Additions compatible with multiplication

Statistically Secure One Multiplication and Additions of Secret Shares

One of the most interesting research topics in cryptography is finding schemes for an efficient fully-homomorphic encryption (FHE), preferably information-theoretically secure schemes, which are not based on unproven computational hardness assumptions. The greatest breakthrough in the field of FHE schemes was made by Gentry [7] in 2009, and since then there were some interesting developments, e...

Additions and Corrections

Jacobians with Complex Multiplication

We construct and study two series of curves whose Jacobians admit complex multiplication. The curves arise as quotients of Galois coverings of the projective line with Galois group metacyclic groups Gq,3 of order 3q with q ≡ 1 mod 3 an odd prime, and Gm of order 2 . The complex multiplications arise as quotients of double coset algebras of the Galois groups of these coverings. We work out the C...

Implementing Multiplication with Split

In look-up table based multiplication schemes, techniques based on tables of squares require less memory than techniques based on direct implementations. In this paper, we present a method to realize an n-bit multiplier using a table of squares for n-bit integers. A new technique to store tables of squares is also presented. The new scheme is shown to compare favorably, in terms of storage requ...

PDBsum additions

PDBsum, http://www.ebi.ac.uk/pdbsum, is a website providing numerous pictorial analyses of each entry in the Protein Data Bank. It portrays the structural features of all proteins, DNA and ligands in the entry, as well as depicting the interactions between them. The latest features, described here, include annotation of human protein sequences with their naturally occurring amino acid variants,...