Hashing to Elliptic Curves of $$j=0$$ and Mordell–Weil Groups
نویسندگان
چکیده
منابع مشابه
On hashing into elliptic curves
We study the hash function from a finite field Fq into an elliptic curve over Fq which has recently been introduced by T. Icart. In particular we slightly adjust and prove the conjectured T. Icart asymptotic formula for the image size of this function.
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At Crypto 2010, Brier et al. proposed the first construction of a hash function into ordinary elliptic curves that was indifferentiable from a random oracle, based on Icart’s deterministic encoding from Crypto 2009. Such a hash function can be plugged into any cryptosystem that requires hashing into elliptic curves, while not compromising proofs of security in the random oracle model. However, ...
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Many cryptographic systems based on elliptic curves are proven secure in the Random Oracle Model, assuming there exist probabilistic functions that map elements in some domain (e.g. bitstrings) onto uniformly and independently distributed points in a curve. When implementing such systems, and in order for the proof to carry over to the implementation, those mappings must be instantiated with co...
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We propose a cryptographic hash function based on the difficulty of computing discrete logarithms in the group of points of an elliptic curve over a finite field. We prove the security of the hash function and analyze the performance. Our implementation of the finite field, the elliptic curve arithmetic, and scalar multiplication is optimized for high throughput on modern 32-bit desktop process...
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ژورنال
عنوان ژورنال: Mathematical Notes
سال: 2020
ISSN: 0001-4346,1573-8876
DOI: 10.1134/s0001434620110140