当前位置: X-MOL 学术Theor. Comput. Sci. › 论文详情
Generic hardness of inversion on ring and its relation to self-bilinear map
Theoretical Computer Science ( IF 0.718 ) Pub Date : 2020-03-25 , DOI: 10.1016/j.tcs.2020.03.009
Takashi Yamakawa; Shota Yamada; Goichiro Hanaoka; Noboru Kunihiro

In this paper, we study the generic hardness of the inversion problem on a ring, which is a problem to compute the inverse of a given prime c by just using additions, subtractions and multiplications on the ring. If the characteristic of an underlying ring is public and coprime to c, then it is easy to compute the inverse of c by using the extended Euclidean algorithm. On the other hand, if the characteristic is hidden, it seems difficult to compute it. For discussing the generic hardness of the inversion problem, we first extend existing generic ring models to capture a ring of an unknown characteristic. Then we prove that there is no generic algorithm to solve the inversion problem in our model when the underlying ring is isomorphic to Zp for a randomly chosen prime p assuming the hardness of factorization of an unbalanced modulus. We also study a relation between the inversion problem on a ring and a self-bilinear map. Namely, we give a construction of a self-bilinear map based on a ring on which the inversion problem is hard, and prove that natural complexity assumptions including the multilinear computational Diffie-Hellman (MCDH) assumption hold w.r.t the resulting sef-bilinear map.
更新日期:2020-03-26

 

全部期刊列表>>
宅家赢大奖
向世界展示您的会议墙报和演示文稿
全球疫情及响应:BMC Medicine专题征稿
新版X-MOL期刊搜索和高级搜索功能介绍
化学材料学全球高引用
ACS材料视界
x-mol收录
自然科研论文编辑服务
南方科技大学
南方科技大学
西湖大学
中国科学院长春应化所于聪-4-8
复旦大学
课题组网站
X-MOL
深圳大学二维材料实验室张晗
中山大学化学工程与技术学院
试剂库存
天合科研
down
wechat
bug