Elliptic Curve Signature Schemes

Equidistribution Among Cosets of Elliptic Curve Points in Intervals

Journal of Mathematical Cryptology ◽

10.1515/jmc-2019-0020 ◽

2020 ◽

Vol 14 (1) ◽

pp. 339-345

Author(s):

Taechan Kim ◽

Mehdi Tibouchi

Keyword(s):

Elliptic Curve ◽

Elliptic Curves ◽

Character Sums ◽

Fault Analysis ◽

Signature Schemes ◽

Large Subgroup

AbstractIn a recent paper devoted to fault analysis of elliptic curve-based signature schemes, Takahashi et al. (TCHES 2018) described several attacks, one of which assumed an equidistribution property that can be informally stated as follows: given an elliptic curve E over 𝔽q in Weierstrass form and a large subgroup H ⊂ E(𝔽q) generated by G(xG, yG), the points in E(𝔽q) whose x-coordinates are obtained from xG by randomly flipping a fixed, sufficiently long substring of bits (and rejecting cases when the resulting value does not correspond to a point in E(𝔽q)) are close to uniformly distributed among the cosets modulo H. The goal of this note is to formally state, prove and quantify (a variant of) that property, and in particular establish sufficient bounds on the size of the subgroup and on the length of the substring of bits for it to hold. The proof relies on bounds for character sums on elliptic curves established by Kohel and Shparlinski (ANTS–IV).

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Cryptanalytic Performance Appraisal of Improved CCH2 Proxy Multisignature Scheme

Mathematical Problems in Engineering ◽

10.1155/2014/429271 ◽

2014 ◽

Vol 2014 ◽

pp. 1-13

Author(s):

Raman Kumar ◽

Nonika Singla

Keyword(s):

Elliptic Curve ◽

Performance Appraisal ◽

Time Complexity ◽

Space Complexity ◽

Elliptic Curve Cryptosystem ◽

Forgery Attack ◽

Signature Schemes ◽

Computational Overhead ◽

Threshold Schemes

Many of the signature schemes are proposed in which thetout ofnthreshold schemes are deployed, but they still lack the property of security. In this paper, we have discussed implementation of improved CCH1 and improved CCH2 proxy multisignature scheme based on elliptic curve cryptosystem. We have represented time complexity, space complexity, and computational overhead of improved CCH1 and CCH2 proxy multisignature schemes. We have presented cryptanalysis of improved CCH2 proxy multisignature scheme and showed that improved CCH2 scheme suffered from various attacks, that is, forgery attack and framing attack.

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