s):  
Bimal K. Meher ◽  
Pramod K. Meher
Keyword(s):  
Finite Field ◽  
High Speed ◽  
Look Up Table ◽  
Finite Field Multiplication ◽  
Field Multiplication ◽  
New Look

scholarly journals EFFICIENT OPERATIONS IN LARGE FINITE FIELDS FOR ELLIPTIC CURVE CRYPTOGRAPHIC

2020 ◽  
Vol 7 (6) ◽  
pp. 141-151
Author(s):  
Yan-Haw Chen ◽  
Chien-Hsing Huang
Keyword(s):  
Finite Field ◽  
Elliptic Curve ◽  
High Speed ◽  
Lookup Table ◽  
Computation Cost ◽  
Encryption And Decryption ◽  
Software Implementations ◽  
Field Multiplication ◽  
Rule Method ◽  
Elliptic Curve Scalar Multiplication

An efficient method to compute the finite field multiplication for Elliptic Curve point multiplication at high speed encryption of the message is presented. The methods of the operations are based on dynamic lookup table and modified Horner rule method. The modified Horner rule method is not only to finite field operations but also to Elliptic curve scalar multiplication in the encryption and decryption. By comparison with using Russian Peasant method and in the new proposed method, one of the advantages of utilizing the proposed algorithm is that in the Elliptic Curve point addition are reduced by a factor of three in GF (2163). Therefore, using the Algorithm 1 running on Intel CPU, computation cost of the multiplication method is above 70% faster than using standard multiplication by Russian Peasant method. Ultimately, the proposed Algorithm 1 for evaluating multiplication can be made regular, simple and suitable for software implementations.  

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