Abstract
ISO 9796-1, published in 1991, was the first standard specifying a digital signature scheme with message recovery. In [4], Coron, Naccache and Stern described an attack on a slight modification of ISO 9796-1. Then, Coppersmith, Halevi and Jutla turned it into an attack against the standard in full [2]. They also proposed five countermeasures for repairing it. In this paper, we show that all these countermeasures can be attacked, either by using already existing techniques (including a very recent one), or by introducing new techniques, one of them based on the decomposition of an integer into sums of two squares.
Chapter PDF
References
Cohen, H.: A Course in Computational Algebraic Number Theory. Graduate Texts in Mathematics 138 Springer-Verlag (1995)
Coppersmith, D., Halevi, S., Jutla, C.: ISO 9796-1 and the new forgery strategy (Working Draft). Research Contribution to P1363 (1999) http://grouper.ieee.org/groups/1363/contrib.html
Cornacchia, G.: Su di un metodo per la risoluzione in numeri unteri dell’ equazione \( \sum\nolimits_{h = 0}^n C _h x^{n - h} y^h = P \). Giornale di Matematiche di Battaglini 46 (1908) 33–90
Coron, J.-S., Naccache, D., Stern, J. P.: On the Security of RSA Padding. Advances in Cryptology-Crypto’ 99-Lecture Notes in Computer Science 1666 Springer-Verlag (1999) 1–18
Girault, M., Misarsky, J.-F.: Selective Forgery of RSA Signatures Using Redundancy. Advances in Cryptology-Eurocrypt’ 97-Lecture Notes in Computer Science 1233 Springer-Verlag (1997) 495–507
Grieu, F.: A Chosen Messages Attack on ISO/IEC 9796-1 Signature Scheme. Advances in Cryptology-Eurocrypt 2000-Lecture Notes in Computer Science 1807 Springer-Verlag (2000) 70–80 (this volume)
Gauss, C.F.: Disquisitiones Arithmeticae. Reissue Edition Springer-Verlag (1986)
Guillou, L.C., Quisquater, J.J., Walker, M., Landrock, P., Shaer, C.: Precautions Taken Against Various Potential Attacks in ISO/IEC DIS 9796, Digital Signature Scheme Giving Message Recovery. Advances in Cryptology-Eurocrypt’ 90-Lecture Notes in Computer Science 473 Springer-Verlag (1991) 465–473
Hellegouarch, Y.: Invitation aux Mathématiques de Fermat-Wiles. Masson (1997)
ISO: ISO/IEC 9796-1, Information technology — Security techniques — Digital signature schemes giving message recovery — Part 1: Mechanisms using redundancy. (1991)
De Jonge, W., Chaum, D.: Attacks on Some RSA Signatures. Advances in Cryptology-Crypto’ 85-Lecture Notes in Computer Science 218 Springer-Verlag (1986) 18–27
Misarsky, J.-F.: A Multiplicative Attack using LLL Algorithm on RSA Signatures with Redundancy. Advances in Cryptology-Crypto’ 97-Lecture Notes in Computer Science 1294 Springer-Verlag (1997) 221–234
Misarsky, J.-F.: How (not) to Design RSA Signature Schemes. Public Key Cryptography-First International Workshop on Pratice and Theory in Public Key Cryptography-PKC’98 Lecture Notes in Computer Science 1431 Springer-Verlag (1998) 14–28
Morain, F.: Courbes elliptiques et tests de primalité. Thesis (1990)
Morain, F., Nicolas, J.-L.: On Cornacchia’s algorithm for solving the diophantine equation u 2 + dv 2 = m. Chapter 2 of [14] ftp://ftp.inria.fr/INRIA/publication/Theses/TU-0144/ch2.ps
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Girault, M., Misarsky, JF. (2000). Cryptanalysis of Countermeasures Proposed for Repairing ISO 9796-1. In: Preneel, B. (eds) Advances in Cryptology — EUROCRYPT 2000. EUROCRYPT 2000. Lecture Notes in Computer Science, vol 1807. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45539-6_6
Download citation
DOI: https://doi.org/10.1007/3-540-45539-6_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67517-4
Online ISBN: 978-3-540-45539-4
eBook Packages: Springer Book Archive