Let [InlineMediaObject not available: see fulltext.] p be a finite field of p elements, where p is prime. The bit security of the Diffie-Hellman function over subgroups of [InlineMediaObject not available: see fulltext.]*p and of an elliptic curve over [InlineMediaObject not available: see fulltext.] p, is considered. It is shown that if the Decision Diffie-Hellman problem is hard in these groups, then the two most significant bits of the Diffie-Hellman function are secure. Under the weaker assumption of the computational (rather than decisional) hardness of the Diffie-Hellman problems, only about (log p)1/2 bits are known to be secure.
|Number of pages||8|
|Journal||Applicable Algebra in Engineering, Communications and Computing|
|Publication status||Published - Jan 2006|