Isogeny graph
18 Seconds to Key Exchange: Limitations of Supersingular Isogeny Diffie-Hellman on Embedded Devices
... supersingular isogeny Diffie-Hellman (SIDH) key exchange [16] is a promising candidate to se- cure the communication on embedded ...the isogeny-graph problem. An isogeny φ is an algebraic map ...
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Supersingular isogeny graphs and endomorphism rings: reductions and solutions
... `-isogeny graph reduces to a different type of endomorphism ring ...an isogeny of `-power degree into degree ` ...`-isogeny graph in Sections 5 and ...
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Towards Isogeny-Based Password-Authenticated Key Establishment
... The first cryptographic construction to use supersingular elliptic curve isogenies is the hash function construction of Charles et al. [7], based on the isogeny graph path-finding problem. Public key ...
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Supersingular Isogeny-Based Designated Verifier Blind Signature
... and isogeny-based ...the isogeny-based cryptography are the supersingular elliptic ...the isogeny graph of su- persingular elliptic ...
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Identification Protocols and Signature Schemes Based on Supersingular Isogeny Problems
... the isogeny graph), however this requires additional points in the public ...horizontal isogeny there are several possible approaches, but we think the most compact is to use the representation in ...
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Faster Cryptographic Hash Function From Supersingular Isogeny Graphs
... expander graph is, informally, a graph with low degree and high ...the isogeny graph of supersingular elliptic curves over finite ...Supersingular isogeny graphs are excellent expander ...
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Isogeny graphs, modular polynomials, and applications
... main theorem of this chapter, the Volcano Theorem, and the rest of the chapter is dedicated to the proof, except for Section 3.10, in which we give an example computation of an isogeny graph. This problem ...
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Towards practical key exchange from ordinary isogeny graphs
... Abstract. We revisit the ordinary isogeny-graph based cryptosystems of Couveignes and Rostovtsev–Stolbunov, long dismissed as impracti- cal. We give algorithmic improvements that accelerate key exchange in ...
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Hard Isogeny Problems over RSA Moduli and Groups with Infeasible Inversion
... an isogeny from one to the other is efficient, then it means the discrete-log problem is equally hard among all the curves in the same isogeny ...the isogeny problem is to look at the isogeny ...
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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 material in §2 are the books ...
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Some Graph Labelings on Middle Graph of Extended Duplicate Graph of a Path
... Let G = G(V,E) be a finite, simple and undirected graph with p vertices and q edges. By a labeling we mean a one-to-one mapping that carries a set of graph elements onto a set of numbers called ...
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New Hybrid Method for Isogeny-based Cryptosystems using Edwards Curves
... an isogeny-based cryptosystem is that it provides signifi- cantly smaller key sizes than other PQC primitives while providing the same level of ...of isogeny-based cryptosystems have been proposed to ...
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Product Cordial Graph in the Context of Some Graph Operations on Gear Graph
... some graph elements in gear ...gear graph. Similar problems can be discussed for the graph obtained by duplication of an edge in gear ...these graph operations of wheel graph, helm ...
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Labelings on Jahangir Graph and Extended Duplicate Graph of Jahangir Graph
... a graph G with vertex set V is a function from V(G) to {0,1} such that if each edge uv is assigned the label f(u)f(v), the number of vertices labeled ‘0’ and the number of vertices labeled ‘1’ differ by atmost 1 ...
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A Faster Software Implementation of the Supersingular Isogeny Diffie-Hellman Key Exchange Protocol
... Since its introduction by Jao and De Feo in 2011, the supersingular isogeny Diffie-Hellman (SIDH) key exchange protocol has positioned itself as a promising candidate for post-quantum cryptography. One salient ...
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The Neighborhood Graph of a Graph
... Several graph valued functions in graph theory were studied, for example, in [4, 5, 6, 7, 8, 9, 10, 11, 12,13, 14, 15, 16] and also several graph valued functions in domination theory were studied, ...
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The Semifull Graph of a Graph
... planar graph G is the minimum number of points not belonging to the boundary of the exterior region in any embedding of G in the ...A graph G is said to be k-minimally nonouterplanar if i(G) = k, k ≥ ...A ...
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Modeling Quantum-Safe Authenticated Key Establishment, and an Isogeny-Based Protocol
... to isogeny-based key establishment and signatures to obtain a truly quantum-safe authenticated key establishment protocol, which can in principle be used to create secure classical channels, even when faced with ...
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Isogeny Secrets can be Traded
... The above protocol is still subject to counterparty risk in the following way: if the data Alice sends Bob to assist his recovery of her secret is faked, then Bob cannot detect this forgery until Alice and Bob have ...
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Groups for which the noncommuting graph is a split graph
... noncommuting graph ∇(G) of G is defined as follows: the vertex set is G \ Z (the noncentral elements of G) and two distinct vertices x and y are joined by an edge iff xy ̸ = ...this graph can be considered ...
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