### Table 6. McEliece compared to some known signature schemes

2001

Cited by 19

### Table 1: Comparison of the characteristics of outsourced signatures vs. client-generated signatures

"... In PAGE 10: ... This problem may be mitigated by using different keys for groups of subscribers or even for every individual subscriber. The pros and cons of signature outsourcing against the client-side signing are summarized in Table1 . As it is concluded, there is no strong argument against the signature outsourcing, but in the contrary we identified several advantages of our proposed signature outsourcing scheme.... ..."

### Table 1. Allowed groups and signature Group

"... In PAGE 8: ... Let (M; g) be a 4 dimensional Einstein spin manifold which is conformally compact with conformal boundary @M = S3=? with ? SU(2). Then the allowed groups and signatures are those listed in Table1 . In case ? = fidg, then (M; g) is isometric to hyperbolic space.... ..."

### Table 1: Examples of Rp conserving SUSY signatures at the Tevatron. Prod. Signature Comments

### TABLE Signature of The group G = Isom X as

### Table 1: Signature for stack operations

2000

"... In PAGE 5: ... Signatures are well-known from the definition of abstract data types. For example, in the description of a stack we have sorts STACK, INT and BOOL, and operators push, pop, and empty, as shown in Table1 . A term of this signature is push(empty, 8).... In PAGE 17: ...Aggregation Aggregation reduces sets of points to points (Table 10). Operation Signature Semantics min, max ! [1D] min( (U)); max( (U)) avg ! [1Dnum] 1 jintvls(U)j P T2intvls(U) sup(T)+inf (T) 2 avg[center] points ! [2D] 1 n P p2U !p avg[center] line ! [2D] 1 kUk P c2sc(U) !c kck avg[center] region ! [2D] 1 M R U (x; y) dU where M = R U dU single ! if 9u : U = fug then u else ? Table1 0: Aggregate Operations In one-dimensional space, where total orders are available, closed sets have minimum and maximum values, and functions (min and max) are provided that extract these. For open and half-open intervals, we choose to let these functions return infimum and supremum values, i.... In PAGE 18: ....2.5 Numeric Properties of Sets For sets of points some well known numeric properties exist (Table 11). Operation Signature Semantics no components ! int [1D] jintvls(U)j no components points ! int jUj no components line ! int jblocks(U)j no components region ! int jfaces(U )j size[duration] ! real [1Dcont] P T2intvls(U) sup (T ) inf (T ) size[length] line ! real kUk size[area] region ! real R U dU perimeter region ! real flength(@U) Table1 1: Numeric Operations For example, the number of components (no components) is the number of disjoint max- imal connected subsets, i.e.... In PAGE 19: ... The time domain inherits arithmetics from the domain of real numbers, to which it is isomorphic. Operation Signature Semantics distance ! real [1Dcont] ju vj ! real [1Dcont] minfju vj jv 2 V g ! real [1Dcont] minfju vj ju 2 U; v 2 V g ! real [2D] dist(u; v) = p(u:x v:x)2 + (u:y v:y)2 ! real [2D] minfdist(u; v)jv 2 V g ! real [2D] minfdist(u; v)ju 2 U; v 2 V g direction point point ! real see below Table1 2: Distance and Direction Operations The direction between points is sometimes of interest. A direction function is thus included that returns the angle of the line from the first to the second point, measured in degrees (0 angle lt; 360).... In PAGE 19: ...ention them because they have to be included in the scope of operations to be lifted, i.e., the kernel algebra. Operation Signature Semantics and, or bool bool ! bool as usual (with strict evaluation) not bool ! bool Table1 3: Boolean Operations 4.2.... In PAGE 20: ... For values of intime types, the two trivial projection operations inst and val are offered, yielding the two components. Operation Signature Semantics deftime moving( ) ! periods dom( ) rangevalues moving( ) ! range( ) [1D] rng( ) locations moving(point) ! points isolated(rng( )) moving(points) ! points isolated(S rng( )) trajectory moving(point) ! line rng( ) n flocations( ) moving(points) ! line S rng( ) n flocations( ) traversed moving(line) ! region ((S rng( )) ) moving(region) ! region S rng( ) routes moving(line) ! line (S rng( )) n ftraversed( ) inst intime( ) ! instant t where u = (t; v) val intime( ) ! v where u = (t; v) Table1 4: Operations for Projection of Temporal Values into Domain and Range All the infinite point sets that result from domain and range projections are represented in collapsed form by the corresponding point set types. For example, a set of instants is represented as a periods value, and an infinite set of regions is represented by the union of the points of the regions, which is represented in turn as a region value.... In PAGE 22: ...o the given domain or range values, e.g., get the part of the moving point when it was within the region, or determine the value of the moving real at time t or within time interval [t1; t2]. Operation Signature Semantics atinstant moving( ) instant ! intime( ) (t; (t) quot; ) atperiods moving( ) periods ! moving( ) f(t; y) 2 jt 2 T g initial moving( ) ! intime( ) limt!inf(dom( )) (t) final moving( ) ! intime( ) limt!sup(dom( )) (t) present moving( ) instant ! bool (t) 6 = ? present moving( ) periods ! bool fatperiods( ; T ) 6 = ; at moving( ) ! moving( ) [1D] f(t; y) 2 jy = bg at moving( ) range( ) ! moving( ) [1D] f(t; y) 2 jy 2 Bg at moving( ) point ! mpoint [2D] f(t; y) 2 jy = ug at moving( ) ! moving(min( ; ))[2D] f(t; y) 2 jy 2 Ug atmin moving( ) ! moving( ) [1D] f(t; y) 2 jy = min(rng( ))g atmax moving( ) ! moving( ) [1D] f(t; y) 2 jy = max(rng( ))g passes moving( ) ! bool fat( ; x) 6= ; Table1 5: Interaction of Temporal Values With Values in Domain and Range In Table 15, the first group of operations concerns interaction with time domain values, the second interaction with range values. Operations atinstant and atperiods restrict a moving entity to a given instant, resulting in a pair (instant, value), or to a given set of time intervals, respectively.... In PAGE 22: ...o the given domain or range values, e.g., get the part of the moving point when it was within the region, or determine the value of the moving real at time t or within time interval [t1; t2]. Operation Signature Semantics atinstant moving( ) instant ! intime( ) (t; (t) quot; ) atperiods moving( ) periods ! moving( ) f(t; y) 2 jt 2 T g initial moving( ) ! intime( ) limt!inf(dom( )) (t) final moving( ) ! intime( ) limt!sup(dom( )) (t) present moving( ) instant ! bool (t) 6 = ? present moving( ) periods ! bool fatperiods( ; T ) 6 = ; at moving( ) ! moving( ) [1D] f(t; y) 2 jy = bg at moving( ) range( ) ! moving( ) [1D] f(t; y) 2 jy 2 Bg at moving( ) point ! mpoint [2D] f(t; y) 2 jy = ug at moving( ) ! moving(min( ; ))[2D] f(t; y) 2 jy 2 Ug atmin moving( ) ! moving( ) [1D] f(t; y) 2 jy = min(rng( ))g atmax moving( ) ! moving( ) [1D] f(t; y) 2 jy = max(rng( ))g passes moving( ) ! bool fat( ; x) 6= ; Table 15: Interaction of Temporal Values With Values in Domain and Range In Table1 5, the first group of operations concerns interaction with time domain values, the second interaction with range values. Operations atinstant and atperiods restrict a moving entity to a given instant, resulting in a pair (instant, value), or to a given set of time intervals, respectively.... In PAGE 23: ....3.3 The Elusive when Operation We now consider (speculate about) an extremely powerful yet conceptually quite simple oper- ation called when, whose signature is shown in Table 16. The idea is that we can restrict a Operation Signature Semantics Syntax when moving( ) ( ! bool) ! moving( ) f(t; y) 2 j p(y)g arg1 op[arg2] Table1 6: The when Operation time dependent value to the periods when its range value fulfils some property specified as a predicate. If we had such an operator, we could express a query such as Restrict a moving region mr to the times when its area was greater 1000 as: mr when[FUN (r:region) area(r) gt; 1000] Here the result would be of type mregion again.... In PAGE 26: ...Signature Semantics derivative mreal ! mreal 0 where 0(t) = lim !0( (t + ) (t))= speed mpoint ! mreal 0 where 0(t) = lim !0 fdistance( (t + ); (t))= turn mpoint ! mreal 0 where 0(t) = lim !0 fdirection( (t + ); (t))= velocity mpoint ! mpoint 0 where 0(t) = lim !0( (t + ) (t))= Table1 7: Derivative Operations between two points, and the vector difference (viewing points as 2D vectors). This leads to three different derivative operations, which we call speed, turn, and velocity, respectively.... In PAGE 27: ... 4.2 Table1 8: Operations on Sets of Database Objects The syntax for applying this operator is arg1 op[arg2; arg3]. The semantics can be defined formally as follows.... ..."

Cited by 114

### Table 2. Group signature entities equivalence in HiPS Group Signature [6] Naming

### Table 7 Signature for regulated coordination style

1906

"... In PAGE 10: ...s a set of rules. Rules regulate the sending and receiving of messages. The event types Sent and Arrived are used to instantiate rules. The signature for the RC style is given in Table7 . We reuse the signature to define and group actors from the GA style.... ..."

Cited by 8

### Table 2.10: The ElGamal signature scheme is an indeterministic signature scheme based on the discrete logarithm problem.

in Advisors

2004