Ray A. Perlner

Quantum resistant public key cryptography: a survey

Public key cryptography is widely used to secure transactions over the Internet. However, advances in quantum computers threaten to undermine the security assumptions upon which currently used public key cryptographic algorithms are based. In this paper, we provide a survey of some of the public key cryptographic algorithms that have been developed that, while not currently in widespread use, are believed to be resistant to quantum computing based attacks and discuss some of the issues that protocol designers may need to consider if there is a need to deploy these algorithms at some point in the future.

Privacy-preserving DRM

This paper describes and contrasts two families of schemes that enable a user to purchase digital content without revealing to anyone what item he has purchased. One of the basic schemes is based on anonymous cash, and the other on blind decryption. In addition to the basic schemes, we present and compare enhancements to the schemes for supporting additional features such as variable costs, enforcement of access restrictions (such as over age 21), and the ability of a user to monitor and prevent covert privacy-leaking between a content-provider-provided box and the content provider. As we will show, the different variants have different properties in terms of amount of privacy leaking, efficiency, and ability for the content provider to prevent sharing of encryption keys or authorization credentials.

An Asymptotically Optimal Structural Attack on the ABC Multivariate Encryption Scheme

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 encryption algorithm based on a fundamentally new idea: hiding the structure of a large matrix algebra over a finite field. We present an attack based on subspace differential invariants inherent to this methodology. The attack is a structural key recovery attack which is asymptotically optimal among all known attacks (including algebraic attacks) on the original scheme and its generalizations.

Security Analysis and Key Modification for ZHFE

ZHFE, designed by Porras et al., is one of the few promising candidates for a multivariate public-key encryption algorithm. In this article we extend and expound upon the existing security analysis on this scheme. We prove security against differential adversaries, complementing a more accurate and robust discussion of resistance to rank and algebraic attacks. We further suggest a modification,

A Classification of Differential Invariants for Multivariate Post-quantum Cryptosystems

ZHFE^-

Improved Attacks for Characteristic-2 Parameters of the Cubic ABC Simple Matrix Encryption Scheme

, a multivariate encryption scheme which retains the security and performance properties of ZHFE while optimizing key size in this theoretical framework.

Optimizing Information Set Decoding Algorithms to Attack Cyclosymmetric MDPC Codes

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 standardized in other standard bodies. The report reviews the mathematical background of pairings. This includes topics such as pairing-friendly elliptic curves and how to compute various pairings. It includes a brief introduction to existing identity-based encryption (IBE) schemes and other cryptographic schemes using pairing technology. The report provides a complete study of the current status of standard activities on pairing-based cryptographic schemes. It explores different application scenarios for pairing-based cryptography schemes. As an important aspect of adopting pairing-based schemes, the report also considers the challenges inherent in validation testing of cryptographic algorithms and modules. Based on the study, the report suggests an approach for including pairing-based cryptography schemes in the NIST cryptographic toolkit. The report also outlines several questions that will require further study if this approach is followed.

Total Break of the SRP Encryption Scheme

Multivariate Public Key Cryptography(MPKC) has become one of a few options for security in the quantum model of computing. Though a few multivariate systems have resisted years of effort from the cryptanalytic community, many such systems have fallen to a surprisingly small pool of techniques. There have been several recent attempts at formalizing more robust security arguments in this venue with varying degrees of applicability. We present an extension of one such recent measure of security against a differential adversary which has the benefit of being immediately applicable in a general setting on unmodified multivariate schemes.