Extracting bits from coordinates of a point of an elliptic curve

Nicolas Gürel

Paper 2005/324

Extracting bits from coordinates of a point of an elliptic curve

Nicolas Gürel

Abstract

In the classic Diffie-Hellman protocol based on a generic group $\G$ , Alice and Bob agree on a common secret $K_{A B}$ (master secret) which is indistinguishable from another element of $\G$ but not from a random bits-string of the same length. In this paper, we present a new deterministic method to extract bits from $K_{A B}$ when $\G$ is an elliptic curve defined over a quadratic extension of a finite field. In the last section, we show that it is also possible to extract a few bits when is an elliptic curve defined over a prime field.

Metadata

Available format(s): PDF PS
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: Elliptic curve cryptosystem key derivation pseudo-random extractors.
Contact author(s): gurel @ lix polytechnique fr
History: 2005-09-13: received
Short URL: https://ia.cr/2005/324
License: CC BY

BibTeX

@misc{cryptoeprint:2005/324,
      author = {Nicolas Gürel},
      title = {Extracting bits from coordinates of a point of an elliptic curve},
      howpublished = {Cryptology {ePrint} Archive, Paper 2005/324},
      year = {2005},
      url = {https://eprint.iacr.org/2005/324}
}