Interpolation of the Elliptic Curve Diffie-Hellman Mapping
نویسندگان
چکیده
We prove lower bounds on the degree of polynomials interpolating the Diffie–Hellman mapping for elliptic curves over finite fields and some related mappings including the discrete logarithm. Our results support the assumption that the elliptic curve Diffie–Hellman key exchange and related cryptosystems are secure.
منابع مشابه
Diffie-Hellman type key exchange protocols based on isogenies
In this paper, we propose some Diffie-Hellman type key exchange protocols using isogenies of elliptic curves. The first method which uses the endomorphism ring of an ordinary elliptic curve $ E $, is a straightforward generalization of elliptic curve Diffie-Hellman key exchange. The method uses commutativity of the endomorphism ring $ End(E) $. Then using dual isogenies, we propose...
متن کاملA NEW PROTOCOL MODEL FOR VERIFICATION OF PAYMENT ORDER INFORMATION INTEGRITY IN ONLINE E-PAYMENT SYSTEM USING ELLIPTIC CURVE DIFFIE-HELLMAN KEY AGREEMENT PROTOCOL
Two parties that conduct a business transaction through the internet do not see each other personally nor do they exchange any document neither any money hand-to-hand currency. Electronic payment is a way by which the two parties transfer the money through the internet. Therefore integrity of payment and order information of online purchase is an important concern. With online purchase the cust...
متن کاملBit Security of the Hyperelliptic Curves Diffie-Hellman Problem
The Diffie-Hellman problem as a cryptographic primitive plays an important role in modern cryptology. The Bit Security or Hard-Core Bits of Diffie-Hellman problem in arbitrary finite cyclic group is a long-standing open problem in cryptography. Until now, only few groups have been studied. Hyperelliptic curve cryptography is an alternative to elliptic curve cryptography. Due to the recent crypt...
متن کاملConjectured Security of the ANSI-NIST Elliptic Curve RNG
An elliptic curve random number generator (ECRNG) has been proposed in ANSI and NIST draft standards. This paper proves that, if three conjectures are true, then the ECRNG is secure. The three conjectures are hardness of the elliptic curve decisional Diffie-Hellman problem and the hardness of two newer problems, the x-logarithm problem and the truncated point problem.
متن کاملOn the Bit Security of Elliptic Curve Diffie-Hellman
This paper gives the first bit security result for the elliptic curve Diffie–Hellman key exchange protocol for elliptic curves defined over prime fields. About 5/6 of the most significant bits of the x-coordinate of the Diffie–Hellman key are as hard to compute as the entire key. A similar result can be derived for the 5/6 lower bits. The paper also generalizes and improves the result for ellip...
متن کامل