Technical Papers and White Papers


Learn more about SecureRF’s quantum-resistant cryptography methods. Read through our technical papers and white papers. If you have additional questions, SecureRF’s engineering team and cryptographers can assist you. Contact us

White Papers

  • “WalnutDSA: A Quantum-Resistant Digital Signature Algorithm,” Iris Anshel, Derek Atkins, Dorian Goldfeld, and Paul E. Gunnells, Updated August 2018.
    • Abstract: This paper introduces WalnutDSATM , a new E-Multiplication-based public-key method which provides efficient verification, allowing low-power and constrained devices to quickly and inexpensively validate digital signatures (e.g., a certificate or authentication). It presents an in-depth discussion of the construction of the digital signature algorithm, analyzes the security of the scheme, provides a proof of security under EUF-CMA, and discusses the practical results from implementations on several constrained devices.  Access the paper.
  • “Ironwood Meta Key Agreement and Authentication Protocol,” Iris Anshel, Derek Atkins, Dorian Goldfeld, and Paul E. Gunnells, Updated August 2018.
    • Abstract: Number theoretic public-key solutions are subject to various quantum attacks making them less attractive for longer-term use. Certain group theoretic constructs show promise in providing quantum-resistant cryptographic primitives. We introduce a new protocol called a Meta Key Agreement and Authentication Protocol (MKAAP) that has some characteristics of a public-key solution and some of a shared-key solution. Then we describe the Ironwood MKAAP, analyze its security, and show how it resists quantum attacks. We also show Ironwood implemented on several IoT devices, measure its performance, and show how it performs better than existing key agreement schemes. Access the paper.
  • “Kayawood, a Key Agreement Protocol,” Iris Anshel, Derek Atkins, Dorian Goldfeld, and Paul E. Gunnells, November 2017.
    • Abstract: This paper introduces Kayawood Key Agreement ProtocolTM (Kayawood KAPTM), a new group-theoretic key agreement protocol, that leverages the known NP-Hard shortest word problem (among others) to provide an Elgamal-style, Diffie-Hellman-like method. This paper also (i) discusses the implementation of and behavioral aspects of Kayawood, (ii) introduces new methods to obfuscate braids using Stochastic Rewriting, and (iii) analyzes and demonstrates Kayawood’s security and resistance to known quantum attacks. Access the Paper
  • “An Introduction to Cryptographic Security Methods and Their Role in Securing Low Resource Computing Devices," Updated March 2017.
    • Abstract: An overview of public-key cryptosystems based on RSA, Diffie-Hellman and Group Theoretic Cryptography, along with a review of next-generation of public-key cryptographic security for low-resource computing devices. Access the Paper
  • “An Introduction to the Mathematics of Braids,” Dr. Iris Anshel, Summer 2015.
    • Abstract: Braids are abstract mathematical objects. The connection between the braid group, which is infinite, and the collections of permutations, which is finite, facilitates the development of cryptographic applications of the braid group including the Algebraic Eraser. Access the Paper
  • “Colored Burau Matrices, E-multiplication, and the Algebraic Eraser Key Agreement Protocol: An introduction to the Algebraic Eraser,” Iris Anshel, Summer 2015. Access the Paper
  • “Security in Low Resource Environments,” January 2006. Abstract: A business paper that focuses on the difficulty current public key protocols have in addressing security issues in low resource environments. Access the Paper

Technical Papers by SecureRF and Others

  • “Key Agreement, The Algebraic Eraser, and Lightweight Cryptography,” Iris Anshel, Michael Anshel, Dorian Goldfeld, and Stephane Lemieux. Access the Paper (A version of this paper was published in December 2006 by The American Mathematical Society in their Contemporary Mathematics series journal called Algebraic Methods in Cryptography.)
  • “Cryptanalysis of Anshel-Anshel-Goldfeld-Lemieux Key Agreement Protocol,” Alex D. Myasnikov and Alexander Ushakov, Submitted on January 30, 2008. Access the Paper
  • “Short Expressions of Permutations as Products and Cryptanalysis of the Algebraic Eraser,” Arkadius Kalka, Mina Teicher, and Boaz Tsaban, Submitted on April 3, 2008 (last revised March 6, 2012). Also published in Advances in Applied Mathematics, Volume 49, Issue 1, July 2012, Pages 57-76. Access the Paper
  • “On the Cryptanalysis of the Generalized Simultaneous Conjugacy Search Problem and the Security of the Algebraic Eraser,” Paul E. Gunnells, Submitted on May 5, 2011. Access the Paper
  • “Defeating the Kalka–Teicher–Tsaban Linear Algebra Attack on the Algebraic Eraser,” Dorian Goldfeld and Paul E. Gunnells, Submitted on February 3, 2012. Access the Paper
  • “Defeating the Ben-Zvi, Blackburn, and Tsaban Attack on the Algebraic Eraser,” Iris Anshel, Derek Atkins, Dorian Goldfeld, and Paul E. Gunnells, Submitted on January 18, 2016. Access the Paper
  • “A Class of Hash Functions Based on the Algebraic Eraser,” Iris Anshel, Derek Atkins, Dorian Goldfeld, and Paul E. Gunnells, Groups Complexity Cryptology, Volume 8, Issue 1, May 2016. View the Peer-Reviewed Article
  • “Post Quantum Group Theoretic Cryptography,” Iris Anshel, Derek Atkins, Dorian Goldfeld and Paul E. Gunnells, November 2016.
    • Abstract: Thanks to Shor’s quantum factoring algorithm, the most prevalent asymmetric cryptographic systems (RSA, ECC) are now known to be vulnerable to attack by sufficiently powerful quantum computers. In this paper, we discuss three Group Theoretic cryptographic protocols known as WalnutDSA (a digital signature algorithm), Hickory (a cryptographic hash function), and IronwoodKAP (a key agreement protocol), in the context of post-quantum cryptography. Unlike the classical public key protocols, the algebra underlying Walnut, Hickory, and Ironwood is non-abelian. We present evidence that these protocols are not susceptible to the quantum attacks known to be effective on RSA and ECC, and conclude that Group Theoretic Cryptography is a viable candidate for post-quantum cryptography. Access the Paper
  • “Hickory Hash: Implementing an Instance of an Algebraic Eraser Hash Function on an MSP430 Microcontroller,” Iris Anshel, Derek Atkins, Dorian Goldfeld, and Paul E. Gunnells, November 2016.
    • Abstract: Recently a novel family of braid based cryptographic hash function candidates was published, claiming to be suitable for use in low resource environments. It was shown that the new hash function family performed extremely well on a range of cryptographic test suites. In this paper, we instantiate an instance of the hash family, called Hickory Hash, fix a set of parameters, implement it on a Texas Instruments MSP430 16-bit microcontroller, and compare its performance characteristics to SHA2. We show that the Hickory Hash can be a viable tool for low-power, constrained devices like those associated with the Internet of Things. Access the Paper