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Chapter and Conference Paper
Efficient Key Recovery for All HFE Signature Variants
The HFE cryptosystem is one of the most popular multi- variate schemes. Especially in the area of digital signatures, the HFEv- variant offers short signatures and high performance. Recently, an instance of th...
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Chapter
Introduction
This chapter gives a short introduction into the field of cryptography. After defining the protection goals of cryptography, we briefly describe the main cryptographic primitives used to achieve these goals. W...
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Chapter
Multivariate Cryptography
This chapter gives an overview of the basic concepts of multivariate cryptography. After recalling the basic definitions on (systems of) multivariate polynomials, we present the main construction methods of mu...
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Chapter
Hidden Field Equations
This chapter deals with the Hidden Field Equations (HFE) cryptosystem and its variants. We start by an introduction of the basic HFE cryptosystem and study its security against direct and rank attacks. Further...
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Chapter
MQDSS
In this chapter we introduce the MQDSS signature scheme, which is one of the few provably secure multivariate public key cryptosystems. We start by a description of the MQ based identification scheme which all...
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Chapter
Solving Polynomial Systems
This chapter considers the known techniques to solve (systems of) nonlinear polynomial equations. After giving a historical overview of the topic, we describe algorithms to solve univariate polynomials of high...
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Chapter and Conference Paper
Efficient Key Generation for Rainbow
Multivariate Cryptography is one of the main candidates for securing communication in a post-quantum world. One of the most promising schemes from this area is the Rainbow signature scheme. While this scheme ...
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Chapter
The Matsumoto-Imai Cryptosystem
This chapter describes the Matsumoto-Imai cryptosystem, which is one of the oldest multivariate public key cryptosystems. After introducing the plain scheme, we discuss its cryptanalysis by the linearization e...
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Chapter
Oil and Vinegar
This chapter deals with multivariate signature schemes following the concept of Oil and Vinegar. After introducing the basic (balanced) Oil and Vinegar (OV) signature scheme, we describe its cryptanalysis by t...
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Chapter
The SimpleMatrix Encryption Scheme
In this chapter we study the Simple Matrix encryption scheme, which is one of the very few multivariate encryption schemes from the SingleField family. After introducing the basic Simple Matrix encryption sche...
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Chapter and Conference Paper
Total Break of the SRP Encryption Scheme
Multivariate Public Key Cryptography (MPKC) is one of the main candidates for secure communication in a post-quantum era. Recently, Yasuda and Sakurai proposed in [7] a new multivariate encryption scheme called S...
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Chapter and Conference Paper
Improved Cryptanalysis of HFEv- via Projection
The HFEv- signature scheme is one of the most studied multivariate schemes and one of the major candidates for the upcoming standardization of post-quantum digital signature schemes. In this paper, we propose ...
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Chapter and Conference Paper
A Practical Multivariate Blind Signature Scheme
Multivariate Cryptography is one of the main candidates for creating post-quantum cryptosystems. Especially in the area of digital signatures, there exist many practical and secure multivariate schemes. Howeve...
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Chapter and Conference Paper
HMFEv - An Efficient Multivariate Signature Scheme
Multivariate Cryptography, as one of the main candidates for establishing post-quantum cryptosystems, provides strong, efficient and well-understood digital signature schemes such as UOV, Rainbow, and Gui. Whi...
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Chapter and Conference Paper
RingRainbow – An Efficient Multivariate Ring Signature Scheme
Multivariate Cryptography is one of the main candidates for creating post-quantum cryptosystems. Especially in the area of digital signatures, there exist many practical and secure multivariate schemes. Howeve...
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Chapter and Conference Paper
Revisiting the Cubic UOV Signature Scheme
As recently been emphasized by NSA and NIST, there is an increasing need for cryptographic schemes being secure against quantum computer attacks. Especially in the area of digital signature schemes, multivaria...
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Chapter and Conference Paper
Revisiting the Efficient Key Generation of ZHFE
ZHFE, proposed by Porras et al. at PQCrypto’14, is one of the very few existing multivariate encryption schemes and a very promising candidate for post-quantum cryptosystems. The only one drawback is its slow ...
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Chapter and Conference Paper
Reducing the Key Size of the SRP Encryption Scheme
Multivariate Public Key Cryptography (MPKC) is one of the main candidates for secure communication in a post-quantum era. Recently, Yasuda and Sakurai proposed in [8] a new multivariate encryption scheme called S...
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Chapter and Conference Paper
The Shortest Signatures Ever
Multivariate Cryptography is one of the main candidates for creating post quantum public key cryptosystems. Especially in the area of digital signatures, there exist many practical and secure multivariate sche...
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Chapter
Post-Quantum Cryptography: State of the Art
Public-key cryptography is indispensable for cyber security. However, as a result of Peter Shor shows, the public-key schemes that are being used today will become insecure once quantum computers reach maturit...
