Anonymous Attribute-Based Credentials in Collaborative Indoor Positioning Systems

Anonymous A ibu e-based C eden ials in Collabo a i e Indoo Posi ioning Sys ems Ra´ ul Casano a-Ma qu´ es1,2 a, Pa el Pascacio2,3 b, Jan Hajny1 c and Joaqu´ ın To es-Sosped a2,4 d 1Depa men o Telecommunica ions, B no Uni e si y o Technology, B no, Czech Republic 2Ins i u e o New Imaging Technologies, Uni e si a Jaume I, Cas ell´ on, Spain 3Elec ical Enginee ing Uni , Tampe e Uni e si y, Tampe e, Finland 4UBIK Geospa ial Solu ions S.L., Cas ell´ on, Spain Keywo ds: A ibu e-based C eden ials, Collabo a i e Indoo Posi ioning Sys ems, P i acy, Anonymi y, Blue oo h Low Ene gy, Wea ables. Abs ac : Collabo a i e Indoo Posi ioning Sys ems (CIPSs) ha e ecen ly ecei ed conside able a en ion, mainly be- cause hey add ess some exis ing limi a ions o adi ional Indoo Posi ioning Sys ems (IPSs). In CIPSs, Blue- oo h Low Ene gy (BLE) can be used o exchange posi ioning da a and p o ide in o ma ion ( he Recei ed Signal S eng h Indica o (RSSI)) o es ablish he ela i e dis ance be ween he ac o s. The collabo a i e mod- els exploi he posi ion o ac o s and he ela i e posi ion among hem o allow posi ioning o ex e nal ac o s o imp o e he accu acy o he exis ing ac o s. Howe e , he adi ional p o ocols (e.g., iBeacon) a e no ye eady o p o iding su icien p i acy p o ec ion. This pape deals wi h p i acy-enhancing echnologies and hei applica ion in CIPS. In pa icula , we ocus on c yp og aphic schemes which allow he e i ica ion o use s wi hou hei iden i ica ion, so-called Anonymous A ibu e-based C eden ial (ABC) schemes. As he main con ibu ion, we p esen a c yp og aphic scheme ha allows secu i y and p i acy- iendly sha ing o loca ion in o ma ion sen h ough BLE ad e ising packe s. In o de o demons a e he p ac icali y o ou scheme, we also p esen he esul s om ou implemen a ion and benchma ks on di e en de ices. 1 INTRODUCTION Wi-Fi and BLE inge p in ing a e popula echniques o p o iding indoo posi ioning. They ely on he signal s eng h om mul iple emi e s (ei he Wi-Fi Access Poin s (APs) o BLE beacons). Howe e , he Recei ed Signal S eng h (RSS) da a used o es ima e he posi ions ha e a s ong noise componen , he e- o e ha ing a gene al posi ioning accu acy a me e le el (i.e., a ew me e s) (Mau z, 2012). In addi ion, he deploymen complexi y, as well as elying on an in as uc u e o beacons and se e s, ha e become a se ious p oblem o la ge o ganiza ions all a ound he wo ld. Wea able-based CIPSs a e inc easingly be- coming popula o e he las ew yea s as a solu ion o add ess hose p oblems in indoo posi ioning (Pas- cacio e al., 2021). The CIPSs use he loca ion o a ah ps://o cid.o g/0000-0001-6653-867X bh ps://o cid.o g/0000-0001-9206-7496 ch ps://o cid.o g/0000-0003-2831-1073 dh ps://o cid.o g/0000-0003-4338-4334 se o ac o s and hei ela i e dis ances o 1) p o ide localiza ion o ex e nal use s and/o 2) imp o e he posi ioning accu acy o he cu en use s ha a e col- labo a ing (Khandke e al., 2019). Wea able de ices a e equipped wi h buil -in ech- nologies such as Wi-Fi and Blue oo h, which a e ca- pable o es ima ing use s’ posi ions and ubiqui y in indoo en i onmen s. In pa icula , CIPSs app oaches based on BLE a e one o he mos popula solu ions. Sma phones can send BLE ad e isemen packe s (e.g., iBeacon), which can be used la e o compu e he ela i e dis ances be ween hem wi h he ga he ed RSS alues. This al e na i e p esen s a s aigh o - wa d deploymen and a good ade-o be ween powe consump ion and pe o mance (Yang e al., 2020). Howe e , high in e -connec i i y o unknown de ices and he lack o s ong communica ion p o ocols in e ms o secu i y and p i acy ep esen a weakness. Malicious ac o s could pe o m a acks such as spoo - ing o ea esd opping in unsecu ed collabo a i e sys- ems (Chebli e al., 2019). These issues encou aged he de elopmen o mo e p i acy- iendly solu ions. Casano a-Ma qués, R., Pascacio, P., Hajny, J. and To es-Sosped a, J. Anonymous A ibu e-based C eden ials in Collabo a i e Indoo Posi ioning Sys ems. DOI: 10.5220/0010582507910797 In P oceedings o he 18 h In e na ional Con e ence on Secu i y and C yp og aphy (SECRYPT 2021), pages 791-797 ISBN: 978-989-758-524-1 Copy igh c 2021 by SCITEPRESS – Science and Technology Publica ions, Lda. All igh s ese ed 791 Exis ing CIPS a e based on cen alized schemes. A se e -based solu ion acili a es mo e complex a - acks such as use aceabili y o linkabili y o com- munica ions. Thus, i is necessa y o mo e o a decen- alized app oach. Building a decen alized CIPS us- ing BLE echnology ep esen s a majo challenge due o he educed space a ailable in BLE packe s, which depends on he Blue oo h e sion (Blue oo h SIG, 2019). This hinde s he use o s anda d algo i hms such as RSA, DH o AES o in o ma ion enc yp- ion and use au hen ica ion. A ibu e-based au hen- ica ion schemes allow use s o anonymously and se- lec i ely p o e possession o hei pe sonal a ibu es such as age, ci izenship, nega i e SARS-CoV-2 es o loca ion da a. Ellip ic cu e c yp og aphy and he educed size o i s keys can ackle he a o emen ioned p oblems and p o ide anonymi y, unlinkabili y, un- aceabili y and selec i e disclosu e o a ibu es. In ligh o he iden i ied p oblems, in his wo k we pu sue he decen aliza ion o collabo a i e indoo posi ioning sys ems based on BLE beacons, while p o iding, h ough ellip ic cu e c yp og aphy and anonymous a ibu e-based au hen ica ion schemes, a secu e and p i acy- iendly sys em o exchanging lo- ca ion da a. 1.1 Rela ed Wo k In he li e a u e he e a e se e al a icles ha add ess anonymi y, secu i y, and p i acy issues o IPSs om di e en pe spec i es (e.g., Wi eless Senso Ne wo k (WSN) o In e ne o Things (IoT)). Howe e , only e y ew o hem ocus on collabo a i e posi ioning and/o BLE beacon app oaches. One o he mos in- e es ing pape s is p oposed by (Kang e al., 2018), which is based on he open-sou ce Eddys one BLE o ma p oposed by (Hassidim e al., 2016). Eddy- s one BLE o ma in oduces a scheme o mi iga e acking and secu i y h ea s. The co e o he scheme is cloud-based Epheme al Iden i ie s (EID), which en- su es only au ho ized membe s o p ope ly iden i y he BLE s anda d beacons. Up o now, a oo li le a en ion has been paid o CIPSs. (Zidek e al., 2018) de eloped a scheme named Bell ock which combines an ecosys em o s anda d beacons and use -based beacons. Bell- ock p o ides access con ol o s anda d beacons and anonymi y o use -based beacons by using h ee echniques o gene a e pseudo-anonymous iden i ie s ( andom, synch onized, and enc yp ed) ha can be unmasked by a se e . (Des ia i e al., 2017) p oposed he Da a T ans- mission Scheme o Indoo Mobile Coope a i e Lo- caliza ion Sys em ha wo ks o e Wi-Fi. The scheme uses AES-128 o enc yp he message, MD5 o con- s uc he HMAC and RSA-2048 o enc yp bo h he AES key and he HMAC. Thei app oach migh no be well sui ed as he sys em emains ulne able o man-in- he-middle a acks du ing he RSA key-pai exchange, leading o a o al loss o con iden iali y and message in eg i y. A key p oblem wi h he a o emen ioned p opos- als lies in se e -dependency, u ning he sys em in o a cen alized en i onmen . This me hod could su e om a ple ho a o pi alls such as denial o se ice (DoS), spoo ing, e c. Some p elimina y wo k on ABCs was ca ied ou se e al decades ago by (Chaum, 1985), (B ands, 2000), and (Camenisch and Lysyanskaya, 2001). In subsequen yea s, much mo e in o ma ion on ABCs has become a ailable abou p ac ical applica ions (A aoui e al., 2015), e oca ion p o ocols (Ca- menisch e al., 2010) and he use o mo e e icien algeb aic s uc u es (Chase e al., 2014), (Ba ki e al., 2016), and (Ringe s e al., 2017). Due o he high compu a ional complexi y equi ed by hese schemes, p ac ical implemen a ion on cons ained de ices is s ill a challenge, esea che s need o ind a scheme ha sa is ies hei speci ic needs. As a as we know, no s udies ha e been published on ABC schemes ap- plied o CIPSs. 1.2 Ou Con ibu ion In o de o ill he gap ound in he li e a u e, we p o- pose a new decen alized p i acy-p ese ing use au- hen ica ion mechanism o CIPSs wi h ABC. Ou solu ion combines ze o-knowledge p oo s wi h a e- oca ion scheme based on li e ime and p o ides anonymi y, unlinkabili y and un aceabili y. The main con ibu ions a e he ollowing: • To he bes o ou knowledge, we p esen he i s decen alized secu i y scheme o CIPSs based on BLE ad e ising. • We de ine a scheme ha p o ide anonymous lo- ca ion da a sha ing, decen alized au hen ica ion and o line e oca ion. • We p o ide a secu i y analysis on he p oposed solu ion. • We desc ibe he implemen a ion esul s. The es o he pape is o ganized as ollows. Sec- ion 2 gi es a b ie o e iew o he sys em model. Sec ion 3 ho oughly de ails he c yp og aphic design o he scheme. Sec ion 4 analyzes he secu i y. Sec- ion 5 p esen s he implemen a ion esul s. Finally, Sec ion 6 epo s some conclusions. SECRYPT 2021 - 18 h In e na ional Con e ence on Secu i y and C yp og aphy 792 2 SYSTEM OVERVIEW The sys em model is depic ed in Figu e 1 and consis s o he ollowing en i ies: •Issue (I): is esponsible o issuing he pe sonal a ibu e mID o a use using he Issue algo i hm. The mID a ibu e ep esen s he use iden i ie ob ained du ing egis a ion in he sys em. The Issue algo i hm p o ides he use wi h c yp o- g aphically signed c eden ials ha a e alid wi hin he sys em. Access c eden ials consis o he al- ues σ,σx0,σx ,σxID . •Re oca ion Au ho i y (RA): emo es in alid use s. Access con ol is achie ed h ough he e- oca ion c eden ial σx , issued om he e oca- ion a ibu e m . A emp ing o au hen ica e wi h he e oked c eden ials will esul in ailu e. To educe he complexi y o he sys em, we will con- side om now on he e oca ion au ho i y and he issue as he same en i y (I). •Use (U): en olls in he sys em o use he col- labo a i e indoo posi ioning sys em. E e y use holds unique c eden ials gene a ed by he issue and he e oca ion en i y (σ,σx0,σx ,σxID ), hen, he use can anonymously p o e hei possession o he e i ie using he Show algo i hm. •Ve i ie (V): e i ies he possession o he use a - ibu e using he Ve i y algo i hm. I he a ibu e owne ship is e i ied success ully, he e i ie will be able o use he loca ion in o ma ion o posi ion hemsel . O he wise, he in o ma ion is ejec ed. Issue Re oca ion Au ho i y Show Ve i y IssueIssue Use Ve i ie Figu e 1: Sys em s uc u e. Ini ially, all de ices egis e ed in he sys em beha e as Use s. When one o hem needs o imp o e i s posi- ion, i empo a ily assumes he ole o Ve i ie . This ole can be used o ensu e ha he in o ma ion is p o- ided by a alid use . The e a e wo modes o ope a ion o he Use and Ve i ie oles: he ac i e mode and he passi e mode. Use ope a ion modes: 1) Ac i e mode: esponds o e i ie eques s and assis s hem wi h posi ioning by ac i ely pa icipa ing in he sys em. 2) Passi e mode: emains unno iced in he sys em and does no espond o e i ie eques s. In his mode, he use does no in e ac wi h he sys em. Ve i ie ope a ion modes: 1) Ac i e mode: ac i ely eques s loca ion da a om nea by use s o imp o e i s posi ion. 2) Passi e mode: emains hidden in he sys em and wai s o o he e i ie s o eques loca ion da a. In his mode, posi ioning is no possible i he e a e no ac i e e i ie s nea by. Figu e 2 depic s each o hese ou modes. Use A ac s in ac i e mode, use B ac s in passi e mode, e i ie C ac s in ac i e mode, and e i ie D ac s in passi e mode. º Ve i ie C Use B Ve i ie D Use A Ve i ie eques Use esponse Figu e 2: Sys em oles and ope a ion modes. These modes o ope a ion a e use ul o imp o ing p i acy in en i onmen s whe e he e a e ew de ices, and i may be easy o de e mine hei iden i y. In his case, he use o e i ie can go in o passi e mode and disappea om he sys em. We will no go in o u he de ails because i is beyond he scope o his pape . 3 CRYPTOGRAPHIC DESIGN This sec ion desc ibes he p o ocol o use au hen i- ca ion in a collabo a i e indoo posi ioning sys em. 3.1 P elimina ies The symbol Hdeno es a secu e hash unc ion. We w i e a$ ←Awhen ais sampled uni o mly a andom om A. Le edeno e a bilinea map G1×G2→GT. 3.2 P o ocol Speci ica ion Fi s , he use mus be egis e ed in he sys em by sending hei pe sonal in o ma ion o he issue . The issue gene a es he c eden ials and sends hem o he use . The use can now legi ima ely pa icipa e in he sys em. This algo i hm will be deno ed as Issue. Anonymous A ibu e-based C eden ials in Collabo a i e Indoo Posi ioning Sys ems 793 When he e i ie wan s o imp o e hei posi ion, a BLE ad e isemen packe wi h a imes amp will be b oadcas . The nea by use s will compu e he p oo o knowledge and ansmi i ia ano he BLE packe . This algo i hm will be deno ed as Show. Finally, he e i ie will ensu e h ough he p oo o knowledge ha he use has alid c eden ials and will use he loca ion in o ma ion o posi ion hemsel . This algo i hm will be deno ed as Ve i y. 3.2.1 Issue To egis e he use in he sys em and gene a e he alid c eden ials, he use and he issue pe o m he algo i hm shown in Figu e 3. Use Issue q,G1,G2,GT,e,g1,g2←G(1τ),pkI (mID)skI= (x0,x ,xID),pkI=gx0 2 m =ww/yyyy mID −−−−−−−−−−−−−−−−−−−−→ σ=g 1 x0+m x +mIDxID 1σx0←σx0 σx ←σx σxID ←σxID σ,σx0,σx ,σxID ←−−−−−−−−−−−−−−−−−−−− S o e: σ,σx0,σx ,σxID Figu e 3: De ini ion o he Issue algo i hm. • The use U pe o ms he ollowing s eps: 1) In oduces pe sonal in o ma ion in he app. 2) Es ablishes a secu e communica ion channel wi h I and sends mID. • The issue I pe o ms he ollowing s eps: 1) Gene a es he use ’s p i a e keys x and xID. 2) Signs he a ibu es m and mID wi h he is- sue ’s sec e key as σ=g 1 x0+m x +mIDxID 1; and compu es auxilia y alues σx0,σx ,σxID , whe e σx0←σx0,σx ←σx , and σxID ←σxID . 3) Sends σand auxilia y alues σx0,σx ,σxID o he use U. 3.2.2 Show and Ve i y To b oadcas he loca ion in o ma ion and he p oo o knowledge, and subsequen ly e i y ha i comes om a legi ima e use , he use and he e i ie will un he algo i hms shown in Figu e 4. • The e i ie V pe o ms he ollowing s eps: 1) Gene a es a nonce based on he cu en ime. 2) C ea es a BLE ad e ising packe wi h he nonce and b oadcas s i . Use Ve i ie q,G1,G2,GT,e,g1,g2←G(1τ),pkI λ= (al i ude,longi ude,la i ude,...)m =ww/yyyy imes amp ←−−−−−−−−−−−−−−−−−− ρ,ρκ,ρ ,ρID $ ←Z∗ q ˆ σ←σρ,ˆ σx0←σρ x0 ˆ σx ←σρ x ,ˆ σxID ←σρ xID κ←gρκ 1σρIDρ xID e←H( κ,ˆ σ,ˆ σx0,ˆ σx ,ˆ σxID , imes amp,λ) sκ←ρκ+eρ sID ←ρID −emID ψ←(ˆ σ,ˆ σx0,ˆ σx ,ˆ σxID ) π←(e,sκ,sID)ψ,π,λ −−−−−−−−−−−−−−−−−→ 0 κ←gsκ 1ˆ σ−e x0ˆ σ−em x ˆ σsID xID e? =H( 0 κ,ˆ σ,ˆ σx0,ˆ σx ,ˆ σxID , imes amp,λ) e(ˆ σx0,g2) = e(ˆ σ,pkI) Figu e 4: De ini ion o he Show and Ve i y algo i hms. • Nea by use s uipe o m he ollowing s eps a e hey ha e ecei ed he imes amp: 1) Checks ha he imes amp gene a ed as a nonce by he e i ie is less han 2 seconds om he cu en ime o a oid eplay a acks. 2) Gene a es he andomize s ρ,ρκ,ρ ,ρID. 3) Compu es ˆ σ,ˆ σx0,ˆ σx ,ˆ σxID , whe e ˆ σ←σρ, ˆ σx0←σρ x0,ˆ σx ←σρ x , and ˆ σxID ←σρ xID . 4) Compu es he a ibu e p oo o knowledge κ as κ←gρκ 1σρIDρ xID . 5) Calcula es he c yp og aphic hash eas H( κ,ˆ σ,ˆ σx0,ˆ σx ,ˆ σxID , imes amp,λ)and he auxilia y p oo o knowledge alues sκ,sID, whe e sκ←ρκ+eρand sID ←ρID −emID. 6) C ea es a BLE ad e ising packe wi h he lo- ca ion in o ma ion λand he p oo o knowl- edge ψ←(ˆ σ,ˆ σx0,ˆ σx ,ˆ σxID ),π←(e,sκ,sID), and ansmi s i by b oadcas . • Nea by e i ie s iexecu e he ollowing s eps a - e ecei ing ψ,π, and λ. 1) Recompu es he a ibu e p oo o knowledge 0 κ as 0 κ←gsκ 1ˆ σ−e x0ˆ σ−em x ˆ σsID xID . 2) Calcula es he c yp og aphic hash using 0 κ as H( 0 κ,ˆ σ,ˆ σx0,ˆ σx ,ˆ σxID , imes amp,λ)and checks i i ma ches he alue o e. 3) Compu es he bilinea pai ing e(ˆ σx0,g2) = e(ˆ σ,pkI) o e i y he c eden ials we e emi ed by he issue . 3.3 Blue oo h In eg a ion The p oposed scheme ansmi s in o ma ion using BLE ad e ising packe s. Blue oo h 4.2 and ea lie SECRYPT 2021 - 18 h In e na ional Con e ence on Secu i y and C yp og aphy 794 de ined a payload size o 31 by es o a single BLE ad e isemen packe . Howe e , since i is imp ac i- cal o pack bo h he posi ioning da a and he p oo o knowledge in o 31 by es, we ha e conside ed e sion 5.0 o he BLE p o ocol. Blue oo h 5.0 in oduced a signi ican imp o emen by inc easing he capaci y o ad e ising packe s. Wi h Low-Ene gy Ad e ising Ex ensions, he ad e isemen payload can hold up o 254 by es (Blue oo h SIG, 2019). To build he s uc u e o he BLE ad e ising packe , we ha e assumed he s uc u e depic ed in Figu e 5. 01 2 345 6 78910 11 12 13 14 15 UUID ψ←(ˆ σ,ˆ σx0,ˆ σx ,ˆ σxID ) 120B 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 ψ 12B π←(e,sκ,sID) 92B λ 22B Figu e 5: De ini ion o he BLE ad e ising payload. The UUID ield occupies 8 by es, he p oo o knowl- edge (ψ,π) consis s o 224 by es, and he e is a ee space o 22 by es o he posi ioning da a (λ). This pa is explained in de ail in Sec ion 5. 4 SECURITY ANALYSIS The p o ocol is composed o he ollowing pa s: he anonymous c eden ials scheme, he e oca ion scheme and he posi ioning in o ma ion. In his sec- ion we p o ide a b ie in o mal secu i y analysis o each o hem. 4.1 Anonymous C eden ials Following he secu i y model de ined by (Chase e al., 2014) o anonymous c eden ial schemes, i is e- qui ed o mee he ollowing p ope ies: •Co ec ness: hones use s can p oduce an accep - ing p oo . •Un o geabili y: dishones use s canno p oduce an accep ing p oo . •Anonymi y: use s canno be iden i ied based on he alues o a ibu es. •Key-Pa ame e Consis ency: e e y public key has a dis inc p i a e key. Based on he andom O acle model in (Camenisch e al., 2019), he c eden ial scheme used in ou sys em has p o en o be secu e unde he n-SCDHI assump- ion (de ined below). De ini ion 1 (n-S ong Compu a ional Di ie-Hell- man In e sion P oblem (SCDHI)).Le Obb(·)on in- pu (m1,...,mn)∈Z∗ q nadd (m1,...,mn) o Q and ou - pu g1/(x0+∑n i=1ximi). Le Odhi(·)on inpu h ou pu hxi. De ine he ad an age o Aas ollows. Ad n−SCDHI(A) = P h(G,g,q)←G oupSe up(1κ), (x0,...,xn)$ ←Z∗ q n+1,(y,m∗ 1,...,m∗ n)← AObb(·),Odh0(·),...,Odhn(·)(g):y=g 1 x0+∑n i=1xim∗ i∧ (m∗ 1,...,m∗ n/∈Qi.(1) SCDHI is ( ,ε)-ha d i no - ime ad e sa y has ad- an age a leas ε. 4.2 Re oca ion Scheme Following he secu i y model de ined by (Camenisch e al., 2016), i is equi ed o mee he ollowing p op- e ies: •Re oca ion Comple eness: un e oked use s will pass he e oca ion check. •Re oca ion Soundness: e oked use s will no pass he e oca ion check. •Re oca ion P i acy: use s will no lose p i acy by p o ing an un e oked e oca ion handle. The e oca ion scheme is based on he epoch’s ex- pi a ion. In ou solu ion, we se he epoch o one week and de ine he e oca ion a ibu e as ollows: m ←ww/yyyy. When he c eden ials expi e, he use mus enew hem, allowing weekly access con ol. We assume ha all use s in he sys em ha e he da e co ec ly se on hei de ices. When a use em- po a ily swi ches o he e i ie ole, hey can p oduce he e oca ion a ibu e wi hou equi ing he use o disclose i . 4.3 Loca ion In o ma ion The posi ioning in o ma ion is he c i ical componen o he sys em. We ou line he esis ance o he p o- ocol agains some o he mos common a acks ha a ec he in eg i y and con iden iali y. Ea esd opping A ack: A audulen use could moni o he communica ions and a emp o de- anonymize a legi ima e use because he in o ma ion is sen in plain ex . Cap u ing communica ions is possible since he in o ma ion is eely ansmi ed. Howe e , emo ing anonymi y and a emp ing o link a speci ic use o posi ioning da a is ex emely di i- cul . Each ime a use ansmi s he posi ion, he c e- den ials a e andomized. Anonymous A ibu e-based C eden ials in Collabo a i e Indoo Posi ioning Sys ems 795 Replay A ack: A malicious use could ca y ou his a ack because he in o ma ion is no al e ed. Bu a e wo seconds, he e i ie ansmi s a new imes amp, in alida ing he packe ’s au hen ica ion. Du ing e i ica ion wi h he new imes amp, e? = H(..., imes amp,...)will p oduce a di e en alue and he e i ica ion will ail. Spoo ing A ack: A dishones use could a emp o impe sona e a legi ima e use and y o p o ide ake in o ma ion o he sys em. This a ack is imp ac ical because a use wi hou alid c eden ials will be unable o au hen ica e he da a. Tampe ing A ack: A malicious use could a emp o modi y an au hen ica ed packe o al e he posi- ioning o use s. This a ack is un easible because in case λis modi ied, e? =H(...,λ)will p oduce a di - e en alue and he e i ica ion will ail. 5 IMPLEMENTATION RESULTS In his sec ion, we p esen he esul s o he imple- men a ion o ou p o ocol on di e en sma phones. Table 1 shows he ha dwa e and so wa e speci ica- ions o he de ices used. Table 1: HW and SW speci ica ions o he sma phones. De ice CPU OS Blue oo h RAM Samsung Galaxy S21+ 5G Exynos 2100 And oid 11 5.0 LE 8 GB Samsung Galaxy S20 FE Exynos 990 And oid 10 5.0 LE 6 GB Samsung Galaxy A52 SDM720G And oid 11 5.0 LE 6 GB Samsung Galaxy A32 MTK D720 Dual + Hexa And oid 11 5.0 LE 4 GB Samsung Galaxy S8 Exynos 8895 And oid 9 5.0 LE 4 GB We ha e used ellip ic cu e c yp og aphy o he im- plemen a ion and design o he p o ocol. The im- plemen a ion is based on he mcl c yp og aphic li- b a y (Shigeo, 2018). I allows us o c ea e po able applica ions be ween di e en de ices and ope a ing sys ems and suppo s he op imal A e pai ing o e BN cu es. We use he 256-bi Ba e o-Naeh ig cu e (BN254) p o ided by he lib a y and compiled i using OpenSSL (The OpenSSL P ojec , 2003) and GMP (G anlund, 2014) as dependencies. We ob- se ed in (Hajny e al., 2018) ha he GMP lib a y achie es he bes pe o mance esul s o bilinea pai - ing ope a ions. Wi h his cu e size, an uncomp essed poin occupies 64 by es and a comp essed poin 33 by es. The size o a scala in ege is 32 by es. To educe he size o he in o ma ion, we ha e consid- e ed ansmi ing he poin s in hei comp essed o m. Fu he mo e, we used he OpenSSL lib a y o com- pu e c yp og aphic hashes. In pa icula , he SHA-2 unc ion wi h a diges size o 224 bi s. We ha e implemen ed he p o ocol in C o mea- su e he pe o mance on a Raspbe yPi 4. The execu- ion on his de ice is in he o de o µs. The sma - phone applica ion has been de eloped in Ja a and Ko lin. The And oid NDK (Na i e De elopmen Ki ) allows us o implemen pa s o ou app in na i e code, using languages such as C and C++. This allows us o call he mcl lib a y unc ions h ough he Ja a Na i e In e ace (JNI). Finally, we benchma k he en i e p o ocol wi hou including he communica ion o e head o e alua e he pe o mance and speed o he algo i hms. The esul s o he execu ion a e shown in Figu e 6. We can see he execu ion o bo h p o ocols akes sligh ly mo e han 10 ms on he slowes de ice. Du ing he de elopmen we used he Ene gy P o ile o And oid S udio and did no de ec an ene gy consump ion impac . Show Ve i y 0 2 4 6 8 1.21 2.88 1.78 3.66 2.87 6.96 3.11 7.26 3.57 7.64 Time [ms] S. Galaxy S21+ 5G S. Galaxy S20 FE S. Galaxy A52 S. Galaxy A32 S. Galaxy S8 Figu e 6: Speed compa ison o he Show and Ve i y algo- i hms. 6 CONCLUSION Ou solu ion allows sha ing anonymous loca ion in- o ma ion in CIPSs using BLE ad e isemen , p o id- ing eal p i acy in a ully decen alized sys em whe e sou ces o da a can be us ed. No wi hs anding he ela i ely limi ed implemen a ion on cons ained de- ices, his wo k o e s aluable insigh s in o he se- cu i y and pe o mance o implemen ing anonymous ABC schemes on CIPSs. As a as we know, we p esen he i s ully decen alized scheme unning o e BLE. Ou app oach has p o en o be e icien on SECRYPT 2021 - 18 h In e na ional Con e ence on Secu i y and C yp og aphy 796 mobile de ices and comple ely easible o eal- ime en i onmen s. Nex , we plan o imp o e he p o ocol o educe he size o he c yp og aphic pa , imp o e he e oca ion scheme, p o ide in o ma ion enc yp- ion, and s a deploymen in eal en i onmen s. ACKNOWLEDGMENT The au ho s g a e ully acknowledge unding om Eu opean Union’s Ho izon 2020 Resea ch and In- no a ion p og amme unde he Ma ie Sklodowska Cu ie g an ag eemen No. 813278 (A-WEAR, h p: //www.a-wea .eu/) and om Minis y o he In e- io o he Czech Republic unde g an VJ01030002. J. To es-Sosped a acknowledges unding om IN- SIGNIA p ojec ( e . PTQ2018-009981, MICINN). REFERENCES A aoui, G., Lalande, J.-F., T ao ´ e, J., Desmoulins, N., Be hom´ e, P., and Gha ou , S. (2015). A p ac ical se - membe ship p oo o p i acy-p ese ing NFC mobile icke ing. 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