[PDF] Top 20 On the cost of computing isogenies between supersingular elliptic curves
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On the cost of computing isogenies between supersingular elliptic curves
... for elliptic curve arithmetic, isogeny computations, and isogeny evaluations: 8 (2-isogeny computation), 12 (2-isogeny evaluation), 14 (point addition), 9 (point ...per-table cost of ap- proximately 5.25N e ... See full document
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Analogue of Vélu's Formulas for Computing Isogenies over Hessian Model of Elliptic Curves
... degree-2 isogenies exist over this curve ...and computing also isogenies over Hessian ...for isogenies of odd de- gree ` = 2r + 1 are extremely costly ((5r + 3)M + 4S + 8rC), which is even ... See full document
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Computing isogenies between Montgomery curves using the action of (0,0)
... the cost of having to implement more algorithms, increasing the size and complexity of an (already complex) implementa- ...for isogenies of even degree and by showing how to avoid (0, 0), we are able to ... See full document
19
Faster Cryptographic Hash Function From Supersingular Isogeny Graphs
... of supersingular elliptic curves over finite ...fields. Supersingular isogeny graphs are excellent expander graphs with asymptotically optimal expansion con- stant ...of computing ... See full document
20
Strongly Secure Authenticated Key Exchange from Supersingular Isogenies
... cryptography, supersingular elliptic curve isogeny is one of the most attractive candidates for post-quantum ...Feo’s supersingular isogeny Diffie-Hellman key exchange (SIDH) [JD14] based on the hard ... See full document
29
A note on the cost of computing odd degree isogenies
... for computing odd degree isogenies using different models of elliptic ...for computing isogenies using Weierstrass curves [17], Edwards, Twisted Edwards and Huff curves ... See full document
16
An Improvment of the Elliptic Net Algorithm
... the Elliptic Net algorithm ...known Elliptic Net algorithm under the condition the density of non-zero digits of r is less than ...the cost of one inverse is about equal to that of ten ...original ... See full document
11
Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves
... that computing a particular isomorphism invariant might be equivalent to solving the elliptic curve isogeny problem, which is believed (or hoped) to be a quantum-resistant hard ... See full document
21
Self-pairings on supersingular elliptic curves with embedding degree $three$
... 19. Lei, H., Jun-Wu, D., Ding-Yi, P.: An implementation of cryptosystems based on tate pairing. Journal of Computer Science and Technology 20(2), 264 – 269 (2005) 20. Lin, X., Zhao, C.A., Zhang, F., Wang, Y.: ... See full document
15
Simple oblivious transfer protocols compatible with Kummer and supersingular isogenies
... is supersingular isogeny ...single elliptic curve is replaced by the set of all supersingular elliptic curves defined over a finite field F p 2 , and exponentiation maps are replaced by ... See full document
31
Supersingular Isogeny Diffie-Hellman Authenticated Key Exchange
... (SIDH). Computing a sequence of isogenies of elliptic curves is a new cryptographic basic operation in some ...of computing an isogeny sequence, which is based on the hardness of ... See full document
30
Hard Isogeny Problems over RSA Moduli and Groups with Infeasible Inversion
... isogenous curves over a sufficiently large field, finding an explicit isogeny between them seems to be hard, even for quantum ...puting isogenies was used in a key-exchange and a public-key ... See full document
54
A Note on Post-Quantum Authenticated Key Exchange from Supersingular Isogenies
... etc. Computing costs were estimated by adding the timings of the corresponding SIDH / SIKE operations in the SIDH library [11], after running the software on a machine powered by a ...the cost of ... See full document
22
On Isogeny Graphs of Supersingular Elliptic Curves over Finite Fields
... The remainder of the paper is organized as follows. In §2 we provide a concise sum- mary of the relevant background on elliptic curves and isogenies between them. Standard references for the ... See full document
14
CSIDH on Other Form of Elliptic Curves
... case, supersingular elliptic curves do not admit such an action of an abelian ...secrete isogenies. The resulting scheme named supersingular isogeny Diffie-Hellman key exchange (SIDH), ... See full document
18
Explicit isogenies of elliptic curves
... given elliptic curve by simply substituting the j-invariant and a suitable “twisting parame- ter” of E into the ...first computing in characteristic zero and then ... See full document
121
Supersingular Isogeny Oblivious Transfer
... estimate between some OT ...about isogenies of elliptic ...the Supersingular Isogeny Diffie-Hellman (SIDH) of [10] is shown in appendix ... See full document
23
The Dark SIDH of Isogenies
... the elliptic curve discrete logarithm problem had become the primary choice for concrete instantiations of fundamental cryptographic protocols, and enabled many new advancements in the ...relationship ... See full document
67
Computing Optimal Ate Pairings on Elliptic Curves with Embedding Degree $9,15$ and $27$
... on elliptic curves with even embedding degree since the advent of pairing-based ...on elliptic curves of embedding degrees k = 9, 15 and 27 which have twists of order ...and cost ... See full document
27
Computing supersingular isogenies on Kummer surfaces
... 2-isogenies between Montgomery curves, but noticed that the square roots were related to rational functions of torsion elements lying above their kernels, so were able to use these higher order ... See full document
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