Rolling up sleeves when subversion's in a field?

Daniel R.  L.  Brown

Paper 2020/074

Rolling up sleeves when subversion's in a field?

Daniel R. L. Brown

Abstract

A nothing-up-my-sleeve number is a cryptographic constant, such as a field size in elliptic curve cryptography, with qualities to assure users against subversion of the number by the system designer. A number with low Kolmogorov descriptional complexity resists being subverted to the extent that the speculated subversion would leave a trace that cannot be hidden within the short description. The roll programming language, a version of Godel's 1930s definition of computability, can somewhat objectively quantify low descriptional complexity, a nothing-up-my-sleeve quality, of a number. For example, curves NIST-P-256, Curve25519, and NIST-P-521 have fields sizes with roll programs of 112, 84, and 63 words (respectively).

Note: Latest versions shortens programs for field sizes of NIST curves P-521 and K-283.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint. MINOR revision.
Keywords: Kolmogorov descriptional complexity subversion
Contact author(s): danibrown @ blackberry com
History: 2020-12-15: revised; 2020-01-26: received; See all versions
Short URL: https://ia.cr/2020/074
License: CC BY

BibTeX

@misc{cryptoeprint:2020/074,
      author = {Daniel R.  L.  Brown},
      title = {Rolling up sleeves when subversion's in a field?},
      howpublished = {Cryptology {ePrint} Archive, Paper 2020/074},
      year = {2020},
      url = {https://eprint.iacr.org/2020/074}
}