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1. Report on Post-Quantum Cryptography
NIST Interagency/Internal Report (NISTIR)
Lidong Chen, Stephen P Jordan, Yi-Kai Liu, Dustin Moody, Rene C Peralta, Ray A Perlner, Daniel C Smith-Tone
In recent years, there has been a substantial amount of research on quantum computers - machines that exploit quantum mechanical phenomena to solve mathematical problems that are difficult or intractable for conventional computers. If large-scale qua ...
2. Vulnerabilities of "McEliece in the World of Escher"
Dustin Moody, Ray A Perlner
Recently, Gligoroski et al. proposed code-based encryption and signature schemes using list
decoding, blockwise triangular private keys, and a nonuniform error pattern based on
"generalized error sets." The general approach was referred to as "McE ...
3. Analogues of Vélu's formulas for Isogenies on Alternate Models of Elliptic Curves
Dustin Moody, Daniel Shumow
Isogenies are the morphisms between elliptic curves, and are accordingly a topic of interest
in the subject. As such, they have been well-studied, and have been used in several
cryptographic applications. Vélu's formulas show how to explicitly ...
4. Improved Indifferentiability Security Bound for the JH Mode
Dustin Moody, Daniel C Smith-Tone, Souradyuti Paul
Indifferentiability security of a hash mode of operation guarantees the mode's resistance against all generic attacks. It is also useful to establish the security of protocols that use hash functions as random functions. The JH hash function was one ...
5. Report on Pairing-based Cryptography
Journal of Research (NIST JRES)
Dustin Moody, Rene C Peralta, Ray A Perlner, Andrew Richard Regenscheid, Allen L Roginsky, Lidong Chen
This report summarizes study results on pairing-based cryptography. The main purpose of the study is to form NIST‰s position on standardizing and recommending pairing-based cryptography schemes
currently published in research literature and standard ...
6. An Asymptotically Optimal Structural Attack on the ABC Multivariate Encryption Scheme
Dustin Moody, Ray A Perlner, Daniel C Smith-Tone
Historically, multivariate public key cryptography has been less than successful at offering
encryption schemes which are both secure and efficient. At PQCRYPTO '13 in Limoges, Tao,
Diene, Tang, and Ding introduced a promising new multivariate e ...
7. Recommendation for Pair-Wise Key-Establishment Schemes Using Integer Factorization Cryptography
Special Publication (NIST SP)
800-56B Rev 1
Elaine B Barker, Lidong Chen, Dustin Moody
This Recommendation specifies key-establishment schemes using integer factorization cryptography, based on ANS X9.44, Key-establishment using Integer Factorization Cryptography [ANS X9.44], which was developed by the Accredited Standards Committee (A ...
8. Elliptic Curves arising from Brahmagupta Quadrilaterals
Farzali Izadi, Foad Khoshnam, Dustin Moody, Arman Zargar
A Brahmagupta quadrilateral is a cyclic quadrilateral whose sides, diagonals, and area are all
integer values. In this article, we characterize the notions of Brahmagupta, introduced by K. R. S. Sastry, by means of elliptic curves. Motivated by ...
9. On integer solutions of x^4+y^4-2z^4-2w^4=0
Dustin Moody, Arman Shamsi Zargar
In this article, we study the quartic Diophantine equation
x^4+y^4-2z^4-2w^4=0. We find non-trivial integer solutions. Furthermore, we show that when a
solution has been found, a series of other solutions can be derived. We do so using two dif ...
10. Character sums determined by low degree isogenies of elliptic curves
Dustin Moody, Christopher Rasmussen
We look at certain character sums determined by isogenies on elliptic curves over finite fields. We prove a congruence condition for character sums attached to arbitrary cyclic isogenies, and produce explicit formulas for isogenies of degree m <= 8.