[PDF] Top 20 CSIDH on Other Form of Elliptic Curves
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CSIDH on Other Form of Elliptic Curves
... an intractable problem on a quantum computer. Basing on this problem, he proposed a key agreement scheme which was rediscovered by Rostovtsev and Stolbunov [15] independently in 2006. Their key agreement scheme, which we ... See full document
18
Elliptic and Hyperelliptic Curves: a Practical Security Analysis
... the curves with m > ...the other NIST curves, and the addition of two residues might result in a carry occupying an additional word, which slows down the ...the other hand, the BN254 curve ... See full document
16
2-Selmer groups and Heegner points on elliptic curves
... This thesis also owes debts to Wei Zhang, who was always kind enough to answer my questions and generous to share his ideas. In particular, I am grateful to him for sending me [Zha14] while it was still in preprint ... See full document
104
A faster way to the CSIDH
... Isogeny-based cryptography. Isogeny-based cryptography is one of the cur- rent proposals for post-quantum cryptography. Already proposed in a talk (but not published) by Couveignes in 1997 [11] and independently ... See full document
17
Point Decomposition Problem in Binary Elliptic Curves
... time of Gaudry’s algorithm, his attack is expected to be more effective than Pollard’s rho algorithm if n ≥ 3 is relatively small and q is large. Diem [2] rigorously showed that ECDLP(q, n) can be solved in an expected ... See full document
13
Fixed Argument Pairing Inversion on Elliptic Curves
... (including other variants of the Tate pairing) defined on the smaller domain is neither easier nor harder than inverting the Tate pairing defined on the lager ... See full document
10
Binary quadratic forms, elliptic curves and Schoof's algorithm
... quadratic form Q(x, y) , also denoted with the triplet (a, b, c) , that in the following will be assumed to be primitive (with gcd(a, b, c) = 1 ...quadratic form Q(x, y) represents m ... See full document
134
A New Family of Pairing-Friendly elliptic curves
... the form of a typical KSS curve, where integer solutions exist only in a restricted set of residue ...BN curves [3]. It appeared possible that the new family of curves was, like the BN curves, ... See full document
16
CSIDH on the surface
... Apart from these benefits, given the limited pool of hard homogeneous spaces available, having the complete supersingular picture at our disposal adds freedom to the parameter selection and leads to a better ... See full document
19
On Isogeny Graphs of Supersingular Elliptic Curves over Finite Fields
... supersingular elliptic curves having j-invariant equal to 0 and ...the other hand, [2] and [4] state that security is based on the hardness ... See full document
14
Explicit n descent on elliptic curves III Algorithms
... • Search through small linear combinations of the basis elements of O until we find an element with reducible minimal polynomial. If n is prime we can then compute a trivialisation as described in Section 6.3. In ... See full document
44
A note on high-security general-purpose elliptic curves
... The curves Curve25519 and Curve1174 have been engineered to facilitate simple, efficient and secure implementation of general-purpose elliptic curve cryptosys- tems, with impressive results ...similar ... See full document
14
On Efficient Pairings on Elliptic Curves over Extension Fields
... the other side, there is much research on the generation of suitable elliptic curves for pairings, namely pairing-friendly curves, which contain the large prime subgroup and the small ... See full document
17
Elliptic curves and Pythagorean triples
... an elliptic surface π : E → P 1 defined over Q , or equivalently, an elliptic curve E over the rational function field Q( t ) ...the other 4 are of type I 2 ... See full document
9
Efficient Pairings Computation on Jacobi Quartic Elliptic Curves
... the elliptic curve. Pairing computation on the Edwards model of elliptic curves has been done successively in [9, 10] and ...using elliptic curves of Weierstrass form can be ... See full document
23
The Q-curve Construction for Endomorphism-Accelerated Elliptic Curves
... The endomorphism therefore lets us replace conventional log 2 N -bit scalar multiplications with ( 1 2 log 2 N)-bit multiexponentiations. In basic binary meth- ods this means halving the loop length, cutting the number ... See full document
26
Scalable Zero Knowledge via Cycles of Elliptic Curves
... Concretely, the approach of [BCCT13] consists of a transformation that takes as input a preprocessing zk-SNARK (such as one from existing implementations), and bootstraps it, via recursive proof composition, into a new ... See full document
49
Complete addition formulas for prime order elliptic curves
... each other is in the final addition, ruling out the exceptional points in all prior ...the other hand, as we mentioned in §1 and as was encountered in [16, ... See full document
25
Revisiting Atomic Patterns for Scalar Multiplications on Elliptic Curves
... In this paper, we revisit EC formulæ in a novel way and propose correspond- ing patterns to optimally benefit from the Straus-Shamir trick, a twice as fast method to evaluate double scalar multiplications [u] P + [v] Q. ... See full document
20
Periods of Tribonacci sequences and elliptic curves
... cubic has one root x = 0 in F 3 and so, one point of order 2 in E( F 3 ) which is (0, 0). The other non trivial points are (2, 1), (2, 2) which are of order 4. Hence, E( F 3 ) ≃ Z /4 Z . Therefore, work on E( F 3 ... See full document
17
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