TY - CHAP

T1 - A complete and explicit security reduction algorithm for RSA-based cryptosystems

AU - Kurosawa, Kaoru

AU - Schmidt-Samoa, Katja

AU - Takagi, Tsuyoshi

PY - 2003

Y1 - 2003

N2 - In this paper, we introduce a conceptually very simple and demonstrative algorithm for finding small solutions (x,y) of ax + y = c mod N, where gcd(a, N) = 1. Our new algorithm is a variant of the Euclidian algorithm. Unlike former methods, it finds a small solution whenever such a solution exists. Further it runs in time script O sign((logN)3), which is the same as the best known previous techniques, e.g. lattice-based solutions. We then apply our algorithm to RSA-OAEP and RSA-Paillier to obtain better security proofs. We believe that there will be many future applications of this algorithm in cryptography.

AB - In this paper, we introduce a conceptually very simple and demonstrative algorithm for finding small solutions (x,y) of ax + y = c mod N, where gcd(a, N) = 1. Our new algorithm is a variant of the Euclidian algorithm. Unlike former methods, it finds a small solution whenever such a solution exists. Further it runs in time script O sign((logN)3), which is the same as the best known previous techniques, e.g. lattice-based solutions. We then apply our algorithm to RSA-OAEP and RSA-Paillier to obtain better security proofs. We believe that there will be many future applications of this algorithm in cryptography.

UR - http://www.scopus.com/inward/record.url?scp=0344196669&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0344196669&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-40061-5_30

DO - 10.1007/978-3-540-40061-5_30

M3 - Chapter

AN - SCOPUS:0344196669

SN - 3540205926

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 474

EP - 491

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

A2 - Laih, Chi Sung

PB - Springer Verlag

ER -