References of "Müller, Volker 50002707"
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See detailTwisted Edwards-Form Elliptic Curve Cryptography for 8-bit AVR-based Sensor Nodes
Chu, Dalin; Groszschädl, Johann UL; Liu, Zhe UL et al

in Chen, Kefei; Xie, Qi; Qiu, Weidong (Eds.) et al Proceedings of the first ACM Workshop on Asia Public-Key Cryptography (ASIAPKC 2013) (2013, May)

Wireless Sensor Networks (WSNs) pose a number of unique security challenges that demand innovation in several areas including the design of cryptographic primitives and protocols. Despite recent progress ... [more ▼]

Wireless Sensor Networks (WSNs) pose a number of unique security challenges that demand innovation in several areas including the design of cryptographic primitives and protocols. Despite recent progress, the efficient implementation of Elliptic Curve Cryptography (ECC) for WSNs is still a very active research topic and techniques to further reduce the time and energy cost of ECC are eagerly sought. This paper presents an optimized ECC implementation that we developed from scratch to comply with the severe resource constraints of 8-bit sensor nodes such as the MICAz and IRIS motes. Our ECC software uses Optimal Prime Fields (OPFs) as underlying algebraic structure and supports two different families of elliptic curves, namely Weierstraß-form and twisted Edwards-form curves. Due to the combination of efficient field arithmetic and fast group operations, we achieve an execution time of 5.8*10^6 clock cycles for a full 158-bit scalar multiplication on an 8-bit ATmega128 microcontroller, which is 2.78 times faster than the widely-used TinyECC library. Our implementation also shows that the energy cost of scalar multiplication on a MICAz (or IRIS) mote amounts to just 19 mJ when using a twisted Edwards curve over a 160-bit OPF. This result compares fairly well with the energy figures of two recently-presented hardware designs of ECC based on twisted Edwards curves. [less ▲]

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See detailA Short Note on Secret Sharing Using Elliptic Curves
Müller, Volker UL

in Proceedings of SECRYPT 2008 (2008)

In this short note, we describe a variant of Shamir's (n, t)-threshold scheme based on elliptic curves. Moreover, we show how pairings of elliptic curves can be used to also provide verifiability for the ... [more ▼]

In this short note, we describe a variant of Shamir's (n, t)-threshold scheme based on elliptic curves. Moreover, we show how pairings of elliptic curves can be used to also provide verifiability for the new elliptic curve based threshold scheme. [less ▲]

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See detailFinding the Eigenvalue in Elkies' Algorithm
Müller, Volker UL; Maurer, Markus

in Experimental Mathematics (2001), 10(2), 275-285

One important part of Elkies' algorithm for computing the group order of an elliptic curve is the search for an eigenvalue of the Frobenius endomorphism. In this paper we compare two well known algorithms ... [more ▼]

One important part of Elkies' algorithm for computing the group order of an elliptic curve is the search for an eigenvalue of the Frobenius endomorphism. In this paper we compare two well known algorithms with two new ideas based on the Babystep Giantstep method. Moreover we show how resultants can be used to speed up this search. Finally we present a fast probabilistic algorithm for checking whether a given rational function is congruent to an entry in a table of rational functions modulo some fixed polynomial. [less ▲]

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See detailSekilas tentang Keamanan di Jaringan Komputer
Müller, Volker UL

in Sintesis - Makalah Universitas Kristen Indonesia (2001)

Detailed reference viewed: 107 (7 UL)
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See detailDifferential Fault Attacks on Elliptic Curve Cryptosystems
Biehl, Ingrid UL; Mey­er, Bernd; Müller, Volker UL

in Proceedings of Crypto 2000 (2000)

In this paper we extend the ideas for differential fault attacks on the RSA cryptosystem to cryptosystems using elliptic curves. We present three different types of at­tacks that can be used to derive ... [more ▼]

In this paper we extend the ideas for differential fault attacks on the RSA cryptosystem to cryptosystems using elliptic curves. We present three different types of at­tacks that can be used to derive information about the secret key if bit errors can be inserted into the elliptic curve computations done in a tamper-proof device. The effec­tiveness of the attacks was proven in a software simula­tion of the described ideas. [less ▲]

Detailed reference viewed: 76 (1 UL)
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See detailEfficient Point Multiplication for Elliptic Curves over Special Optimal Exten­sion Fields
Müller, Volker UL

in Proceedings of Public-Key Cryptography and Computational Number Theo­ry Conference (2000)

I generalize an idea of Gallant, Lambert, Vanstone for fast multipli­cation of points on elliptic curves with efficient endomorphisms. I describe how this generaliza­tion improves point multiplication for ... [more ▼]

I generalize an idea of Gallant, Lambert, Vanstone for fast multipli­cation of points on elliptic curves with efficient endomorphisms. I describe how this generaliza­tion improves point multiplication for elliptic curves defined over optimal extension fields. Finally we present practical results for the new algo­rithm compared to Gal­lant's algorithm. [less ▲]

Detailed reference viewed: 59 (2 UL)
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See detailComputing Discrete Logarithms in Real Quadratic Congruence Function Fields of Large Genus
Müller, Volker UL; Stein, Andreas; Thiel, Christoph

in Mathematics of Computation (1999), 68(226), 807-822

We present a sub-exponential algorithm for computing discrete loga­rithms in real quadratic congruence function fields of sufficiently large genus. We prove the correctness and the expected running time ... [more ▼]

We present a sub-exponential algorithm for computing discrete loga­rithms in real quadratic congruence function fields of sufficiently large genus. We prove the correctness and the expected running time of the algorithm. The algorithm is a gene­ralization of a similar algorithm for quadratic number fields. [less ▲]

Detailed reference viewed: 52 (0 UL)
See detailA Few Remarks on the Security of Internet Applications
Müller, Volker UL

in Proceedings of he First International Workshop on Information Integration and Web-based Applications & Services (1999)

In this short publication, I present a few facts on the security of some cur­rent In­ternet applications. Since one strong focus of this conference was the us­age of the In­ternet for electronic business ... [more ▼]

In this short publication, I present a few facts on the security of some cur­rent In­ternet applications. Since one strong focus of this conference was the us­age of the In­ternet for electronic business applications, I address two applica­tions often used in electronic business: electronic mail (E-mail) and se­cure ac­cess of web pages using the SSL protocol. It should be noted that all the facts presented in the note are well-known to security experts and not new. It might however be helpful for the ordinary of electronic commerce to become more aware of some security-related problems of the Internet. [less ▲]

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See detailFast Multiplication on Elliptic Curves over Small Fields of Characteristic Two
Müller, Volker UL

in Journal of Cryptology (1998), 11(4), 219-234

The paper shows how Frobenius expansions can be used to speed up mul­tiplication of points on elliptic curves that are defined over very small fields of charac­teristic two. The Frobenius expansion ... [more ▼]

The paper shows how Frobenius expansions can be used to speed up mul­tiplication of points on elliptic curves that are defined over very small fields of charac­teristic two. The Frobenius expansion algorithm is analyzed in theory and in practice. It can gain significant improvements in practical applica­tions. These curves are there­fore especially interesting for implementations of elliptic curve cryptosystems. [less ▲]

Detailed reference viewed: 92 (1 UL)
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See detailDiscrete Logarithm Based Cryptosystems in Quadratic Function Fields of Charac­teristic 2
Müller, Volker UL; Vanstone, Scott; Zuccherato, Robert

in Designs, Codes & Cryptography (1998), 14(2), 159-178

We describe a public key cryptosystem which works in quadratic function fields of characteristic two. Formulas for arithmetic are explicitly giv­en. The security of the system is based on the discrete ... [more ▼]

We describe a public key cryptosystem which works in quadratic function fields of characteristic two. Formulas for arithmetic are explicitly giv­en. The security of the system is based on the discrete logarithm problem in these fields. Therefore we also describe a Discrete Logarithm algorithm based on the ideas of Pohlig and Hell­man, especially adopted to quadratic function fields of charac­teristic two. [less ▲]

Detailed reference viewed: 41 (2 UL)
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See detailOn the Reduction of Composed Relations from the Number Field Sieve
Denny, Thomas; Müller, Volker UL

in Proceedings of the 2nd Algorithmic Number Theory Symposium (ANTS II) (1996)

A very important step in the number field sieve for computing dis­crete loga­rithms in finite fields is the combination of so called relations. These combina­tions are used in the final linear algebra ... [more ▼]

A very important step in the number field sieve for computing dis­crete loga­rithms in finite fields is the combination of so called relations. These combina­tions are used in the final linear algebra step to find the discrete logarithm. From a practical point of view, it is highly desirable to find combinations with as few as possible non zero entries, since this property speeds up the linear alge­bra part. In this paper we present a new algorithm for computing combina­tions which shows significant im­pro­ve­m­ents in practice to existing other algorithms. [less ▲]

Detailed reference viewed: 137 (1 UL)
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See detailA Public Key Cryptosystem based on Elliptic Curves over Z/nZ Equivalent to Factoring
Biehl, Ingrid UL; Meyer, Bernd; Müller, Volker UL

in Advances in Cryptology - Eurocrypt '96 (1996)

The paper describes a new cryptosystem for elliptic curves over the ring Z/nZ which is equivalent to the Rabin-Williams cryptosystem. We prove that breaking the new cryptosystem is equivalent to factoring ... [more ▼]

The paper describes a new cryptosystem for elliptic curves over the ring Z/nZ which is equivalent to the Rabin-Williams cryptosystem. We prove that breaking the new cryptosystem is equivalent to factoring the modulus n. [less ▲]

Detailed reference viewed: 34 (1 UL)
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See detailCounting the Number of Points on Elliptic Curves over Finite Fields of Characteristic Greater than Three
Lehmann, Frank; Maurer, Markus; Müller, Volker UL et al

in Proceedings of Algorithmic Number Theory Symposium I, Lecture Notes in Computer Science (1994)

The paper describes the implementation of the Algorithm of Atkin and Elkies for computing the group order of elliptic curves over large prime fields. The focus of the paper lays on algorithmical aspects ... [more ▼]

The paper describes the implementation of the Algorithm of Atkin and Elkies for computing the group order of elliptic curves over large prime fields. The focus of the paper lays on algorithmical aspects of the Atkin/Elkies algorithm. Practical data and running times are given. [less ▲]

Detailed reference viewed: 51 (2 UL)
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See detailComputing the number of points of elliptic curves over finite fields
Buchmann, Johannes; Müller, Volker UL

in Computing the number of points of elliptic curves over finite fields (1991)

In this paper we report on our implementation of a combination of the Babystep-Giantstep Algorithm and the Algorithm of Schoof for computing group or­ders of elliptic curves over finite fields. This paper ... [more ▼]

In this paper we report on our implementation of a combination of the Babystep-Giantstep Algorithm and the Algorithm of Schoof for computing group or­ders of elliptic curves over finite fields. This paper is a summary of the results in my Master Thesis. [less ▲]

Detailed reference viewed: 61 (4 UL)