Timestamping is a cryptographic technique providing us with a proof-of-existence of a digital document at a given time. Combining both digital signature and provable time-stamping guarantees authentication, integrity and non-repudiation of electronic documents. In this paper, we introduce such a service, so called signtiming. Our scheme is based on an ID-based aggregate signature and is secure in the random oracle model.

We study binary self-dual codes with a fixed point free automorphism of order three. All binary codes of that type can be obtained by a cubic construction that generalizes Turyn's. We regard such "cubic" codes of length 3/spl lscr/ as codes of length /spl lscr/ over the ring F/sub 2//spl times/F/sub 4/. Classical notions of Type II codes, shadow codes, and weight enumerators are adapted to that ring. Two infinite families of cubic codes are introduced. New extremal binary codes in lengths /spl les/ 66 are constructed by a randomized algorithm. Necessary conditions for the existence of a cubic [72,36,16] Type II code are derived.

In this paper we propose a method which enables us to construct almost optimal broadcast schemes on an n-dimensional hypercube in the circuit switched, /spl Delta/-port model. In this model, an initiator must inform all the nodes of the network in a sequence of rounds. During a round, vertices communicate along arc-disjoint dipaths. Our construction is based on particular sequences of nested binary codes having the property that each code can inform the next one in a single round. This last property is insured by a flow technique and results about symmetric flow networks. We apply the method to design new schemes improving and generalizing the previous results. Our schemes are the best possible algebraic schemes, and they are optimal in the case n=2/sup p/-1.

We introduce linear cyclic codes over the ring F/sub 2/+uF/sub 2/={0,1,u,u~=u+1}, where u/sup 2/=0 and study them by analogy with the Z/sub 4/ case. We give the structure of these codes on this new alphabet. Self-dual codes of odd length exist as in the case of Z/sub 4/-codes. Unlike the Z/sub 4/ case, here free codes are not interesting. Some nonfree codes give rise to optimal binary linear codes and extremal self-dual codes through a linear Gray map.

We give a simple decoding algorithm to decode linear cyclic codes of odd length over the ring R=F/sub 2/+uF/sub 2/={0,1,u,u~=u+1}, where u/sup 2/=0. A spectral representation of the cyclic codes over R is given and a BCH-like bound is given for the Lee distance of the codes. The ring R shares many properties of Z/sub 4/ and F/sub 4/ and admits a linear "Gray map".

We give a method to compute the complete weight distribution of translates of linear codes over Z/sub 4/. The method follows known ideas that have already been used successfully by others for Hamming weight distributions. For the particular case of quaternary Preparata codes, we obtain that the number of distinct complete weights for the dual Preparata codes and the number of distinct complete coset weight enumerators for the Preparata codes are both equal to ten, independent of the code length.

Type II Z/sub 4/-codes are introduced as self-dual codes over the integers modulo 4 containing the all-one vector and with Euclidean weights multiple of 8. Their weight enumerators are characterized by means of invariant theory. A notion of extremality for the Euclidean weight is introduced. Their binary images under the Gray map are formally self-dual with even weights. Extended quadratic residue Z/sub 4/-codes are the main example of this family of codes. They are obtained by Hensel lifting of the classical binary quadratic residue codes. Their binary images have good parameters. With every type II Z/sub 4/-code is associated via construction A modulo 4 an even unimodular lattice (type II lattice). In dimension 32, we construct two unimodular lattices of norm 4 with an automorphism of order 31. One of them is the Barnes-Wall lattice BW32.

We construct new self-dual and isodual codes over the integers module 4. The binary images of these codes under the Gray map are nonlinear, but formally self-dual. The construction involves Hensel lifting of binary cyclic codes. Quaternary quadratic residue codes are obtained by Hensel lifting of the classical binary quadratic residue codes. Repeated Hensel lifting produces a universal code defined over the 2-adic integers. We investigate the connections between this universal code and the codes defined over Z/sub 4/, the composition of the automorphism group, and the structure of idempotents over Z/sub 4/. We also derive a square root bound on the minimum Lee weight, and explore the connections with the finite Fourier transform. Certain self-dual codes over Z/sub 4/ are shown to determine even unimodular lattices, including the extended quadratic residue code of length q+1, where q/spl equiv/-1(mod8) is a prime power. When q=23, the quaternary Golay code determines the Leech lattice in this way. This is perhaps the simplest construction for this remarkable lattice that is known.>