In [3], Jhanwar and Barua presented an improvement of the Boneh-Gentry-Hamburg (BGH) scheme. In addition to reducing the time complexity of the algorithm to find a solution of the equation ax~2 + Sy~2 ≡ 1 mod n, their scheme reduces the number of equations to be solved by combining existing solutions. In [2], Susilo et al. extended the Jhanwar-Barua scheme, reducing more the number of equations to be solved. This paper presents a security flaw that appears in both schemes and shows that they are not IND-ID-CPA secure.
展开▼
