Differential Elliptic Point Addition in Twisted Edwards Curves

2013 ◽  
Author(s):  
L. Marin
Keyword(s):  
Elliptic Point ◽  
Edwards Curves ◽  
Twisted Edwards Curves

scholarly journals The Pairing Computation on Edwards Curves

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Hongfeng Wu ◽  
Liangze Li ◽  
Fan Zhang
Keyword(s):  
Geometric Interpretation ◽  
Tate Pairing ◽  
Quadric Surfaces ◽  
Edwards Curves ◽  
Explicit Formulae ◽  
Pairing Computation ◽  
Twisted Edwards Curves ◽  
Group Law

We propose an elaborate geometry approach to explain the group law on twisted Edwards curves which are seen as the intersection of quadric surfaces in place. Using the geometric interpretation of the group law, we obtain the Miller function for Tate pairing computation on twisted Edwards curves. Then we present the explicit formulae for pairing computation on twisted Edwards curves. Our formulae for the doubling step are a little faster than that proposed by Arène et al. Finally, to improve the efficiency of pairing computation, we present twists of degrees 4 and 6 on twisted Edwards curves.

scholarly journals Compression for trace zero points on twisted Edwards curves

2016 ◽  
Vol 10 (1) ◽  
Author(s):  
Giulia Bianco ◽  
Elisa Gorla
Keyword(s):  
Elliptic Curves ◽  
Edwards Curves ◽  
Twisted Edwards Curves ◽  
Zero Points

AbstractWe propose two optimal representations for the elements of trace zero subgroups of twisted Edwards curves. For both representations, we provide efficient compression and decompression algorithms. The efficiency of the algorithm is compared with the efficiency of similar algorithms on elliptic curves in Weierstrass form.

Efficient message transmission via twisted Edwards curves

2020 ◽  
Vol 70 (6) ◽  
pp. 1511-1520
Author(s):  
Bariş Bülent Kirlar
Keyword(s):  
Discrete Logarithm ◽  
Encryption Scheme ◽  
Message Transmission ◽  
Edwards Curves ◽  
Diffie Hellman ◽  
Digital Signature Algorithm ◽  
Message Recovery ◽  
Secure Message Transmission ◽  
Chosen Ciphertext Attack ◽  
Twisted Edwards Curves

AbstractIn this paper, we suggest a novel public key scheme by incorporating the twisted Edwards model of elliptic curves. The security of the proposed encryption scheme depends on the hardness of solving elliptic curve version of discrete logarithm problem and Diffie-Hellman problem. It then ensures secure message transmission by having the property of one-wayness, indistinguishability under chosen-plaintext attack (IND-CPA) and indistinguishability under chosen-ciphertext attack (IND-CCA). Moreover, we introduce a variant of Nyberg-Rueppel digital signature algorithm with message recovery using the proposed encryption scheme and give some countermeasures to resist some wellknown forgery attacks.

Deterministic Encoding into Twisted Edwards Curves

2016 ◽  
pp. 285-297 ◽  
Author(s):  
Wei Yu ◽  
Kunpeng Wang ◽  
Bao Li ◽  
Xiaoyang He ◽  
Song Tian
Keyword(s):  
Edwards Curves ◽  
Twisted Edwards Curves
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