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1 ARCIVED PUBLICATIO Th hd pulon, FIPS Pulon 8- dd Oor 8, ws suprsdd on Mrh 6, nd s provdd hr only for hsorl purposs. For h mos urrn rvson of hs pulon, s: hp://sr.ns.gov/pulons/pusfips.hml#fps8-.

2 FIPS PUB 8- FEDERAL IFORMATIO PROCESSIG STADARDS PUBLICATIO Sur sh Sndrd SS CATEGORY: COMPUTER SECURITY SUBCATEGORY: CRYPTOGRAPY Informon Thnology Lorory onl Insu of Sndrds nd Thnology Ghrsurg, MD Oor 8 U.S. Dprmn of Commr Crlos M. Gurrz, Srry onl Insu of Sndrds nd Thnology Prk Gllghr, Ang Dror

3 FOREWORD Th Fdrl Informon Prossng Sndrds Pulon Srs of h onl Insu of Sndrds nd Thnology IST s h offl srs of pulons rlng o sndrds nd gudlns dopd nd promulgd undr h provsons of h Fdrl Informon Sury Mngmn A FISMA of. Commns onrnng FIPS pulons r wlomd nd should ddrssd o h Dror, Informon Thnology Lorory, onl Insu of Sndrds nd Thnology, Buru Drv, Sop 89, Ghrsurg, MD C Furln, Dror Informon Thnology Lorory

4 Asr Ths sndrd spfs fv hsh lgorhms h n usd o gnr dgss of mssgs. Th dgss r usd o d whhr mssgs hv n hngd sn h dgss wr gnrd. Ky words: ompur sury, rypogrphy, mssg dgs, hsh funon, hsh lgorhm, Fdrl Informon Prossng Sndrds, Sur sh Sndrd.

5 Fdrl Informon Prossng Sndrds Pulon 8- Oor 8 Announng h SECURE AS STADARD Fdrl Informon Prossng Sndrds Pulons FIPS PUBS r ssud y h onl Insu of Sndrds nd Thnology IST fr pprovl y h Srry of Commr pursun o Son 5 of h Informon Thnology Mngmn Rform A of 996 Pul Lw -6, nd h Compur Sury A of 987 Pul Lw -5.. m of Sndrd: Sur sh Sndrd SS FIPS PUB 8-.. Cgory of Sndrd: Compur Sury Sndrd, Crypogrphy.. Explnon: Ths Sndrd spfs fv sur hsh lgorhms - SA-, SA-, SA- 56, SA-8, nd SA-5 - for ompung ondnsd rprsnon of lron d mssg. Whn mssg of ny lngh lss hn 6 s for SA-, SA- nd SA-56 or lss hn 8 s for SA-8 nd SA-5 s npu o hsh lgorhm, h rsul s n oupu lld mssg dgs. Th mssg dgss rng n lngh from 6 o 5 s, dpndng on h lgorhm. Sur hsh lgorhms r yplly usd wh ohr rypogrph lgorhms, suh s dgl sgnur lgorhms nd kyd-hsh mssg uhnon ods, or n h gnron of rndom numrs s. Th fv hsh lgorhms spfd n hs Sndrd r lld sur us, for gvn lgorhm, s ompuonlly nfsl o fnd mssg h orrsponds o gvn mssg dgs, or o fnd wo dffrn mssgs h produ h sm mssg dgs. Any hng o mssg wll, wh vry hgh proly, rsul n dffrn mssg dgs. Ths wll rsul n vrfon flur whn h sur hsh lgorhm s usd wh dgl sgnur lgorhm or kyd-hsh mssg uhnon lgorhm. Ths Sndrd suprsds FIPS 8- [FIPS 8-].. Approvng Auhory: Srry of Commr. 5. Mnnn Agny: U.S. Dprmn of Commr, onl Insu of Sndrds nd Thnology IST, Informon Thnology Lorory ITL. 6. Applly: Ths Sndrd s ppll o ll Fdrl dprmns nd gns for h proon of snsv unlssfd nformon h s no suj o Tl Und Ss Cod v

6 Son 5 USC 5 nd h s no whn nonl sury sysm s dfnd n Tl Und Ss Cod Son 5 USC 5. Ths sndrd shll mplmnd whnvr sur hsh lgorhm s rqurd for Fdrl pplons, nludng us y ohr rypogrph lgorhms nd proools. Th dopon nd us of hs Sndrd s vll o prv nd ommrl orgnzons. 7. Spfons: Fdrl Informon Prossng Sndrd FIPS 8-, Sur sh Sndrd SS ffxd. 8. Implmnons: Th sur hsh lgorhms spfd hrn my mplmnd n sofwr, frmwr, hrdwr or ny omnon hrof. Only lgorhm mplmnons h r vldd y IST wll onsdrd s omplyng wh hs sndrd. Informon ou h vldon progrm n ond hp://sr.ns.gov/groups/stm/ndx.hml. 9. Implmnon Shdul: Gudn rgrdng h sng nd vldon o FIPS 8- nd s rlonshp o FIPS - n found n IG. of h Implmnon Gudn for FIPS PUB - nd h Crypogrph Modul Vldon Progrm hp://sr.ns.gov/groups/stm/mvp/ndx.hml.. Pns: Implmnons of h sur hsh lgorhms n hs sndrd my ovrd y U.S. or forgn pns.. Expor Conrol: Crn rypogrph dvs nd hnl d rgrdng hm r suj o Fdrl xpor onrols. Expors of rypogrph moduls mplmnng hs sndrd nd hnl d rgrdng hm mus omply wh hs Fdrl rgulons nd lnsd y h Buru of Expor Admnsron of h U.S. Dprmn of Commr. Informon ou xpor rgulons s vll : hp:// Qulfons: Whl s h nn of hs Sndrd o spfy gnrl sury rqurmns for gnrng mssg dgs, onformn o hs Sndrd dos no ssur h prulr mplmnon s sur. Th rsponsl uhory n h gny or dprmn shll ssur h n ovrll mplmnon provds n pl lvl of sury. Ths Sndrd wll rvwd vry fv yrs n ordr o ssss s dquy.. Wvr Produr: Th Fdrl Informon Sury Mngmn A FISMA dos no llow for wvrs o Fdrl Informon Prossng Sndrds FIPS h r md mndory y h Srry of Commr.. Whr o On Cops of h Sndrd: Ths pulon s vll lronlly y ssng hp://sr.ns.gov/pulons/. Ohr ompur sury pulons r vll h sm w s. v

7 Fdrl Informon Prossng Sndrds Pulon 8- Spfons for h SECURE AS STADARD Tl of Conns. ITRODUCTIO.... DEFIITIOS.... GLOSSARY OF TERMS AD ACROYMS.... ALGORITM PARAMETERS, SYMBOLS, AD TERMS..... Prmrs..... Symols nd Oprons...5. OTATIO AD COVETIOS...7. BIT STRIGS AD ITEGERS...7. OPERATIOS O WORDS...8. FUCTIOS AD COSTATS.... FUCTIOS..... SA- Funons..... SA- nd SA-56 Funons..... SA-8 nd SA-5 Funons.... COSTATS..... SA- Consns..... SA- nd SA-56 Consns..... SA-8 nd SA-5 Consns PREPROCESSIG PADDIG TE MESSAGE SA-, SA- nd SA SA-8 nd SA PARSIG TE PADDED MESSAGE SA-, SA- nd SA SA-8 nd SA SETTIG TE IITIAL AS VALUE SA SA SA SA SA SECURE AS ALGORITMS SA SA- Prprossng SA- sh Compuon Alrn Mhod for Compung SA- Mssg Dgs...9

8 6. SA SA-56 Prprossng SA-56 sh Compuon SA SA SA-5 Prprossng SA-5 sh Compuon SA TRUCATIO OF A MESSAGE DIGEST...5 APPEDIX A: ADDITIOAL IFORMATIO...6 A. SECURITY OF TE SECURE AS ALGORITMS...6 A. IMPLEMETATIO OTES...6 A. OBJECT IDETIFIERS...6 APPEDIX B: REFERECES...7

9 . ITRODUCTIO Ths Sndrd spfs fv sur hsh lgorhms, SA-, SA-, SA-56, SA-8, nd SA-5. All fv of h lgorhms r rv, on-wy hsh funons h n pross mssg o produ ondnsd rprsnon lld mssg dgs. Ths lgorhms nl h drmnon of mssg s ngry: ny hng o h mssg wll, wh vry hgh proly, rsul n dffrn mssg dgs. Ths propry s usful n h gnron nd vrfon of dgl sgnurs nd mssg uhnon ods, nd n h gnron of rndom numrs or s. Eh lgorhm n dsrd n wo sgs: prprossng nd hsh ompuon. Prprossng nvolvs pddng mssg, prsng h pddd mssg no m- loks, nd sng nlzon vlus o usd n h hsh ompuon. Th hsh ompuon gnrs mssg shdul from h pddd mssg nd uss h shdul, long wh funons, onsns, nd word oprons o rvly gnr srs of hsh vlus. Th fnl hsh vlu gnrd y h hsh ompuon s usd o drmn h mssg dgs. Th fv lgorhms dffr mos sgnfnly n h sury srnghs h r provdd for h d ng hshd. Th sury srnghs of hs fv hsh funons nd h sysm s whol whn h of hm s usd wh ohr rypogrph lgorhms, suh s dgl sgnur lgorhms nd kyd-hsh mssg uhnon ods, n found n [SP 8-57] nd [SP 8-7]. Addonlly, h fv lgorhms dffr n rms of h sz of h loks nd words of d h r usd durng hshng. Fgur prsns h s proprs of hs hsh lgorhms. Algorhm Mssg Sz s Blok Sz s Word Sz s Mssg Dgs Sz s SA- < SA- < 6 5 SA-56 < SA-8 < SA-5 < Fgur : Sur sh Algorhm Proprs

10 . DEFIITIOS. Glossry of Trms nd Aronyms B A nry dg hvng vlu of or. By FIPS IST SA SP Word A group of gh s. Fdrl Informon Prossng Sndrd. onl Insu of Sndrds nd Thnology. Sur sh Algorhm. Spl Pulon A group of hr s ys or 6 s 8 ys, dpndng on h sur hsh lgorhm.. Algorhm Prmrs, Symols, nd Trms.. Prmrs Th followng prmrs r usd n h sur hsh lgorhm spfons n hs Sndrd.,,,, h Workng vrls h r h w- words usd n h ompuon of h hsh vlus,. Th h hsh vlu. s h nl hsh vlu; s h fnl hsh vlu nd s usd o drmn h mssg dgs. j Th j h word of h h hsh vlu, whr s h lf-mos word of hsh vlu. K k l Consn vlu o usd for h ron of h hsh ompuon. umr of zros ppndd o mssg durng h pddng sp. Lngh of h mssg, M, n s. m umr of s n mssg lok, M. M Mssg o hshd.

11 M Mssg lok, wh sz of m s. M Th j h word of h h mssg lok, whr M s h lf-mos word of j mssg lok. n T w W umr of s o rod or shfd whn word s oprd upon. umr of loks n h pddd mssg. Tmporry w- word usd n h hsh ompuon. umr of s n word. Th h w- word of h mssg shdul... Symols nd Oprons Th followng symols r usd n h sur hsh lgorhm spfons; h oprs on w- words. Bws AD opron. Bws OR nlusv-or opron. Bws XOR xlusv-or opron. Bws omplmn opron. Addon modulo w. << Lf-shf opron, whr x << n s ond y dsrdng h lf-mos n s of h word x nd hn pddng h rsul wh n zros on h rgh. >> Rgh-shf opron, whr x >> n s ond y dsrdng h rghmos n s of h word x nd hn pddng h rsul wh n zros on h lf. Th followng oprons r usd n h sur hsh lgorhm spfons: ROTL n x ROTR n x Th ro lf rulr lf shf opron, whr x s w- word nd n s n ngr wh n < w, s dfnd y ROTL n xx << n x >> w - n. Th ro rgh rulr rgh shf opron, whr x s w- word nd n s n ngr wh n < w, s dfnd y ROTR n xx >> n x << w - n. 5

12 SR n x Th rgh shf opron, whr x s w- word nd n s n ngr wh n < w, s dfnd y SR n xx >> n. 6

13 . OTATIO AD COVETIOS. B Srngs nd Ingrs Th followng rmnology rld o srngs nd ngrs wll usd.. A hx dg s n lmn of h s {,,, 9,,, f}. A hx dg s h rprsnon of - srng. For xmpl, h hx dg 7 rprsns h - srng, nd h hx dg rprsns h - srng.. A word s w- srng h my rprsnd s squn of hx dgs. To onvr word o hx dgs, h - srng s onvrd o s hx dg quvln, s dsrd n ov. For xmpl, h - srng n xprssd s f, nd h 6- srng n xprssd s ff. Throughou hs spfon, h g-ndn onvnon s usd whn xprssng oh - nd 6- words, so h whn h word, h mos sgnfn s sord n h lf-mos poson.. An ngr my rprsnd s word or pr of words. A word rprsnon of h mssg lngh, l, n s, s rqurd for h pddng hnqus of S. 5.. An ngr wn nd - nlusv my rprsnd s - word. Th ls sgnfn four s of h ngr r rprsnd y h rgh-mos hx dg of h word rprsnon. For xmpl, h ngr s rprsnd y h hx word. Th sm holds ru for n ngr wn nd 6 - nlusv, whh my rprsnd s 6- word. If Z s n ngr, Z < 6, hn Z X Y, whr X < nd Y <. Sn X nd Y n rprsnd s - words x nd y, rspvly, h ngr Z n rprsnd s h pr of words x, y. Ths propry s usd for SA-, SA- nd SA-56. 7

14 If Z s n ngr, Z < 8, hn Z 6 X Y, whr X < 6 nd Y < 6. Sn X nd Y n rprsnd s 6- words x nd y, rspvly, h ngr Z n rprsnd s h pr of words x, y. Ths propry s usd for SA-8 nd SA-5.. For h sur hsh lgorhms, h sz of h mssg lok - m s - dpnds on h lgorhm. For SA-, SA- nd SA-56, h mssg lok hs 5 s, whh r rprsnd s squn of sxn - words. For SA-8 nd SA-5, h mssg lok hs s, whh r rprsnd s squn of sxn 6- words.. Oprons on Words Th followng oprons r ppld o w- words n ll fv sur hsh lgorhms. SA-, SA- nd SA-56 opr on - words w, nd SA-8 nd SA-5 opr on 6- words w6.. Bws logl word oprons:,,, nd s S..... Addon modulo w. Th opron x y s dfnd s follows. Th words x nd y rprsn ngrs X nd Y, whr X < w nd Y < w. For posv ngrs U nd V, l U modv h rmndr upon dvdng U y V. Compu Z X Y mod w. Thn Z < w. Convr h ngr Z o word, z, nd dfn zx y.. Th rgh shf opron SR n x, whr x s w- word nd n s n ngr wh n < w, s dfnd y SR n xx >> n. Ths opron s usd n h SA-, SA-56, SA-8, nd SA-5 lgorhms.. Th ro rgh rulr rgh shf opron ROTR n x, whr x s w- word nd n s n ngr wh n < w, s dfnd y ROTR n xx >> n x << w - n. 8

15 Thus, ROTR n x s quvln o rulr shf roon of x y n posons o h rgh. Ths opron s usd y h SA-, SA-56, SA-8, nd SA-5 lgorhms. 5. Th ro lf rulr lf shf opron, ROTL n x, whr x s w- word nd n s n ngr wh n < w, s dfnd y ROTL n xx << n x >> w - n. Thus, ROTL n x s quvln o rulr shf roon of x y n posons o h lf. Ths opron s usd only n h SA- lgorhm. 6. o h followng quvln rlonshps, whr w s fxd n h rlonshp: ROTL n x ROTR n x ROTR w-n x ROTL w-n x 9

16 . FUCTIOS AD COSTATS. Funons Ths son dfns h funons h r usd y h of h lgorhms. Alhough h SA-, SA-56, SA-8, nd SA-5 lgorhms ll us smlr funons, hr dsrpons r sprd no sons for SA- nd SA-56 S... nd for SA-8 nd SA- 5 S..., sn h npu nd oupu for hs funons r words of dffrn szs. Eh of h lgorhms nlud Chx, y, z nd Mjx, y, z funons; h xlusv-or opron n hs funons my rpld y ws OR opron nd produ dnl rsuls... SA- Funons SA- uss squn of logl funons, f, f,, f 79. Eh funon f, whr < 79, oprs on hr - words, x, y, nd z, nd produs - word s oupu. Th funon f x, y, z s dfnd s follows: Chx, y, zx y x z 9 Pryx, y, zx y z 9 f x, y, z. Mjx, y, zx y x z y z 59 Pryx, y, zx y z SA- nd SA-56 Funons SA- nd SA-56 oh us sx logl funons, whr h funon oprs on - words, whh r rprsnd s x, y, nd z. Th rsul of h funon s nw - word. Ch x, y, z x y x z. Mj x, y, z x y x z y z. { 56 } 56 { } x ROTR x ROTR x ROTR x. x ROTR 6 x ROTR x ROTR 5 x.5 {56} σ ROTR 7 x x ROTR 8 x SR x.6 {56} σ ROTR 7 x ROTR 9 x SR x.7 x.. SA-8 nd SA-5 Funons SA-8 nd SA-5 oh us sx logl funons, whr h funon oprs on 6- words, whh r rprsnd s x, y, nd z. Th rsul of h funon s nw 6- word.

17 Ch x, y, z x y x z.8 Mj x, y, z x y x z y z.9 { 5 } 5 { } x ROTR 8 x ROTR x ROTR 9 x. x ROTR x ROTR 8 x ROTR x. {5} σ ROTR x x ROTR 8 x SR 7 x. {5} σ ROTR 9 x ROTR 6 x SR 6 x. x. Consns.. SA- Consns SA- uss squn of ghy onsn - words, K, K,, K 79, whh r gvn y d9 9 K. 8fd 59 6d SA- nd SA-56 Consns SA- nd SA-56 us h sm squn of sxy-four onsn - words, {56} {56} {56} K, K, K, K 6. Ths words rprsn h frs hry-wo s of h fronl prs of h u roos of h frs sxy-four prm numrs. In hx, hs onsn words r from lf o rgh 8f ff 95d ff 9f8 5d5 d d 75d7 8df 9d67 9f7 969 f786 f9d6 d96f 78 59d 76f988d d 78 f597f7 6f d d6df 58d f d989 d6996 f d8 59f 686ff 78f f fff 56 f9f7 6778f.. SA-8 nd SA-5 Consns SA-8 nd SA-5 us h sm squn of ghy onsn 6- words, {5} {5} {5} K, K, K, K 79. Ths words rprsn h frs sxy-four s of h fronl prs of h u roos of h frs ghy prm numrs. In hx, hs onsn words r from lf o rgh 8f98d78 779f65d 5ffdf 95d5889d

18 9565f858 59ff65d9 9f8f9f9 5d5d6d88 d f dd5ff 75d7f7896f 8df696 9d f7f fd f7868f5 f9d688d d96f ddfd 76f988d df 866dd 7898ff f597f7f 6fd88f d f dff d6df5d 58d9d95df 65758f6d d f8f df d989d6f58 d f d8 968dd df d88 59f ffd68 78f85dff 78566f7f6 8878f fff68 56d8d9 f9f f d86877 d7dd6d f57df7f6d78 6f67776f 67d58986 f98f9d 757 8d77f57d d679d 5d6 597f99f657 5f6fd6f

19 5. PREPROCESSIG Prprossng shll k pl for hsh ompuon gns. Ths prprossng onsss of hr sps: pddng h mssg, M S. 5., prsng h pddd mssg no mssg loks S. 5., nd sng h nl hsh vlu, S Pddng h Mssg Th mssg, M, shll pddd for hsh ompuon gns. Th purpos of hs pddng s o nsur h h pddd mssg s mulpl of 5 or s, dpndng on h lgorhm. 5.. SA-, SA- nd SA-56 Suppos h h lngh of h mssg, M, s l s. Appnd h o h nd of h mssg, followd y k zro s, whr k s h smlls, non-ngv soluon o h quon l k 8mod5. Thn ppnd h 6- lok h s qul o h numr l xprssd usng nry rprsnon. For xmpl, h 8- ASCII mssg hs lngh 8, so h mssg s pddd wh on, hn 8 zro s, nd hn h mssg lngh, o om h 5- pddd mssg l Th lngh of h pddd mssg should now mulpl of 5 s. 5.. SA-8 nd SA-5 Suppos h lngh of h mssg M, n s, s l s. Appnd h o h nd of h mssg, followd y k zro s, whr k s h smlls non-ngv soluon o h quon l k 896 mod. Thn ppnd h 8- lok h s qul o h numr l xprssd usng nry rprsnon. For xmpl, h 8- ASCII mssg hs lngh 8, so h mssg s pddd wh on, hn zro s, nd hn h mssg lngh, o om h - pddd mssg l Th lngh of h pddd mssg should now mulpl of s.

20 5. Prsng h Pddd Mssg Afr mssg hs n pddd, mus prsd no m- loks for h hsh ompuon n gn. 5.. SA-, SA- nd SA-56 For SA-, SA- nd SA-56, h pddd mssg s prsd no 5- loks, M, M,, M. Sn h 5 s of h npu lok my xprssd s sxn - words, h frs s of mssg lok r dnod M, h nx s r M, nd so on up o M SA-8 nd SA-5 For SA-8 nd SA-5, h pddd mssg s prsd no - loks, M, M,, M. Sn h s of h npu lok my xprssd s sxn 6- words, h frs 6 s of mssg lok r dnod M, h nx 6 s r M, nd so on up o M Sng h Inl sh Vlu Bfor hsh ompuon gns for h of h sur hsh lgorhms, h nl hsh vlu,, mus s. Th sz nd numr of words n dpnds on h mssg dgs sz. 5.. SA- For SA-, h nl hsh vlu,, shll onss of h followng fv - words, n hx: 675 fd89 98df 576 df 5.. SA- For SA-, h nl hsh vlu,, shll onss of h followng gh - words, n hx: 5 59d8 67d57 7dd7 f7599 ff 68585

21 6 7 6f98f7 ff 5.. SA-56 For SA-56, h nl hsh vlu,, shll onss of hx: f7 5ff5 557f f8d9 5d9 7 h followng gh - words, n Ths words wr ond y kng h frs hry-wo s of h fronl prs of h squr roos of h frs gh prm numrs. 5.. SA-8 For SA-8, h nl hsh vlu,, shll onss of h followng gh 6- words, n hx: 9d5d59d d dd7 5fd8f ff dd6f98f dff Ths words wr ond y kng h frs sxy-four s of h fronl prs of h squr roos of h nnh hrough sxnh prm numrs SA-5 For SA-5, h nl hsh vlu,, shll onss of h hx: 69667f98 followng gh 6- words, n 5

22 f7f9f8 5ff55fd6f 557fd68d f f8d9fd6 5d9779 Ths words wr ond y kng h frs sxy-four s of h fronl prs of h squr roos of h frs gh prm numrs. 6

23 6. SECURE AS ALGORITMS In h followng sons, h hsh lgorhms r no dsrd n sndng ordr of sz. SA- 56 s dsrd for SA- us h spfon for SA- s dnl o SA- 56, xp h dffrn nl hsh vlus r usd, nd h fnl hsh vlu s rund o s for SA-. Th sm s ru for SA-5 nd SA-8, xp h h fnl hsh vlu s rund o 8 s for SA-8. For h of h sur hsh lgorhms, hr my xs lrn ompuon mhods h yld dnl rsuls; on xmpl s h lrnv SA- ompuon dsrd n S Suh lrn mhods my mplmnd n onformn o hs sndrd. 6. SA- 6 SA- my usd o hsh mssg, M, hvng lngh of l s, whr l <. Th lgorhm uss mssg shdul of ghy - words, fv workng vrls of s h, nd hsh vlu of fv - words. Th fnl rsul of SA- s 6- mssg dgs. Th words of h mssg shdul r lld W, W,, W 79. Th fv workng vrls r lld,,, d, nd. Th words of h hsh vlu r lld,, K,, whh wll hold h nl hsh vlu,, rpld y h sussv nrmd hsh vlu fr h mssg lok s prossd,, nd ndng wh h fnl hsh vlu,. SA- lso uss sngl mporry word, T. 6.. SA- Prprossng. Pd h mssg, M, ordng o S. 5..;. Prs h pddd mssg no 5- mssg loks, M, M,, M, ordng o S. 5..; nd. S h nl hsh vlu,, s spfd n S SA- sh Compuon Th SA- hsh ompuon uss funons nd onsns prvously dfnd n S... nd S..., rspvly. Addon s prformd modulo. Afr prprossng s ompld, h mssg lok, M, M,, M, s prossd n ordr, usng h followng sps: For o : {. Prpr h mssg shdul, {W }: 7

24 M 5 W ROTL 6 8 W W W W Inlz h fv workng vrls,,,, d, nd, wh h - s hsh vlu: d. For o 79: { T ROTL d d W K d f ROTL T,, 5 }. Compu h h nrmd hsh vlu : d } Afr rpng sps on hrough four ol of ms.., fr prossng M, h rsulng 6- mssg dgs of h mssg, M, s 8

25 6.. Alrn Mhod for Compung SA- Mssg Dgs Th SA- hsh ompuon mhod dsrd n S. 6.. ssums h h mssg shdul W, W,, W 79 s mplmnd s n rry of ghy - words. Ths s ffn from h sndpon of h mnmzon of xuon m, sn h ddrsss of W -,, W -6 n sp of S. 6.. r sly ompud. owvr, f mmory s lmd, n lrnv s o rgrd {W } s rulr quu h my mplmnd usng n rry of sxn - words, W, W,, W 5. Th lrn mhod h s dsrd n hs son ylds h sm mssg dgs s h SA- ompuon mhod dsrd n S Alhough hs lrn mhod svs sxy-four - words of sorg, s lkly o lnghn h xuon m du o h nrsd omplxy of h ddrss ompuons for h {W } n sp. For hs lrn SA- mhod, l MASKf n hx. As n S. 6.., ddon s prformd modulo. Assumng h h prprossng s dsrd n S. 6.. hs n prformd, h prossng of M s s follows: For o : {. For o 5: { W M }. Inlz h fv workng vrls,,,, d, nd, wh h - s hsh vlu: d. For o 79: { s MASK If { } 6 hn W ROTL W s s MASK s 8 MASK s MASK W W W s 9

26 T ROTL d d W K d f ROTL T s,, 5 }. Compu h h nrmd hsh vlu : d } Afr rpng sps on hrough four ol of ms.., fr prossng M, h rsulng 6- mssg dgs of h mssg, M, s 6. SA-56 SA-56 my usd o hsh mssg, M, hvng lngh of s, whr. Th lgorhm uss mssg shdul of sxy-four - words, gh workng vrls of s h, nd hsh vlu of gh - words. Th fnl rsul of SA-56 s 56- mssg dgs. l 6 < l Th words of h mssg shdul r lld W, W,, W 6. Th gh workng vrls r lld,,, d,, f, g, nd h. Th words of h hsh vlu r lld, whh wll hold h nl hsh vlu,, rpld y h sussv nrmd hsh vlu fr h mssg lok s prossd,, nd ndng wh h fnl hsh vlu,. SA- 56 lso uss wo mporry words, T nd T. 7,,, K 6.. SA-56 Prprossng. Pd h mssg, M, ordng o S. 5..;

27 . Prs h pddd mssg no 5- mssg loks, M, M,, M, ordng o S. 5..; nd. S h nl hsh vlu,, s spfd n S SA-56 sh Compuon Th SA-56 hsh ompuon uss funons nd onsns prvously dfnd n S... nd S..., rspvly. Addon s prformd modulo. Afr prprossng s ompld, h mssg lok, usng h followng sps: For o : {. Prpr h mssg shdul, { W }: M, M,, M, s prossd n ordr, W M 5 σ 6 6 {56} { 56} W W 7 σ W 5 W 6. Inlz h gh workng vrls,,,, d,, f, g, nd h, wh h - s hsh vlu: d f g h For o 6: {

28 {56} {56} {56},,,, T T d T d f f g g h Mj T W K g f Ch h T }. Compu h h nrmd hsh vlu : h g f d } Afr rpng sps on hrough four ol of ms.., fr prossng M, h rsulng 56- mssg dgs of h mssg, M, s SA- SA- my usd o hsh mssg, M, hvng lngh of l s, whr l < 6. Th funon s dfnd n h x sm mnnr s SA-56 Son 6., wh h followng wo xpons:. Th nl hsh vlu,, shll s s spfd n S. 5..; nd. Th - mssg dgs s ond y runng h fnl hsh vlu,, o s lf-mos s:

29 SA-5 8 SA-5 my usd o hsh mssg, M, hvng lngh of l s, whr l <. Th lgorhm uss mssg shdul of ghy 6- words, gh workng vrls of 6 s h, nd hsh vlu of gh 6- words. Th fnl rsul of SA-5 s 5- mssg dgs. Th words of h mssg shdul r lld W, W,, W 79. Th gh workng vrls r lld,,, d,, f, g, nd h. Th words of h hsh vlu r lld,, K, 7, whh wll hold h nl hsh vlu,, rpld y h sussv nrmd hsh vlu fr h mssg lok s prossd,, nd ndng wh h fnl hsh vlu,. SA- 5 lso uss wo mporry words, T nd T. 6.. SA-5 Prprossng. Pd h mssg, M, ordng o S. 5..;. Prs h pddd mssg no - mssg loks, M, M,, M, ordng o S. 5..; nd. S h nl hsh vlu,, s spfd n S SA-5 sh Compuon Th SA-5 hsh ompuon uss funons nd onsns prvously dfnd n S... nd S..., rspvly. Addon s prformd modulo 6. Afr prprossng s ompld, h mssg lok, M, M,, M, s prossd n ordr, usng h followng sps: For o : {. Prpr h mssg shdul, {W }: W M 5 σ 6 79 {5} {5} W W 7 σ W 5 W 6. Inlz h gh workng vrls,,,, d,, f, g, nd h, wh h - s hsh vlu:

30 7 6 5 h g f d. For o 79: { {5} {5} {5},,,, T T d T d f f g g h Mj T W K g f Ch h T }. Compu h h nrmd hsh vlu : h g f d }

31 Afr rpng sps on hrough four ol of ms.., fr prossng M, h rsulng 5- mssg dgs of h mssg, M, s SA-8 8 SA-8 my usd o hsh mssg, M, hvng lngh of l s, whr l <. Th lgorhm s dfnd n h x sm mnnr s SA-5 S. 6., wh h followng wo xpons:. Th nl hsh vlu,, shll s s spfd n S. 5..; nd. Th 8- mssg dgs s ond y runng h fnl hsh vlu,, o s lf-mos 8 s: 5 7. TRUCATIO OF A MESSAGE DIGEST Som pplon my rqur hsh funon wh mssg dgs lngh dffrn hn hos provdd y h hsh funons n hs Sndrd. In suh ss, rund mssg dgs my usd, whry hsh funon wh lrgr mssg dgs lngh s ppld o h d o hshd, nd h rsulng mssg dgs s rund y slng n ppropr numr of h lfmos s. For gudlns on hoosng h lngh of h rund mssg dgs nd nformon ou s sury mplons for h rypogrph pplon h uss, s SP

32 APPEDIX A: Addonl Informon A. Sury of h Sur sh Algorhms Th sury of h fv hsh lgorhms, SA-, SA-, SA-56, SA-8, nd SA-5 s dsussd n [SP 8-7]. A. Implmnon os Exmpls of SA-, SA-, SA-56, SA-8 nd SA-5 r vll hp://sr.ns.gov/groups/st/oolk/xmpls.hml. A. Oj Idnfrs Oj dnfrs OIDs for h SA-, SA-, SA-56, SA-8 nd SA-5 lgorhms r posd hp://sr.ns.gov/groups/st/rypo_pps_nfr/sor/lgorhms.hml. 6

33 APPEDIX B: REFERECES [FIPS 8-] [SP 8-57] [SP 8-7] IST, Fdrl Informon Prossng Sndrds Pulon 8-, Sur sh Sndrds SS, Augus. IST Spl Pulon SP 8-57, Pr, Rommndon for Ky Mngmn: Gnrl, Augus 5. IST Spl Pulon SP 8-7, Rommndon for Applons Usng Approvd sh Algorhms, Drf July 8. 7