Abstract
This paper describes new algorithms for computing a modular inverse e − 1 given coprime integers e and f. Contrary to previously reported methods, we neither rely on the extended Euclidean algorithm, nor impose conditions on e or f. The main application of our gcd-free technique is the computation of an RSA private key in both standard and CRT modes based on simple modular arithmetic operations, thus boosting real-life implementations on crypto-accelerated devices.
Chapter PDF
Similar content being viewed by others
Keywords
References
Atkin, A.O.L., Morain, F.: Elliptic curves and primality proving. Mathematics of Computation 61, 29–68 (1993)
Boneh, D., Franklin, M.: Efficient generation of shared RSA keys. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 425–439. Springer, Heidelberg (1997)
Bosma, W., van der Hulst, M.-P.: Faster primality testing. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 652–656. Springer, Heidelberg (1990)
Derôme, M.F.A.: Generating RSA keys without the Euclid algorithm. Electronics Letters 29(1), 19–21 (1993)
Dussé, S.R., Kaliski Jr., B.S.: A cryptographic library for the Motorola DSP 56000. In: Damgård, I.B. (ed.) EUROCRYPT 1990. LNCS, vol. 473, pp. 230–244. Springer, Heidelberg (1991)
Fischer, W., Seifert, J.-P.: Note on fast computation of secret RSA exponents. In: Batten, L.M., Seberry, J. (eds.) ACISP 2002. LNCS, vol. 2384, pp. 136–143. Springer, Heidelberg (2002)
Joye, M., Paillier, P.: Constructive methods for the generation of prime numbers. In: Proc. of the 2nd NESSIE Workshop, Egham, UK, September 12–13 (2001)
Knuth, D.E.: The Art of Computer Programming, 2nd edn. Seminumerical Algorithms, vol. 2. Addison-Wesley, Reading (1981)
Quisquater, J.-J., Couvreur, C.: Fast decipherment algorithm for RSA public-key cryptosystem. Electronics Letters 18, 905–907 (1982)
Riesel, H.: Prime Numbers and Computer Methods for Factorization. Birkhäuser, Basel (1985)
Rivest, R.L., Shamir, A., Adleman, L.M.: A method for obtaining digital signatures and public-key cryptoystems. Communications of the ACM 21(2), 120–126 (1978)
Solovay, R., Strassen, V.: A fast Monte-Carlo test for primality. SIAM Journal on Computing 6, 84–85 (1977)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Joye, M., Paillier, P. (2003). GCD-Free Algorithms for Computing Modular Inverses. In: Walter, C.D., Koç, Ç.K., Paar, C. (eds) Cryptographic Hardware and Embedded Systems - CHES 2003. CHES 2003. Lecture Notes in Computer Science, vol 2779. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45238-6_20
Download citation
DOI: https://doi.org/10.1007/978-3-540-45238-6_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40833-8
Online ISBN: 978-3-540-45238-6
eBook Packages: Springer Book Archive