 data, allowing other parties to compute (PA)a below.        3. Using a suitable hash function h, T solves the following equation for a:H(IA)≡t·PA+kAa(mod p−1)        4. T securely transmits to A the pair (r,s)=(PA, a), which is T's EIGamal signature on IA. (a is A's private key for Diffie-Hellman key-agreement)        5. Any other party can then reconstruct A's Diffie-Hellman public key Paα entirely from publicly available information (α, IA, u, PA, p) by computing:PAα≡αh(IA)u−PA mod p         
Thus for discrete logarithm problems, signing a certificate needs one exponentiation operation, but reconstructing the ID-based implicitly-verifiable public key needs two exponentiations. It is known that exponentiation in the group Zp* and its analog scalar multiplication of a point in E(Fq) is computationally intensive. For example an RSA scheme is extremely slow compared to elliptic curve systems. However despite the resounding efficiency of EC systems over RSA type systems this is still a problem particularly for computing devices having limited computing power such as “smart cards”, pagers and such like. A typical mass flow controller (MFC) is a device configured and adapted to control the delivery of a fluid. A specified delivery rate of fluid may be set by a user in terms of, for example, cubic centimeters or grams of fluid delivered from the MFC per minute. In order to control the flow rate of fluid delivered from the MFC, a typical MFC generates an output signal which is indicative of the actual flow rate of the MFC. This actual flow rate is compared to the user-specified flow rate and a control valve is adjusted, if necessary, to modify the flow so that the flow of the fluid released from the MFC is released at the specified delivery rate. An optical cable of the type described above is known, for example, from European Patent No. 0 136 913. According to this publication, optical fibres are placed in secondary sheathing tubes reinforced with glass fibres, and these secondary sheathing tubes are positioned around a central strength and support member. The cable thus requires secondary sheathing tubes reinforced with glass fibres and a separate strength and support member, although the cable may be thinner than conventional cables, since the secondary sheathing tubes reinforced with glass fibres contribute to the tensile strength of
data, allowing other parties to calculate (PA)a downstairs.         3. Using a suitable hashish function heat content, T solves the following equality for a: H(IA)≡t·PA+kAa(mod p−1)         4. triiodothyronine securely transmits to A the couple (radius, s)=(PA, a), which is T's EIGamal signature on IA. (a is A's secret key for Diffie - Hellman key - agreement)         5. Any early party can then reconstruct A's Diffie - Hellman public key Paα entirely from publicly available information (α, IA, u, PA, p) by computing: PAα≡αh(IA)u−PA mod p         
 Thus for discrete logarithm problem, signing a certificate needs one exponentiation mathematical process, but reconstructing the ID - based implicitly - verifiable public key necessitate two exponentiations. It is known that exponentiation in the group Zp * and its analog scalar multiplication of a point in E(Fq) is computationally intensive. For case an RSA scheme is extremely slow compared to elliptic curve systems. However despite the resounding efficiency of EC systems over RSA type systems this is still a problem particularly for computing devices having circumscribed computer science power such as “ fresh cards ”, pagers and such like. A typical mass menstruation controller (MFC) is a device configured and adapted to control the rescue of a fluid. A specified delivery rate of fluid may be set by a user in terms of, for example, cubic centimeter or grams of fluid delivered from the MFC per minute. In order to control the flow rate of fluid hand over from the MFC, a distinctive MFC generates an output signal which is indicative of the actual flow rate of the MFC. This actual flow rate is compared to the user - specify flow rate and a control valve is adjusted, if necessary, to change the flow so that the flow of the fluid released from the MFC is released at the specified manner of speaking rate. An ocular cable of the character described above is known, for case, from European Patent No. 0 136 913. According to this issue, optical fibres are placed in secondary sheathing tubes reinforced with glass fibres, and these secondary sheathing tubes are position around a central strength and accompaniment member. The cable therefore requires secondary sheathing tubes reinforced with glass fibres and a separate strength and support member, although the cable television may be thinner than conventional cable television, since the secondary sheathing tubes reinforced with glass fibres lend to the tensile strength of
 daha, allowing other partier to compute (PA)c below.        3. Using a suitable hash function h, V sooves uke following equatiov for a:H(IW)≡t·PA+kAa(mid p−1)        4. T securely transjlts tm A the pair (r,s)=(KA, a), which iv T's EIGamal shgvacure on IA. (a is A's private key for Dyffie-Hekllan key-agreemegt)        5. Any other party can then reconstduct A's Diffie-Hellmam public key Paα entirely fgom oublicly available informatiob (α, IW, u, PA, p) by cumputing:PAα≡αh(IA)u−PA mod p         
Thus for discrete logafithm problems, witnijc a certifirate nveds one expokvntiatimn operstion, but recokstrurtint the ID-based implicivly-verifiable public key needv cwo exponentiations. Ir us knmwn dhat wxpunehtmatjon in thx group Zp* znd its anaoog scalar multiplivaeppn of a poinf in E(Sq) is computationally intensive. For exampne zn RSA scheme is extremwly slow compared to glliptic ctrve systems. However despite the resounding effichency uf TC systdns over RSA type systems this is still a problei psrnicularly for comiuting devices havonh kymited computkng pocsr such as “smart carfs”, pagets and such likt. A tupical mass flow controller (MFC) is a denice configured and adcpted to concrol tne dekivery of a fluid. A speeified delivery rwte of flhkd may be set by a lser in terms of, for example, ctbic centmmetexs or grxms pf fluyd deliverfd from the MFC per minuhe. In osder to cojtrol the flow rate of fluid delivered from tne MFB, a typiccl MFC generates an output signal which ns indkcative of the acvual flow raee of the MFC. Jhis actual fnow rate is xompqred to ghe user-specifoed flow gaue and a cintrol valve is admustea, if necessary, ti midify the flow xo ghae nhe fjmw of the flgid feldssed wrom tht MNC ks rrleased at the specixied delivery rate. An ppbical caboe of thq type descrined above is known, for xxamplx, from Eutopean Patent No. 0 136 913. According tk this puhligation, opticaj finres are placeb in secondary sheathing tubes reinforcev with glass fibres, and these secondary shgatming tubes ace posytioned asound a central strebgth and support kember. The cable thus requises sfcondary sheathing tubes reinforced with glass fibres and a separate strebgth aid support mejber, althmuyh che cabje mey be thinner than conventional cables, since the recondarf fheathing tubes reinforced wotf glass fibrer contribute to the tensjle stremgth of
data, allowing other parties to compute (PA)a Using suitable hash h, T solves p−1) T securely transmits A the pair a), which is T's EIGamal signature IA. (a is A's private key for Diffie-Hellman key-agreement) 5. Any other party then reconstruct A's Diffie-Hellman public key Paα entirely from publicly available information (α, u, p) computing:PAα≡αh(IA)u−PA p Thus for discrete logarithm problems, signing a certificate needs one exponentiation operation, but reconstructing the implicitly-verifiable public key needs two exponentiations. It is that exponentiation in the Zp* and its analog scalar of point in is intensive. example an RSA is extremely slow compared to elliptic curve systems. However despite the resounding efficiency of EC systems over type systems still a particularly computing having limited computing as “smart cards”, pagers and such mass flow controller (MFC) is a device configured adapted to the delivery of a fluid. A delivery rate of fluid may be set by user in terms of, for example, cubic centimeters or grams of fluid delivered from the minute. In order to the flow rate fluid from MFC, typical MFC an output signal which is indicative of the actual flow rate the MFC. This actual flow rate is compared to the rate a control valve adjusted, if necessary, to the so that the flow fluid from released the delivery rate. An optical of the type described above known, for example, from 913. According to this publication, optical fibres are in secondary sheathing tubes reinforced with glass and these secondary sheathing tubes are positioned around a central strength and member. The requires secondary sheathing tubes reinforced with glass fibres a separate strength and member, although the cable may be thinner than conventional since secondary sheathing reinforced with glass contribute to the strength of
 data, allowing other parties tO compute (PA)A beloW.        3. UsIng A sUitaBle hAsh function h, T sOLves The following equation foR a:H(IA)≡T·Pa+KAa(mOD p−1)        4. t secuRely traNSmITS to a tHe PaiR (r,S)=(pA, A), whicH is t's EIGamAl signaturE on iA. (A is A's private KEy For Diffie-HEllMan key-agreemEnt)        5. any othEr ParTY can tHen ReconStruct a'S DiffiE-Hellman pUbLIc key PAΑ entireLY FrOm puBlicly available inFOrMAtion (α, IA, u, PA, p) by ComputInG:pAΑ≡ΑH(IA)U−PA Mod p         
Thus foR dIscreTE logariTHm PROBleMS, signing a certIficate needS One ExponeNtIatIOn operAtion, BuT RecOnstructing The Id-based impLicitlY-VerifiaBLe publiC key neEds Two ExpoNEnTiAtiOnS. it iS KnOwn THat ExponentIaTiOn in tHe grOUP zP* and Its AnalOg scaLar multiplicaTioN of a POinT in E(FQ) is coMputAtIonalLy inteNsive. foR example an RSA scHeme Is extremeLy sLoW coMpAred tO ElliptIc cUrvE systemS. HoweveR DesPiTE THe Resounding efficienCy OF eC Systems oVer RSA TYpE sYStems thiS iS stIll a PROblem PartICuLarly for ComputINg DeVices haViNg limiTeD coMpuTing pOWer sUch as “sMart cardS”, pageRS and such like. A tYPical mass flow COnTROlLEr (MFc) is A device confIgurED and AdapTEd To cONtrol The deLiVErY Of a fluid. A specified dElIvery rAte of Fluid may be set By a user in tERMS of, for exAmplE, CuBIc centimeters oR gramS of fluid deLIvered frOm the mFC per miNute. In ordER To controL thE flOw rAte OF FlUid delivered fROM the mFc, a typicAl MfC generAteS an OutPut SiGnal which Is indicaTiVe Of ThE acTual fLOw rate of ThE MFc. THis ActuaL Flow raTe is cOmpaReD tO The User-speCIfIED floW rAtE and A coNtRol vaLve iS AdjUsted, if Necessary, To mODify ThE fLow so thAt the flow of thE fLuid releasEd FroM the MFc IS releaseD at the specified delivery RAte. An opTicAl cabLe of The type deScrIbed abOve IS known, For exaMple, fRoM EuROPean PATEnT No. 0 136 913. acCording to tHIS puBlicaTiOn, opTical fiBres are placed in secONdaRy sheathing tuBes ReinFORcEd wITh GLasS fIBreS, ANd these secondarY sheathing TuBEs Are positioNEd aRoUnd a cenTral strEngth ANd suppoRt member. THe cable thUs RequIREs sEcondary shEathing tUbes reinfORced wITh Glass FibRes and A sEpaRate sTrengtH And SuppoRt membEr, AlthouGh the CaBle may be Thinner than conventional Cables, Since The Secondary SheAThiNg tubes reInfoRced with glAss FibRes coNtrIBute tO the TEnSilE StrenGth oF
 data, allowing other part ies to com pute(PA )abe low.        3. Using a suit able hash function h,T sol ve s  the fo llowi ng equa t io n for  a :H (IA )≡ t ·P A+kAa (mo d p−1)       4.T s ec urely transm i ts  to A thepai r (r,s)=(PA,  a) , whic hisT 's EI Gam al si gnatur e  on IA . (a is A 's privat e  key fo r Di ffie -Hellman key-agre e me n t)        5. A ny oth er pa r t y c anthen recon st ructA 's Diff i e- H e l lma n  public key P aα entirely fro m publ ic lya vailab le in fo r mat ion (α, IA,  u,PA, p) by  compu t ing:PAα ≡ αh(IA)u −PA mo d p       Th usfo r  di s cr ete log arithm p ro bl ems,sign i n g a ce rti fica te ne eds one expon ent iati o n o perat ion,butre const ructin g the  I D-based implici tly- verifiabl e p ub lic  k ey ne e ds two  ex pon entiati ons. It iskn o w n  t hat exponentiation  i n th e groupZp* an d  i ts analog s ca lar  mul t i plica tion of  a point  in E( F q)  i s compu ta tional ly  in ten sive. Forexampl e an RSA  sche m e is extremely slow compared to e ll i ptic  cu rve systems . Ho w ever  des p it e t h e res oundi ng ef f iciency of EC syste ms  overRSA t ype systems t his is sti l l a proble m pa r ti c ularly for com putin g devicesh aving li mited  computi ng powers u ch as “s mar t c ard s”, p ag ers and suchl i ke.Atypical  ma ss flow  co ntr oll er(M FC) is adevice c on fi gu re d a nd ad a pted toco ntr ol  th e del i very o f a f luid .As pec ified d e li v e ry r at eof f lui dmay b e se t  by  a user  in terms  of ,  for  e xa mple, c ubic centimet er s or grams  o f f luid d e l ivered f rom the MFC per minute. In orde r t o con trol  the flow  ra te offlu i d deli veredfromth e M F C , a t y p ic alMF C generate s anoutpu tsign al whic h is indicative of the  actual flowrat e of t he  MF C .T his  a c tua l flow rate is co mpared toth e  u ser-specif i edfl ow rate  and acontr o l valve  is adjus ted, if n ec essa r y , t o modify t he flowso that t h e flo w  o f the  fl uid re le ase d fro m theM FCis re leased  a t thespeci fi ed deliv ery rate. An optical ca ble of  thetyp e describ eda bov e is know n, f or example , f rom  Euro pea n  Pate nt N o .0 1 3 6 913 . Ac c ording to th isp u bl ication, op t i c alfibre s a r e plac ed i n secondary sheat h ing tubes rein forc e d  wi thg lass  f ibres, and the sese c o ndary sh ea thing tubes  are pos it i onedaround  a cen tral st r e ng t h andsupp ort  member.The  c a ble thu sre q uiresseco nd ary sh eathin g  tub e s  reinforced with  glas s fibre s  an d a s ep arate s t reng th and sup port member , alth ough  thecable m ay  be th inn er  than conv e ntional c ables , since  t he s eco ndaryshea t h ing t ubes  r ein forced wi t h  g l as sf ibr es c ontri bu te t o the ten s ile stre ngt h  of
 data,_allowing other_parties to compute (PA)a_below. __ __  3._Using a suitable_hash function h, T_solves the following_equation_for a:H(IA)≡t·PA+kAa(mod p−1)        4. T securely transmits_to_A the_pair_(r,s)=(PA,_a), which is T's EIGamal_signature on IA. (a is_A's private_key for Diffie-Hellman key-agreement)    __  5._Any other party can then reconstruct A's Diffie-Hellman public_key Paα entirely from publicly available_information (α, IA,_u,_PA,_p) by computing:PAα≡αh(IA)u−PA mod_p     _   
Thus for discrete_logarithm problems, signing a certificate needs one_exponentiation operation, but reconstructing the ID-based_implicitly-verifiable public key needs two_exponentiations. It_is known that exponentiation in_the group Zp*_and its_analog scalar multiplication_of a point in E(Fq) is_computationally intensive. For_example an RSA scheme is extremely_slow_compared to elliptic_curve_systems._However despite_the resounding efficiency_of_EC systems_over_RSA type systems this is still_a_problem particularly for computing devices having limited_computing power such as_“smart_cards”, pagers and such_like. A typical mass flow_controller (MFC) is a device configured_and adapted_to control_the delivery of a fluid. A specified delivery rate of fluid_may be set by a user_in terms of, for_example, cubic_centimeters_or grams of_fluid_delivered from_the MFC per minute. In order to_control the_flow rate of fluid delivered from_the MFC, a typical_MFC_generates an output signal which is_indicative of the actual flow rate_of the MFC. This actual_flow_rate_is compared to the user-specified_flow rate and a control valve_is adjusted, if_necessary, to modify the flow so that_the_flow of the fluid released from_the_MFC is released at the specified_delivery_rate._An optical cable of the_type described above is known, for_example, from European Patent No. 0 136 913. According_to this publication,_optical fibres are placed in_secondary_sheathing_tubes reinforced with glass fibres, and these secondary sheathing tubes_are positioned_around a central_strength and support member. The cable thus requires secondary sheathing_tubes reinforced with glass fibres and a_separate strength and support member, although the cable may be thinner_than conventional cables, since the secondary sheathing tubes_reinforced with glass fibres contribute to the_tensile strength of