Publications Volker Müller Logo UKDW

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Publications in English Publications in Indonesian Publications in German Theses

Image Watermarking Using the Discrete Cosine Transform and the MD5 Cryptographic Hash Function, Proceedings of The 1st Conference on Telematics System, Services, and Applications 2004, May 2004, ITB Bandung.

Abstract: We describe an image watermarking algorithm that uses the Discrete Cosine Transform together with a cryptographic hash function to embed copyright information of limited size into an image.

Experimental Results for Timing Attacks on Elliptic Curve Cryptosystems, Proceedings of the National Seminar on "Penerapan dan Pemanfaatan Mobile Application dalam Dunia Bisnis, Industri dan Pendidikan", Atma Jaya University, Sep. 2003.

Abstract:We describe practical results for four versions of a timing attack for fast point multiplication on elliptic curves. A software simulation for the basic left-to-right fast multiplication algorithm is used to perform these experiments. The results show that timing attacks can be a serious thread for elliptic curve cryptosystem implementations and should therefore be anticipated.

Efficient Point Multiplication for Elliptic Curves over Special Optimal Extension Fields., in "Public-Key Cryptography and Computational Number Theory", September 11-15, 2000, Warschau, Poland, Ed. Walter de Gruyter, 197 - 207, 2001.

Abstract:    We generalize an idea of Gallant, Lambert, Vanstone for fast multiplication of points on elliptic curves with efficient endomorphisms. We 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.

Finding the Eigenvalue in Elkies' Algorithm. Experimental Mathematics, 10 (2), 275 - 285, 2001 (with Markus Maurer).

Abstract:    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.

Differential Fault Attacks on Elliptic Curve Cryptosystems, Advances in Cryptology - Crypto 2000 Proceedings, Lecture Notes in Computer Science Vol. 1880, Ed. Mihir Bellare, Springer-Verlag, 131 - 146, 2000 (with Bernd Meyer).

Abstract:     In this paper we extend the ideas for differential fault attacks on the RSA cryptosystem to schemes 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 in a tamper-proof device. The effectiveness of the attacks was proven in a software simulation of the described ideas.

Computing Discrete Logarithms in Real Quadratic Congruence Function Fields of Large Genus.    Mathematics of Computation, 68 (226), 807 - 822, 1999 (with Andreas Stein, Christoph Thiel).

Abstract:    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.

A Few Remarks on the Security of Internet Applications, Proceedings of "The First International Workshop on Information Integration and Web-based Applications & Services",  Universitas Gadjah Mada, Yogyakarta, Indonesia, 1999, (html version)

Abstract:    In this short note I present a few facts on the security of some current Internet applications. Since one strong focus of the First International Workshop on Information Integration and Web-Based Application Services 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.

Discrete Logarithm Based Cryptosystems in Quadratic Function Fields of Characteristic 2.  Designs, Codes and Cryptography, 14 (2), 159 - 178, 1998 (with Scott Vanstone, Robert Zuccherato).

Abstract:   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 DL algorithm based on the ideas of  Pohlig and Hellman, especially adopted to quadratic function fields of characteristic two.

Efficient Algorithms for Multiplication on Elliptic Curves. Proceedings of "GI - Arbeitskonferenz Chipkarten 1998",  TU München, 1998.

Abstract:    The efficiency of elliptic curve cryptosystems depends heavily on fast multiplication algorithms. In this paper we examine four different algorithms for this problem. All algorithms read the bits of the multiplier from the high order to the low order bit. Block versions are also derived. Running time data show that the new algorithms can be up to 25 % faster than the standard fast multiplication algorithm.

Fast Multiplication on Elliptic Curves over Small Fields of Characteristic Two.  Journal of Cryptology, 11 (4), 219 - 234, 1998.

Abstract:     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 practice and can gain significant improvements in practical applications. These curves are therefore especially interesting for implementations of elliptic curve cryptosystems.

On the Generation of Cryptographically Strong Elliptic Curves. Preprint, 1998 (with Sachar Paulus).

Abstract:     In this paper we experimentally compare two well known algorithms for finding elliptic curves suitable as basis of elliptic curve public key cryptosystems. The first algorithm consists of random choice with testing strict security criteria, the second one constructs elliptic curves which satisfy these criteria. We compare practical running times of LiDIA implementations of both algorithms.

On the reduction of composed relations from the number field sieve. Proceedings of Algorithmic Number Theory Symposium II, Lecture Notes in Computer Science Vol. 1122, 75 - 90, 1996 (with Thomas F. Denny).

Abstract:    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 the used in the final linear algebra step to find the discrete logarithm. From a practical view it is highly desirable to find combinations with as few as possible non zero entries, since this speeds up the linear algebra part. In this paper we present a new algorithm for computing combinations which shows significant improvements in practice.

A Public Key Cryptosystem based on Elliptic Curves over Z/nZ Equivalent to Factoring. Advances in Cryptology - Eurocrypt '96, Lecture Notes in Computer Science Vol. 1070, Ed. Ueli Maurer, 49 - 59, 1996 (with Ingrid Biehl, Bernd Meyer).

Abstract:     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.

Counting the Number of Points on Elliptic Curves over Finite Fields of Characteristic Greater than Three. Proceedings of Algorithmic Number Theory Symposium I, Lecture Notes in Computer Science 877 , 60 - 70, 1994 (with Frank Lehmann, Markus Maurer, Victor Shoup).

Abstract:    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.

Computing the number of points of elliptic curves over finite fields.   Proceedings of the 1991 International Symposium on symbolic and algebraic computation, Bonn, 179 - 182, 1991 (with Johannes Buchmann).

Abstract:      In this paper we report on our implementation of the combination of the Babystep-Giantstep Algorithm and the Algorithm of Schoof for computing group orders of elliptic curves.

Kriptografi Kunci Publik Berbasis Kurva Eliptik - Sebuah Perkenalan Sederhana, Proceeding "National Seminar on Electrical Engineering 2003", Vol. 1(1), Ahmad Dahlan University Yogyakarta, Oct. 2003, p. 215 - 220.

Abstract:Makalah ini menjelaskan dengan kata sesederhana mungkin teori dasar tentang kurva eliptik dan pemakaiannya dalam kriptografi, yaitu kriptosistem (ECC) dan sistem tanda tangan elektronis (ECDSA) berbasis kurva eliptik. Pemakaian kurva eliptik mempunyai beberapa keunggulan dibanding kriptosistem kunci publik lain. Oleh karena itu, ECC dan ECDSA semakin populer, misalnya untuk wireless applications.

Kajian Public Key Infrastructure: Implementasi Certification Authority, Proceedings of the National Seminar on "Penerapan dan Pemanfaatan Mobile Application dalam Dunia Bisnis, Industri dan Pendidikan", Atma Jaya University, Sep. 2003, p. ?? (dengan A. Sjamsjiar Rachman).

Abstract:Dalam tulisan ini, sebuah pembandingan antara dua paradigma untuk mengembangkan sebuah certification authority dilakukan. Paper ini adalah ringkasan dari tesis S2 Bapak A. Sjamsjiar Rachman yang ditulis di TE UGM di bawah bimbingan saya.

Penulisan Karya Ilmiah dengan MS-Word, Tip dan Trik, Pra-Versi dari tanggal 02-11-2002, Manuskrip, 2002.

Abstract:Text processor seperti MS-Word sangat membantu dalam penulisan karya ilmiah. Sayangnya, kadang-kadang pengetahuan tentang pemakaian MS-Word untuk menulis sebuah laporan berpuluh-puluh halaman masih terbatas pada operasi-operasi dasar. Dalam tulisan ini saya mencoba menjelaskan beberapa features MS-Word yang mendukung penulisan karya ilmiah. File untuk spell checking bahasa Indonesia bisa diakses lewat link ini.

Implementasi Aritmetika Efisien untuk Finite Field GF(2^32)^k. AITI, Jurnal Teknologi Informasi, Universitas Kristen Satya Wacana, Vol. 1 No. 1, Feb. 2003, p. 1 - 10 (dengan Edy Salim).

Abstract:Kami melapor tentang hasil implementasi aritmetika untuk finite field dengan derajat 6, 7, atau 8 dan karakteristik yang bisa disimpan dalam satu register sebesar 32 bit. Field ini sangat cocok untuk implementasi dalam prosesor ber-register 32 bit seperti Intel-Pentium. Kami juga menjelaskan aplikasi aritmetika ini untuk kriptosistem berbasis kurva eliptik.

Sekilas tentang Keamanan di Jaringan Komputer. Pre-version, akan diterbitkan di "Sintesis", Makalah Jurusan Teknik, Universitas Kristen Duta Wacana, Yogyakarta, Indonesia, 2001.

Abstract:  Dalam makalah ini saya menjelaskan beberapa masalah keamanan yang muncul di dalam jaringan komputer dan mengajukan beberapa saran untuk meminimalkan masalah-masalah tersebut (Article in indonesian language).

Elliptische Kurven und Public Key Kryptographie.  DuD Datenschutz und Datensicherheit, Jahrgang 22, 9/1998 (mit Sachar Paulus).

Abstract:    The article gives a simple introduction to elliptic curve cryptosystems, written for non experts, who want to learn the basics about this popular type of public key cryptosystem. We present some basic definitions, simple algorithms for arithmetic and explain the use of the group of points for encryption. The article is written in German language.

Zur Erzeugung kryptographisch starker Elliptischer Kurven.  DuD Datenschutz und Datensicherheit, Jahrgang 22, 9/1998 (mit Sachar Paulus).

Abstract:    The article is essentially a German translation of the paper "On the Generation of Cryptographically strong Elliptic Curves" given above.

Doctoral Thesis in Computer Science: Ein Algorithmus zur Bestimmung der Punktanzahl elliptischer Kurven über endlichen Körpern der Charakteristik größer drei. University of Saarland, Saarbrücken, 1995.

Abstract:   In my Doctoral Thesis I examine the Algorithm of Atkin and the Algorithm of Elkies in Atkin's version for the computation of the group order of elliptic curves over finite fields of sufficiently large characteristic. The theory of both algorithms is explained and a description of an implementation for large prime fields is given. The Thesis is written in German.

Diploma in Computer Science: Die Berechnung der Punktanzahl von elliptischen Kurven über endlichen Primkörpern. University of Saarland, Saarbrücken, 1991.

Abstract:  In my diploma thesis I describe Shanks' Babystep-Giantstep Algorithm and the Algorithm of Schoof for the computation of the group order of elliptic curves over "large" prime fields. Moreover a combination of these two algorithms is developed. Practical running time data for all three algorithms are given. The thesis is written in German.