In this paper, a generalized Montgomery multiplication algorithm in GF(2m) using the Toeplitz matrix-vector representation is presented. The hardware architectures derived from this algorithm provide low-complexity bit-parallel systolic multipliers with trinomials and pentanomials. The results reveal that our proposed multipliers reduce the space complexity of approximately 15% compared with an existing systolic Montgomery multiplier for trinomials. Moreover, the proposed architectures have the features of regularity, modularity, and local interconnection. Accordingly, they are well suited to VLSI implementation.

The authors present a multiparty signature generation (MSG) scheme of the Digital Signature Algorithm (FIPS 186-1). The scheme is based on a simple idea, however, it is much more convenient in usability in the real world than existing MSGs. The scheme has the following properties: (1) valid signatures are generated with odd n split private keys, (2) broadcast messages between the key holders are hidden from them, so that the n key holders do not need to process signature generation simultaneously, (3) even if up to t (= ) split keys are stolen, the adversary can get no information on the private key, (4) the scheme is as secure as the original signature algorithm against chosen message attack, and (5) the scheme is efficient in the sense that an implementation on smart card has demonstrated practical performance for interactive use with human user.