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|00000000| 46 72 6f 6d 20 66 61 71 | 2d 65 64 69 74 6f 72 40 |From faq|-editor@|
|00000010| 72 73 61 2e 63 6f 6d 20 | 4d 6f 6e 20 41 75 67 20 |rsa.com |Mon Aug |
|00000020| 32 32 20 31 39 3a 34 35 | 3a 30 33 20 31 39 39 34 |22 19:45|:03 1994|
|00000030| 0a 46 72 6f 6d 3a 20 66 | 61 71 2d 65 64 69 74 6f |.From: f|aq-edito|
|00000040| 72 40 72 73 61 2e 63 6f | 6d 0a 4e 65 77 73 67 72 |r@rsa.co|m.Newsgr|
|00000050| 6f 75 70 73 3a 20 73 63 | 69 2e 63 72 79 70 74 2c |oups: sc|i.crypt,|
|00000060| 74 61 6c 6b 2e 70 6f 6c | 69 74 69 63 73 2e 63 72 |talk.pol|itics.cr|
|00000070| 79 70 74 6f 2c 61 6c 74 | 2e 73 65 63 75 72 69 74 |ypto,alt|.securit|
|00000080| 79 2e 72 69 70 65 6d 2c | 73 63 69 2e 61 6e 73 77 |y.ripem,|sci.answ|
|00000090| 65 72 73 2c 74 61 6c 6b | 2e 61 6e 73 77 65 72 73 |ers,talk|.answers|
|000000a0| 2c 61 6c 74 2e 61 6e 73 | 77 65 72 73 2c 6e 65 77 |,alt.ans|wers,new|
|000000b0| 73 2e 61 6e 73 77 65 72 | 73 0a 53 75 62 6a 65 63 |s.answer|s.Subjec|
|000000c0| 74 3a 20 52 53 41 20 43 | 72 79 70 74 6f 67 72 61 |t: RSA C|ryptogra|
|000000d0| 70 68 79 20 54 6f 64 61 | 79 20 46 41 51 20 28 31 |phy Toda|y FAQ (1|
|000000e0| 2f 33 29 0a 53 75 70 65 | 72 73 65 64 65 73 3a 20 |/3).Supe|rsedes: |
|000000f0| 3c 63 72 79 70 74 6f 67 | 72 61 70 68 79 2d 66 61 |<cryptog|raphy-fa|
|00000100| 71 2f 72 73 61 2f 70 61 | 72 74 31 5f 37 37 35 33 |q/rsa/pa|rt1_7753|
|00000110| 37 31 33 30 33 40 72 74 | 66 6d 2e 6d 69 74 2e 65 |71303@rt|fm.mit.e|
|00000120| 64 75 3e 0a 46 6f 6c 6c | 6f 77 75 70 2d 54 6f 3a |du>.Foll|owup-To:|
|00000130| 20 70 6f 73 74 65 72 0a | 44 61 74 65 3a 20 31 39 | poster.|Date: 19|
|00000140| 20 41 75 67 20 31 39 39 | 34 20 30 32 3a 32 36 3a | Aug 199|4 02:26:|
|00000150| 33 37 20 47 4d 54 0a 4f | 72 67 61 6e 69 7a 61 74 |37 GMT.O|rganizat|
|00000160| 69 6f 6e 3a 20 6e 6f 6e | 65 0a 52 65 70 6c 79 2d |ion: non|e.Reply-|
|00000170| 54 6f 3a 20 66 61 71 2d | 65 64 69 74 6f 72 40 72 |To: faq-|editor@r|
|00000180| 73 61 2e 63 6f 6d 0a 4e | 4e 54 50 2d 50 6f 73 74 |sa.com.N|NTP-Post|
|00000190| 69 6e 67 2d 48 6f 73 74 | 3a 20 62 6c 6f 6f 6d 2d |ing-Host|: bloom-|
|000001a0| 70 69 63 61 79 75 6e 65 | 2e 6d 69 74 2e 65 64 75 |picayune|.mit.edu|
|000001b0| 0a 58 2d 4c 61 73 74 2d | 55 70 64 61 74 65 64 3a |.X-Last-|Updated:|
|000001c0| 20 31 39 39 34 2f 30 36 | 2f 31 33 0a 4f 72 69 67 | 1994/06|/13.Orig|
|000001d0| 69 6e 61 74 6f 72 3a 20 | 66 61 71 73 65 72 76 40 |inator: |faqserv@|
|000001e0| 62 6c 6f 6f 6d 2d 70 69 | 63 61 79 75 6e 65 2e 4d |bloom-pi|cayune.M|
|000001f0| 49 54 2e 45 44 55 0a 0a | 41 72 63 68 69 76 65 2d |IT.EDU..|Archive-|
|00000200| 6e 61 6d 65 3a 20 63 72 | 79 70 74 6f 67 72 61 70 |name: cr|yptograp|
|00000210| 68 79 2d 66 61 71 2f 72 | 73 61 2f 70 61 72 74 31 |hy-faq/r|sa/part1|
|00000220| 0a 4c 61 73 74 2d 6d 6f | 64 69 66 69 65 64 3a 20 |.Last-mo|dified: |
|00000230| 39 33 2f 30 39 2f 32 30 | 0a 56 65 72 73 69 6f 6e |93/09/20|.Version|
|00000240| 3a 20 32 2e 30 0a 44 69 | 73 74 72 69 62 75 74 69 |: 2.0.Di|stributi|
|00000250| 6f 6e 2d 61 67 65 6e 74 | 3a 20 74 6d 70 40 6e 65 |on-agent|: tmp@ne|
|00000260| 74 63 6f 6d 2e 63 6f 6d | 0a 0a 0a 28 54 68 69 73 |tcom.com|...(This|
|00000270| 20 64 6f 63 75 6d 65 6e | 74 20 68 61 73 20 62 65 | documen|t has be|
|00000280| 65 6e 20 62 72 6f 75 67 | 68 74 20 74 6f 20 79 6f |en broug|ht to yo|
|00000290| 75 20 69 6e 20 70 61 72 | 74 20 62 79 20 43 52 41 |u in par|t by CRA|
|000002a0| 4d 2e 20 20 53 65 65 20 | 74 68 65 0a 62 6f 74 74 |M.  See |the.bott|
|000002b0| 6f 6d 20 66 6f 72 20 6d | 6f 72 65 20 69 6e 66 6f |om for m|ore info|
|000002c0| 72 6d 61 74 69 6f 6e 2c | 20 69 6e 63 6c 75 64 69 |rmation,| includi|
|000002d0| 6e 67 20 69 6e 73 74 72 | 75 63 74 69 6f 6e 73 20 |ng instr|uctions |
|000002e0| 6f 6e 20 68 6f 77 20 74 | 6f 0a 6f 62 74 61 69 6e |on how t|o.obtain|
|000002f0| 20 75 70 64 61 74 65 73 | 2e 29 0a 0a 3d 3d 3d 0a | updates|.)..===.|
|00000300| 0a 0a 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |..      |        |
|00000310| 20 20 20 20 20 20 20 20 | 20 20 20 20 41 6e 73 77 |        |    Answ|
|00000320| 65 72 73 20 54 6f 0a 20 | 20 20 20 20 20 20 20 20 |ers To. |        |
|00000330| 20 20 20 20 20 20 20 20 | 46 52 45 51 55 45 4e 54 |        |FREQUENT|
|00000340| 4c 59 20 41 53 4b 45 44 | 20 51 55 45 53 54 49 4f |LY ASKED| QUESTIO|
|00000350| 4e 53 0a 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |NS.     |        |
|00000360| 20 20 20 20 41 62 6f 75 | 74 20 54 6f 64 61 79 27 |    Abou|t Today'|
|00000370| 73 20 43 72 79 70 74 6f | 67 72 61 70 68 79 0a 0a |s Crypto|graphy..|
|00000380| 0a 0a 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |..      |        |
|00000390| 20 20 20 20 20 20 20 20 | 20 20 20 20 50 61 75 6c |        |    Paul|
|000003a0| 20 46 61 68 6e 0a 20 20 | 20 20 20 20 20 20 20 20 | Fahn.  |        |
|000003b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 52 53 41 20 |        |    RSA |
|000003c0| 4c 61 62 6f 72 61 74 6f | 72 69 65 73 0a 20 20 20 |Laborato|ries.   |
|000003d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000003e0| 20 20 31 30 30 20 4d 61 | 72 69 6e 65 20 50 61 72 |  100 Ma|rine Par|
|000003f0| 6b 77 61 79 0a 20 20 20 | 20 20 20 20 20 20 20 20 |kway.   |        |
|00000400| 20 20 20 20 20 20 20 20 | 52 65 64 77 6f 6f 64 20 |        |Redwood |
|00000410| 43 69 74 79 2c 20 43 41 | 20 20 39 34 30 36 35 0a |City, CA|  94065.|
|00000420| 0a 0a 0a 20 20 20 43 6f | 70 79 72 69 67 68 74 20 |...   Co|pyright |
|00000430| 28 63 29 20 31 39 39 33 | 20 52 53 41 20 4c 61 62 |(c) 1993| RSA Lab|
|00000440| 6f 72 61 74 6f 72 69 65 | 73 2c 20 61 20 64 69 76 |oratorie|s, a div|
|00000450| 69 73 69 6f 6e 20 6f 66 | 20 52 53 41 20 44 61 74 |ision of| RSA Dat|
|00000460| 61 20 53 65 63 75 72 69 | 74 79 2c 0a 20 20 20 20 |a Securi|ty,.    |
|00000470| 20 20 49 6e 63 2e 20 41 | 6c 6c 20 72 69 67 68 74 |  Inc. A|ll right|
|00000480| 73 20 72 65 73 65 72 76 | 65 64 2e 0a 0a 20 20 20 |s reserv|ed...   |
|00000490| 56 65 72 73 69 6f 6e 20 | 32 2e 30 2c 20 64 72 61 |Version |2.0, dra|
|000004a0| 66 74 20 32 66 0a 20 20 | 20 4c 61 73 74 20 75 70 |ft 2f.  | Last up|
|000004b0| 64 61 74 65 3a 20 53 65 | 70 74 65 6d 62 65 72 20 |date: Se|ptember |
|000004c0| 32 30 2c 20 31 39 39 33 | 0a 0a 0a 0a 2d 2d 2d 2d |20, 1993|....----|
|000004d0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000004e0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000004f0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000500| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000510| 2d 2d 2d 2d 0a 20 20 20 | 20 20 20 20 20 20 20 20 |----.   |        |
|00000520| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 54 61 |        |      Ta|
|00000530| 62 6c 65 20 6f 66 20 43 | 6f 6e 74 65 6e 74 73 0a |ble of C|ontents.|
|00000540| 0a 5b 20 70 61 72 74 20 | 31 20 5d 0a 0a 31 20 47 |.[ part |1 ]..1 G|
|00000550| 65 6e 65 72 61 6c 20 0a | 20 20 20 20 20 20 20 31 |eneral .|       1|
|00000560| 2e 31 20 20 57 68 61 74 | 20 69 73 20 65 6e 63 72 |.1  What| is encr|
|00000570| 79 70 74 69 6f 6e 3f 20 | 0a 20 20 20 20 20 20 20 |yption? |.       |
|00000580| 31 2e 32 20 20 57 68 61 | 74 20 69 73 20 61 75 74 |1.2  Wha|t is aut|
|00000590| 68 65 6e 74 69 63 61 74 | 69 6f 6e 3f 20 57 68 61 |henticat|ion? Wha|
|000005a0| 74 20 69 73 20 61 20 64 | 69 67 69 74 61 6c 20 73 |t is a d|igital s|
|000005b0| 69 67 6e 61 74 75 72 65 | 3f 20 0a 20 20 20 20 20 |ignature|? .     |
|000005c0| 20 20 31 2e 33 20 20 57 | 68 61 74 20 69 73 20 70 |  1.3  W|hat is p|
|000005d0| 75 62 6c 69 63 2d 6b 65 | 79 20 63 72 79 70 74 6f |ublic-ke|y crypto|
|000005e0| 67 72 61 70 68 79 3f 20 | 0a 20 20 20 20 20 20 20 |graphy? |.       |
|000005f0| 31 2e 34 20 20 57 68 61 | 74 20 61 72 65 20 74 68 |1.4  Wha|t are th|
|00000600| 65 20 61 64 76 61 6e 74 | 61 67 65 73 20 61 6e 64 |e advant|ages and|
|00000610| 20 64 69 73 61 64 76 61 | 6e 74 61 67 65 73 20 6f | disadva|ntages o|
|00000620| 66 20 70 75 62 6c 69 63 | 2d 6b 65 79 20 0a 20 20 |f public|-key .  |
|00000630| 20 20 20 20 20 20 20 20 | 20 20 63 72 79 70 74 6f |        |  crypto|
|00000640| 67 72 61 70 68 79 20 6f | 76 65 72 20 73 65 63 72 |graphy o|ver secr|
|00000650| 65 74 2d 6b 65 79 20 63 | 72 79 70 74 6f 67 72 61 |et-key c|ryptogra|
|00000660| 70 68 79 3f 20 0a 20 20 | 20 20 20 20 20 31 2e 35 |phy? .  |     1.5|
|00000670| 20 20 49 73 20 63 72 79 | 70 74 6f 67 72 61 70 68 |  Is cry|ptograph|
|00000680| 79 20 70 61 74 65 6e 74 | 61 62 6c 65 20 69 6e 20 |y patent|able in |
|00000690| 74 68 65 20 55 2e 53 2e | 3f 20 0a 20 20 20 20 20 |the U.S.|? .     |
|000006a0| 20 20 31 2e 36 20 20 49 | 73 20 63 72 79 70 74 6f |  1.6  I|s crypto|
|000006b0| 67 72 61 70 68 79 20 65 | 78 70 6f 72 74 61 62 6c |graphy e|xportabl|
|000006c0| 65 20 66 72 6f 6d 20 74 | 68 65 20 55 2e 53 2e 3f |e from t|he U.S.?|
|000006d0| 20 0a 0a 32 20 52 53 41 | 20 0a 20 20 20 20 20 20 | ..2 RSA| .      |
|000006e0| 20 32 2e 31 20 20 57 68 | 61 74 20 69 73 20 52 53 | 2.1  Wh|at is RS|
|000006f0| 41 3f 20 0a 20 20 20 20 | 20 20 20 32 2e 32 20 20 |A? .    |   2.2  |
|00000700| 57 68 79 20 75 73 65 20 | 52 53 41 20 72 61 74 68 |Why use |RSA rath|
|00000710| 65 72 20 74 68 61 6e 20 | 44 45 53 3f 20 0a 20 20 |er than |DES? .  |
|00000720| 20 20 20 20 20 32 2e 33 | 20 20 48 6f 77 20 66 61 |     2.3|  How fa|
|00000730| 73 74 20 69 73 20 52 53 | 41 3f 20 0a 20 20 20 20 |st is RS|A? .    |
|00000740| 20 20 20 32 2e 34 20 20 | 48 6f 77 20 6d 75 63 68 |   2.4  |How much|
|00000750| 20 65 78 74 72 61 20 6d | 65 73 73 61 67 65 20 6c | extra m|essage l|
|00000760| 65 6e 67 74 68 20 69 73 | 20 63 61 75 73 65 64 20 |ength is| caused |
|00000770| 62 79 20 75 73 69 6e 67 | 20 52 53 41 3f 20 0a 20 |by using| RSA? . |
|00000780| 20 20 20 20 20 20 32 2e | 35 20 20 57 68 61 74 20 |      2.|5  What |
|00000790| 77 6f 75 6c 64 20 69 74 | 20 74 61 6b 65 20 74 6f |would it| take to|
|000007a0| 20 62 72 65 61 6b 20 52 | 53 41 3f 20 0a 20 20 20 | break R|SA? .   |
|000007b0| 20 20 20 20 32 2e 36 20 | 20 41 72 65 20 73 74 72 |    2.6 | Are str|
|000007c0| 6f 6e 67 20 70 72 69 6d | 65 73 20 6e 65 63 65 73 |ong prim|es neces|
|000007d0| 73 61 72 79 20 69 6e 20 | 52 53 41 3f 20 0a 20 20 |sary in |RSA? .  |
|000007e0| 20 20 20 20 20 32 2e 37 | 20 20 48 6f 77 20 6c 61 |     2.7|  How la|
|000007f0| 72 67 65 20 61 20 6d 6f | 64 75 6c 75 73 20 28 6b |rge a mo|dulus (k|
|00000800| 65 79 29 20 73 68 6f 75 | 6c 64 20 62 65 20 75 73 |ey) shou|ld be us|
|00000810| 65 64 20 69 6e 20 52 53 | 41 3f 20 0a 20 20 20 20 |ed in RS|A? .    |
|00000820| 20 20 20 32 2e 38 20 20 | 48 6f 77 20 6c 61 72 67 |   2.8  |How larg|
|00000830| 65 20 73 68 6f 75 6c 64 | 20 74 68 65 20 70 72 69 |e should| the pri|
|00000840| 6d 65 73 20 62 65 3f 20 | 0a 20 20 20 20 20 20 20 |mes be? |.       |
|00000850| 32 2e 39 20 20 48 6f 77 | 20 64 6f 65 73 20 6f 6e |2.9  How| does on|
|00000860| 65 20 66 69 6e 64 20 72 | 61 6e 64 6f 6d 20 6e 75 |e find r|andom nu|
|00000870| 6d 62 65 72 73 20 66 6f | 72 20 6b 65 79 73 3f 20 |mbers fo|r keys? |
|00000880| 0a 20 20 20 20 20 20 20 | 32 2e 31 30 20 20 57 68 |.       |2.10  Wh|
|00000890| 61 74 20 69 66 20 75 73 | 65 72 73 20 6f 66 20 52 |at if us|ers of R|
|000008a0| 53 41 20 72 75 6e 20 6f | 75 74 20 6f 66 20 64 69 |SA run o|ut of di|
|000008b0| 73 74 69 6e 63 74 20 70 | 72 69 6d 65 73 3f 20 0a |stinct p|rimes? .|
|000008c0| 20 20 20 20 20 20 20 32 | 2e 31 31 20 20 48 6f 77 |       2|.11  How|
|000008d0| 20 64 6f 20 79 6f 75 20 | 6b 6e 6f 77 20 69 66 20 | do you |know if |
|000008e0| 61 20 6e 75 6d 62 65 72 | 20 69 73 20 70 72 69 6d |a number| is prim|
|000008f0| 65 3f 20 0a 20 20 20 20 | 20 20 20 32 2e 31 32 20 |e? .    |   2.12 |
|00000900| 20 48 6f 77 20 69 73 20 | 52 53 41 20 75 73 65 64 | How is |RSA used|
|00000910| 20 66 6f 72 20 65 6e 63 | 72 79 70 74 69 6f 6e 20 | for enc|ryption |
|00000920| 69 6e 20 70 72 61 63 74 | 69 63 65 3f 20 0a 20 20 |in pract|ice? .  |
|00000930| 20 20 20 20 20 32 2e 31 | 33 20 20 48 6f 77 20 69 |     2.1|3  How i|
|00000940| 73 20 52 53 41 20 75 73 | 65 64 20 66 6f 72 20 61 |s RSA us|ed for a|
|00000950| 75 74 68 65 6e 74 69 63 | 61 74 69 6f 6e 20 69 6e |uthentic|ation in|
|00000960| 20 70 72 61 63 74 69 63 | 65 3f 20 0a 20 20 20 20 | practic|e? .    |
|00000970| 20 20 20 32 2e 31 34 20 | 20 44 6f 65 73 20 52 53 |   2.14 | Does RS|
|00000980| 41 20 68 65 6c 70 20 64 | 65 74 65 63 74 20 61 6c |A help d|etect al|
|00000990| 74 65 72 65 64 20 64 6f | 63 75 6d 65 6e 74 73 20 |tered do|cuments |
|000009a0| 61 6e 64 20 74 72 61 6e | 73 6d 69 73 73 69 6f 6e |and tran|smission|
|000009b0| 20 65 72 72 6f 72 73 3f | 20 0a 20 20 20 20 20 20 | errors?| .      |
|000009c0| 20 32 2e 31 35 20 20 57 | 68 61 74 20 61 72 65 20 | 2.15  W|hat are |
|000009d0| 61 6c 74 65 72 6e 61 74 | 69 76 65 73 20 74 6f 20 |alternat|ives to |
|000009e0| 52 53 41 3f 20 0a 20 20 | 20 20 20 20 20 32 2e 31 |RSA? .  |     2.1|
|000009f0| 36 20 20 49 73 20 52 53 | 41 20 63 75 72 72 65 6e |6  Is RS|A curren|
|00000a00| 74 6c 79 20 69 6e 20 75 | 73 65 20 74 6f 64 61 79 |tly in u|se today|
|00000a10| 3f 20 0a 20 20 20 20 20 | 20 20 32 2e 31 37 20 20 |? .     |  2.17  |
|00000a20| 49 73 20 52 53 41 20 61 | 6e 20 6f 66 66 69 63 69 |Is RSA a|n offici|
|00000a30| 61 6c 20 73 74 61 6e 64 | 61 72 64 20 74 6f 64 61 |al stand|ard toda|
|00000a40| 79 3f 20 0a 20 20 20 20 | 20 20 20 32 2e 31 38 20 |y? .    |   2.18 |
|00000a50| 20 49 73 20 52 53 41 20 | 61 20 64 65 20 66 61 63 | Is RSA |a de fac|
|00000a60| 74 6f 20 73 74 61 6e 64 | 61 72 64 3f 20 57 68 79 |to stand|ard? Why|
|00000a70| 20 69 73 20 61 20 64 65 | 20 66 61 63 74 6f 20 73 | is a de| facto s|
|00000a80| 74 61 6e 64 61 72 64 20 | 69 6d 70 6f 72 74 61 6e |tandard |importan|
|00000a90| 74 3f 20 0a 20 20 20 20 | 20 20 20 32 2e 31 39 20 |t? .    |   2.19 |
|00000aa0| 20 49 73 20 52 53 41 20 | 70 61 74 65 6e 74 65 64 | Is RSA |patented|
|00000ab0| 3f 20 0a 20 20 20 20 20 | 20 20 32 2e 32 30 20 20 |? .     |  2.20  |
|00000ac0| 43 61 6e 20 52 53 41 20 | 62 65 20 65 78 70 6f 72 |Can RSA |be expor|
|00000ad0| 74 65 64 20 66 72 6f 6d | 20 74 68 65 20 55 2e 53 |ted from| the U.S|
|00000ae0| 2e 3f 20 0a 0a 5b 20 70 | 61 72 74 20 32 20 5d 0a |.? ..[ p|art 2 ].|
|00000af0| 0a 33 20 4b 65 79 20 4d | 61 6e 61 67 65 6d 65 6e |.3 Key M|anagemen|
|00000b00| 74 20 0a 20 20 20 20 20 | 20 20 33 2e 31 20 20 57 |t .     |  3.1  W|
|00000b10| 68 61 74 20 6b 65 79 20 | 6d 61 6e 61 67 65 6d 65 |hat key |manageme|
|00000b20| 6e 74 20 69 73 73 75 65 | 73 20 61 72 65 20 69 6e |nt issue|s are in|
|00000b30| 76 6f 6c 76 65 64 20 69 | 6e 20 70 75 62 6c 69 63 |volved i|n public|
|00000b40| 2d 6b 65 79 20 0a 20 20 | 20 20 20 20 20 20 20 20 |-key .  |        |
|00000b50| 20 20 63 72 79 70 74 6f | 67 72 61 70 68 79 3f 20 |  crypto|graphy? |
|00000b60| 0a 20 20 20 20 20 20 20 | 33 2e 32 20 20 57 68 6f |.       |3.2  Who|
|00000b70| 20 6e 65 65 64 73 20 61 | 20 6b 65 79 3f 20 0a 20 | needs a| key? . |
|00000b80| 20 20 20 20 20 20 33 2e | 33 20 20 48 6f 77 20 64 |      3.|3  How d|
|00000b90| 6f 65 73 20 6f 6e 65 20 | 67 65 74 20 61 20 6b 65 |oes one |get a ke|
|00000ba0| 79 20 70 61 69 72 3f 20 | 0a 20 20 20 20 20 20 20 |y pair? |.       |
|00000bb0| 33 2e 34 20 20 53 68 6f | 75 6c 64 20 61 20 70 75 |3.4  Sho|uld a pu|
|00000bc0| 62 6c 69 63 20 6b 65 79 | 20 6f 72 20 70 72 69 76 |blic key| or priv|
|00000bd0| 61 74 65 20 6b 65 79 20 | 62 65 20 73 68 61 72 65 |ate key |be share|
|00000be0| 64 20 61 6d 6f 6e 67 20 | 75 73 65 72 73 3f 20 0a |d among |users? .|
|00000bf0| 20 20 20 20 20 20 20 33 | 2e 35 20 20 57 68 61 74 |       3|.5  What|
|00000c00| 20 61 72 65 20 63 65 72 | 74 69 66 69 63 61 74 65 | are cer|tificate|
|00000c10| 73 3f 20 0a 20 20 20 20 | 20 20 20 33 2e 36 20 20 |s? .    |   3.6  |
|00000c20| 48 6f 77 20 61 72 65 20 | 63 65 72 74 69 66 69 63 |How are |certific|
|00000c30| 61 74 65 73 20 75 73 65 | 64 3f 20 0a 20 20 20 20 |ates use|d? .    |
|00000c40| 20 20 20 33 2e 37 20 20 | 57 68 6f 20 69 73 73 75 |   3.7  |Who issu|
|00000c50| 65 73 20 63 65 72 74 69 | 66 69 63 61 74 65 73 20 |es certi|ficates |
|00000c60| 61 6e 64 20 68 6f 77 3f | 20 0a 20 20 20 20 20 20 |and how?| .      |
|00000c70| 20 33 2e 38 20 20 57 68 | 61 74 20 69 73 20 61 20 | 3.8  Wh|at is a |
|00000c80| 43 53 55 2c 20 6f 72 2c | 20 48 6f 77 20 64 6f 20 |CSU, or,| How do |
|00000c90| 63 65 72 74 69 66 79 69 | 6e 67 20 61 75 74 68 6f |certifyi|ng autho|
|00000ca0| 72 69 74 69 65 73 20 73 | 74 6f 72 65 20 74 68 65 |rities s|tore the|
|00000cb0| 69 72 20 0a 20 20 20 20 | 20 20 20 20 20 20 20 20 |ir .    |        |
|00000cc0| 70 72 69 76 61 74 65 20 | 6b 65 79 73 3f 20 0a 20 |private |keys? . |
|00000cd0| 20 20 20 20 20 20 33 2e | 39 20 20 41 72 65 20 63 |      3.|9  Are c|
|00000ce0| 65 72 74 69 66 79 69 6e | 67 20 61 75 74 68 6f 72 |ertifyin|g author|
|00000cf0| 69 74 69 65 73 20 73 75 | 73 63 65 70 74 69 62 6c |ities su|sceptibl|
|00000d00| 65 20 74 6f 20 61 74 74 | 61 63 6b 3f 20 0a 20 20 |e to att|ack? .  |
|00000d10| 20 20 20 20 20 33 2e 31 | 30 20 20 57 68 61 74 20 |     3.1|0  What |
|00000d20| 69 66 20 74 68 65 20 63 | 65 72 74 69 66 79 69 6e |if the c|ertifyin|
|00000d30| 67 20 61 75 74 68 6f 72 | 69 74 79 27 73 20 6b 65 |g author|ity's ke|
|00000d40| 79 20 69 73 20 6c 6f 73 | 74 20 6f 72 20 63 6f 6d |y is los|t or com|
|00000d50| 70 72 6f 6d 69 73 65 64 | 3f 20 0a 20 20 20 20 20 |promised|? .     |
|00000d60| 20 20 33 2e 31 31 20 20 | 57 68 61 74 20 61 72 65 |  3.11  |What are|
|00000d70| 20 43 65 72 74 69 66 69 | 63 61 74 65 20 52 65 76 | Certifi|cate Rev|
|00000d80| 6f 63 61 74 69 6f 6e 20 | 4c 69 73 74 73 20 28 43 |ocation |Lists (C|
|00000d90| 52 4c 73 29 3f 20 0a 20 | 20 20 20 20 20 20 33 2e |RLs)? . |      3.|
|00000da0| 31 32 20 20 57 68 61 74 | 20 68 61 70 70 65 6e 73 |12  What| happens|
|00000db0| 20 77 68 65 6e 20 61 20 | 6b 65 79 20 65 78 70 69 | when a |key expi|
|00000dc0| 72 65 73 3f 20 0a 20 20 | 20 20 20 20 20 33 2e 31 |res? .  |     3.1|
|00000dd0| 33 20 20 57 68 61 74 20 | 68 61 70 70 65 6e 73 20 |3  What |happens |
|00000de0| 69 66 20 49 20 6c 6f 73 | 65 20 6d 79 20 70 72 69 |if I los|e my pri|
|00000df0| 76 61 74 65 20 6b 65 79 | 3f 20 0a 20 20 20 20 20 |vate key|? .     |
|00000e00| 20 20 33 2e 31 34 20 20 | 57 68 61 74 20 68 61 70 |  3.14  |What hap|
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|00000e40| 2e 31 35 20 20 48 6f 77 | 20 73 68 6f 75 6c 64 20 |.15  How| should |
|00000e50| 49 20 73 74 6f 72 65 20 | 6d 79 20 70 72 69 76 61 |I store |my priva|
|00000e60| 74 65 20 6b 65 79 3f 20 | 0a 20 20 20 20 20 20 20 |te key? |.       |
|00000e70| 33 2e 31 36 20 20 48 6f | 77 20 64 6f 20 49 20 66 |3.16  Ho|w do I f|
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|00000e90| 27 73 20 70 75 62 6c 69 | 63 20 6b 65 79 3f 20 0a |'s publi|c key? .|
|00000ea0| 20 20 20 20 20 20 20 33 | 2e 31 37 20 20 48 6f 77 |       3|.17  How|
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|00000ec0| 72 65 6d 61 69 6e 20 76 | 61 6c 69 64 20 62 65 79 |remain v|alid bey|
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|00000f90| 20 20 20 34 2e 31 20 20 | 57 68 61 74 20 69 73 20 |   4.1  |What is |
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|00000fc0| 20 57 68 61 74 20 69 73 | 20 74 68 65 20 73 69 67 | What is| the sig|
|00000fd0| 6e 69 66 69 63 61 6e 63 | 65 20 6f 66 20 6f 6e 65 |nificanc|e of one|
|00000fe0| 2d 77 61 79 20 66 75 6e | 63 74 69 6f 6e 73 20 66 |-way fun|ctions f|
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|00001000| 20 0a 20 20 20 20 20 20 | 20 34 2e 33 20 20 57 68 | .      | 4.3  Wh|
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|00001030| 20 20 20 20 20 34 2e 34 | 20 20 57 68 61 74 20 69 |     4.4|  What i|
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|00001070| 20 0a 20 20 20 20 20 20 | 20 34 2e 35 20 20 48 61 | .      | 4.5  Ha|
|00001080| 73 20 66 61 63 74 6f 72 | 69 6e 67 20 62 65 65 6e |s factor|ing been|
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|000013c0| 20 20 20 36 2e 37 20 20 | 57 68 61 74 20 69 73 20 |   6.7  |What is |
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|000013f0| 20 20 20 20 20 20 20 36 | 2e 38 20 20 57 68 61 74 |       6|.8  What|
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|00001650| 20 57 68 61 74 20 69 73 | 20 4b 65 72 62 65 72 6f | What is| Kerbero|
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|00001670| 57 68 61 74 20 61 72 65 | 20 52 43 32 20 61 6e 64 |What are| RC2 and|
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|000016f0| 52 45 46 3f 20 0a 0a 2d | 2d 2d 2d 2d 2d 2d 2d 2d |REF? ..-|--------|
|00001700| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001710| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001720| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001730| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 0a 0a 0a 31 20 |--------|---...1 |
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|00001970| 20 73 6f 20 74 68 61 74 | 20 6e 6f 20 6f 6e 65 20 | so that| no one |
|00001980| 65 6c 73 65 20 62 65 73 | 69 64 65 73 20 42 6f 62 |else bes|ides Bob|
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|00001b60| 72 79 70 74 69 6f 6e 20 | 6b 65 79 2e 20 49 6e 20 |ryption |key. In |
|00001b70| 61 20 73 79 6d 6d 65 74 | 72 69 63 20 63 72 79 70 |a symmet|ric cryp|
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|00001bc0| 74 69 6f 6e 20 6b 65 79 | 73 2e 0a 0a 43 72 79 70 |tion key|s...Cryp|
|00001bd0| 74 6f 67 72 61 70 68 79 | 20 68 61 73 20 62 65 65 |tography| has bee|
|00001be0| 6e 20 61 72 6f 75 6e 64 | 20 66 6f 72 20 6d 69 6c |n around| for mil|
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|00003a10| 34 2c 32 30 30 2c 37 37 | 30 2c 20 62 79 20 4d 2e |4,200,77|0, by M.|
|00003a20| 0a 48 65 6c 6c 6d 61 6e | 2c 20 57 2e 20 44 69 66 |.Hellman|, W. Dif|
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|00003aa0| 69 6d 69 6c 61 72 20 70 | 61 74 65 6e 74 73 20 68 |imilar p|atents h|
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|00003af0| 69 67 68 74 73 20 74 6f | 20 62 6f 74 68 20 0a 70 |ights to| both .p|
|00003b00| 61 74 65 6e 74 73 20 61 | 72 65 20 68 65 6c 64 20 |atents a|re held |
|00003b10| 62 79 20 50 75 62 6c 69 | 63 20 4b 65 79 20 50 61 |by Publi|c Key Pa|
|00003b20| 72 74 6e 65 72 73 20 28 | 50 4b 50 29 2c 20 6f 66 |rtners (|PKP), of|
|00003b30| 20 53 75 6e 6e 79 76 61 | 6c 65 2c 20 43 61 6c 69 | Sunnyva|le, Cali|
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|00004c40| 0a 32 20 52 53 41 0a 0a | 32 2e 31 20 57 68 61 74 |.2 RSA..|2.1 What|
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|00004cd0| 61 6d 69 72 2c 20 61 6e | 64 20 4c 65 6f 6e 61 72 |amir, an|d Leonar|
|00004ce0| 64 20 41 64 6c 65 6d 61 | 6e 0a 5b 37 34 5d 2e 20 |d Adlema|n.[74]. |
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|00004d90| 69 6d 65 20 74 6f 20 28 | 70 2d 31 29 28 71 2d 31 |ime to (|p-1)(q-1|
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|00004e70| 20 54 68 65 20 66 61 63 | 74 6f 72 73 20 70 20 61 | The fac|tors p a|
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|00004ea0| 74 72 6f 79 65 64 2e 20 | 0a 0a 49 74 20 69 73 20 |troyed. |..It is |
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|00004ee0| 20 64 20 66 72 6f 6d 20 | 74 68 65 20 70 75 62 6c | d from |the publ|
|00004ef0| 69 63 20 0a 6b 65 79 20 | 28 6e 2c 65 29 2e 20 49 |ic .key |(n,e). I|
|00004f00| 66 20 6f 6e 65 20 63 6f | 75 6c 64 20 66 61 63 74 |f one co|uld fact|
|00004f10| 6f 72 20 6e 20 69 6e 74 | 6f 20 70 20 61 6e 64 20 |or n int|o p and |
|00004f20| 71 2c 20 68 6f 77 65 76 | 65 72 2c 20 74 68 65 6e |q, howev|er, then|
|00004f30| 20 6f 6e 65 20 63 6f 75 | 6c 64 20 0a 6f 62 74 61 | one cou|ld .obta|
|00004f40| 69 6e 20 74 68 65 20 70 | 72 69 76 61 74 65 20 6b |in the p|rivate k|
|00004f50| 65 79 20 64 2e 20 54 68 | 75 73 20 74 68 65 20 65 |ey d. Th|us the e|
|00004f60| 6e 74 69 72 65 20 73 65 | 63 75 72 69 74 79 20 6f |ntire se|curity o|
|00004f70| 66 20 52 53 41 20 69 73 | 20 70 72 65 64 69 63 61 |f RSA is| predica|
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|00004fa0| 6f 72 69 6e 67 20 69 73 | 20 64 69 66 66 69 63 75 |oring is| difficu|
|00004fb0| 6c 74 3b 20 61 6e 20 65 | 61 73 79 20 66 61 63 74 |lt; an e|asy fact|
|00004fc0| 6f 72 69 6e 67 20 6d 65 | 74 68 6f 64 20 0a 77 6f |oring me|thod .wo|
|00004fd0| 75 6c 64 20 60 60 62 72 | 65 61 6b 27 27 20 52 53 |uld ``br|eak'' RS|
|00004fe0| 41 20 28 73 65 65 20 51 | 75 65 73 74 69 6f 6e 73 |A (see Q|uestions|
|00004ff0| 20 32 2e 35 20 61 6e 64 | 20 34 2e 34 29 2e 0a 0a | 2.5 and| 4.4)...|
|00005000| 48 65 72 65 20 69 73 20 | 68 6f 77 20 52 53 41 20 |Here is |how RSA |
|00005010| 63 61 6e 20 62 65 20 75 | 73 65 64 20 66 6f 72 20 |can be u|sed for |
|00005020| 70 72 69 76 61 63 79 20 | 61 6e 64 20 61 75 74 68 |privacy |and auth|
|00005030| 65 6e 74 69 63 61 74 69 | 6f 6e 20 28 69 6e 20 70 |enticati|on (in p|
|00005040| 72 61 63 74 69 63 65 2c | 20 0a 61 63 74 75 61 6c |ractice,| .actual|
|00005050| 20 75 73 65 20 69 73 20 | 73 6c 69 67 68 74 6c 79 | use is |slightly|
|00005060| 20 64 69 66 66 65 72 65 | 6e 74 3b 20 73 65 65 20 | differe|nt; see |
|00005070| 51 75 65 73 74 69 6f 6e | 73 20 32 2e 31 32 20 61 |Question|s 2.12 a|
|00005080| 6e 64 20 32 2e 31 33 29 | 3a 0a 0a 52 53 41 20 70 |nd 2.13)|:..RSA p|
|00005090| 72 69 76 61 63 79 20 28 | 65 6e 63 72 79 70 74 69 |rivacy (|encrypti|
|000050a0| 6f 6e 29 3a 20 73 75 70 | 70 6f 73 65 20 41 6c 69 |on): sup|pose Ali|
|000050b0| 63 65 20 77 61 6e 74 73 | 20 74 6f 20 73 65 6e 64 |ce wants| to send|
|000050c0| 20 61 20 70 72 69 76 61 | 74 65 20 6d 65 73 73 61 | a priva|te messa|
|000050d0| 67 65 2c 20 0a 6d 2c 20 | 74 6f 20 42 6f 62 2e 20 |ge, .m, |to Bob. |
|000050e0| 41 6c 69 63 65 20 63 72 | 65 61 74 65 73 20 74 68 |Alice cr|eates th|
|000050f0| 65 20 63 69 70 68 65 72 | 74 65 78 74 20 63 20 62 |e cipher|text c b|
|00005100| 79 20 65 78 70 6f 6e 65 | 6e 74 69 61 74 69 6e 67 |y expone|ntiating|
|00005110| 3a 20 63 20 3d 20 6d 5e | 65 20 0a 6d 6f 64 20 6e |: c = m^|e .mod n|
|00005120| 2c 20 77 68 65 72 65 20 | 65 20 61 6e 64 20 6e 20 |, where |e and n |
|00005130| 61 72 65 20 42 6f 62 27 | 73 20 70 75 62 6c 69 63 |are Bob'|s public|
|00005140| 20 6b 65 79 2e 20 54 6f | 20 64 65 63 72 79 70 74 | key. To| decrypt|
|00005150| 2c 20 42 6f 62 20 61 6c | 73 6f 20 0a 65 78 70 6f |, Bob al|so .expo|
|00005160| 6e 65 6e 74 69 61 74 65 | 73 3a 20 6d 20 3d 20 63 |nentiate|s: m = c|
|00005170| 5e 64 20 6d 6f 64 20 6e | 2c 20 61 6e 64 20 72 65 |^d mod n|, and re|
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|00005190| 6e 61 6c 20 6d 65 73 73 | 61 67 65 20 6d 3b 0a 74 |nal mess|age m;.t|
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|000051b0| 62 65 74 77 65 65 6e 20 | 65 20 61 6e 64 20 64 20 |between |e and d |
|000051c0| 65 6e 73 75 72 65 73 20 | 74 68 61 74 20 42 6f 62 |ensures |that Bob|
|000051d0| 20 63 6f 72 72 65 63 74 | 6c 79 20 72 65 63 6f 76 | correct|ly recov|
|000051e0| 65 72 73 20 6d 2e 0a 53 | 69 6e 63 65 20 6f 6e 6c |ers m..S|ince onl|
|000051f0| 79 20 42 6f 62 20 6b 6e | 6f 77 73 20 64 2c 20 6f |y Bob kn|ows d, o|
|00005200| 6e 6c 79 20 42 6f 62 20 | 63 61 6e 20 64 65 63 72 |nly Bob |can decr|
|00005210| 79 70 74 2e 20 0a 0a 52 | 53 41 20 61 75 74 68 65 |ypt. ..R|SA authe|
|00005220| 6e 74 69 63 61 74 69 6f | 6e 3a 20 73 75 70 70 6f |nticatio|n: suppo|
|00005230| 73 65 20 41 6c 69 63 65 | 20 77 61 6e 74 73 20 74 |se Alice| wants t|
|00005240| 6f 20 73 65 6e 64 20 61 | 20 73 69 67 6e 65 64 20 |o send a| signed |
|00005250| 64 6f 63 75 6d 65 6e 74 | 20 6d 20 74 6f 20 42 6f |document| m to Bo|
|00005260| 62 2e 20 0a 41 6c 69 63 | 65 20 63 72 65 61 74 65 |b. .Alic|e create|
|00005270| 73 20 61 20 64 69 67 69 | 74 61 6c 20 73 69 67 6e |s a digi|tal sign|
|00005280| 61 74 75 72 65 20 73 20 | 62 79 20 65 78 70 6f 6e |ature s |by expon|
|00005290| 65 6e 74 69 61 74 69 6e | 67 3a 20 73 20 3d 20 6d |entiatin|g: s = m|
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|000052b0| 20 64 20 61 6e 64 20 6e | 20 62 65 6c 6f 6e 67 20 | d and n| belong |
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|000052d0| 61 69 72 2e 20 53 68 65 | 20 73 65 6e 64 73 20 73 |air. She| sends s|
|000052e0| 20 61 6e 64 20 6d 20 74 | 6f 20 42 6f 62 2e 20 0a | and m t|o Bob. .|
|000052f0| 54 6f 20 76 65 72 69 66 | 79 20 74 68 65 20 73 69 |To verif|y the si|
|00005300| 67 6e 61 74 75 72 65 2c | 20 42 6f 62 20 65 78 70 |gnature,| Bob exp|
|00005310| 6f 6e 65 6e 74 69 61 74 | 65 73 20 61 6e 64 20 63 |onentiat|es and c|
|00005320| 68 65 63 6b 73 20 74 68 | 61 74 20 74 68 65 20 6d |hecks th|at the m|
|00005330| 65 73 73 61 67 65 20 6d | 20 0a 69 73 20 72 65 63 |essage m| .is rec|
|00005340| 6f 76 65 72 65 64 3a 20 | 6d 20 3d 20 73 5e 65 20 |overed: |m = s^e |
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|00005360| 6e 64 20 6e 20 62 65 6c | 6f 6e 67 20 74 6f 20 41 |nd n bel|ong to A|
|00005370| 6c 69 63 65 27 73 20 70 | 75 62 6c 69 63 20 0a 6b |lice's p|ublic .k|
|00005380| 65 79 2e 0a 0a 54 68 75 | 73 20 65 6e 63 72 79 70 |ey...Thu|s encryp|
|00005390| 74 69 6f 6e 20 61 6e 64 | 20 61 75 74 68 65 6e 74 |tion and| authent|
|000053a0| 69 63 61 74 69 6f 6e 20 | 74 61 6b 65 20 70 6c 61 |ication |take pla|
|000053b0| 63 65 20 77 69 74 68 6f | 75 74 20 61 6e 79 20 73 |ce witho|ut any s|
|000053c0| 68 61 72 69 6e 67 20 6f | 66 20 0a 70 72 69 76 61 |haring o|f .priva|
|000053d0| 74 65 20 6b 65 79 73 3a | 20 65 61 63 68 20 70 65 |te keys:| each pe|
|000053e0| 72 73 6f 6e 20 75 73 65 | 73 20 6f 6e 6c 79 20 6f |rson use|s only o|
|000053f0| 74 68 65 72 20 70 65 6f | 70 6c 65 27 73 20 70 75 |ther peo|ple's pu|
|00005400| 62 6c 69 63 20 6b 65 79 | 73 20 61 6e 64 20 68 69 |blic key|s and hi|
|00005410| 73 20 6f 72 20 0a 68 65 | 72 20 6f 77 6e 20 70 72 |s or .he|r own pr|
|00005420| 69 76 61 74 65 20 6b 65 | 79 2e 20 41 6e 79 6f 6e |ivate ke|y. Anyon|
|00005430| 65 20 63 61 6e 20 73 65 | 6e 64 20 61 6e 20 65 6e |e can se|nd an en|
|00005440| 63 72 79 70 74 65 64 20 | 6d 65 73 73 61 67 65 20 |crypted |message |
|00005450| 6f 72 20 76 65 72 69 66 | 79 20 61 20 73 69 67 6e |or verif|y a sign|
|00005460| 65 64 20 0a 6d 65 73 73 | 61 67 65 2c 20 75 73 69 |ed .mess|age, usi|
|00005470| 6e 67 20 6f 6e 6c 79 20 | 70 75 62 6c 69 63 20 6b |ng only |public k|
|00005480| 65 79 73 2c 20 62 75 74 | 20 6f 6e 6c 79 20 73 6f |eys, but| only so|
|00005490| 6d 65 6f 6e 65 20 69 6e | 20 70 6f 73 73 65 73 73 |meone in| possess|
|000054a0| 69 6f 6e 20 6f 66 20 74 | 68 65 20 63 6f 72 72 65 |ion of t|he corre|
|000054b0| 63 74 20 0a 70 72 69 76 | 61 74 65 20 6b 65 79 20 |ct .priv|ate key |
|000054c0| 63 61 6e 20 64 65 63 72 | 79 70 74 20 6f 72 20 73 |can decr|ypt or s|
|000054d0| 69 67 6e 20 61 20 6d 65 | 73 73 61 67 65 2e 20 0a |ign a me|ssage. .|
|000054e0| 0a 0a 32 2e 32 20 57 68 | 79 20 75 73 65 20 52 53 |..2.2 Wh|y use RS|
|000054f0| 41 20 72 61 74 68 65 72 | 20 74 68 61 6e 20 44 45 |A rather| than DE|
|00005500| 53 3f 0a 0a 52 53 41 20 | 69 73 20 6e 6f 74 20 61 |S?..RSA |is not a|
|00005510| 6e 20 61 6c 74 65 72 6e | 61 74 69 76 65 20 6f 72 |n altern|ative or|
|00005520| 20 72 65 70 6c 61 63 65 | 6d 65 6e 74 20 66 6f 72 | replace|ment for|
|00005530| 20 44 45 53 3b 20 72 61 | 74 68 65 72 20 69 74 20 | DES; ra|ther it |
|00005540| 73 75 70 70 6c 65 6d 65 | 6e 74 73 0a 44 45 53 20 |suppleme|nts.DES |
|00005550| 28 6f 72 20 61 6e 79 20 | 6f 74 68 65 72 20 66 61 |(or any |other fa|
|00005560| 73 74 20 62 75 6c 6b 20 | 65 6e 63 72 79 70 74 69 |st bulk |encrypti|
|00005570| 6f 6e 20 63 69 70 68 65 | 72 29 20 61 6e 64 20 69 |on ciphe|r) and i|
|00005580| 73 20 75 73 65 64 20 74 | 6f 67 65 74 68 65 72 20 |s used t|ogether |
|00005590| 77 69 74 68 20 44 45 53 | 20 0a 69 6e 20 61 20 73 |with DES| .in a s|
|000055a0| 65 63 75 72 65 20 63 6f | 6d 6d 75 6e 69 63 61 74 |ecure co|mmunicat|
|000055b0| 69 6f 6e 73 20 65 6e 76 | 69 72 6f 6e 6d 65 6e 74 |ions env|ironment|
|000055c0| 2e 20 28 4e 6f 74 65 3a | 20 66 6f 72 20 61 6e 20 |. (Note:| for an |
|000055d0| 65 78 70 6c 61 6e 61 74 | 69 6f 6e 20 6f 66 20 44 |explanat|ion of D|
|000055e0| 45 53 2c 0a 73 65 65 20 | 51 75 65 73 74 69 6f 6e |ES,.see |Question|
|000055f0| 20 35 2e 31 2e 29 0a 0a | 52 53 41 20 61 6c 6c 6f | 5.1.)..|RSA allo|
|00005600| 77 73 20 74 77 6f 20 69 | 6d 70 6f 72 74 61 6e 74 |ws two i|mportant|
|00005610| 20 66 75 6e 63 74 69 6f | 6e 73 20 6e 6f 74 20 70 | functio|ns not p|
|00005620| 72 6f 76 69 64 65 64 20 | 62 79 20 44 45 53 3a 20 |rovided |by DES: |
|00005630| 73 65 63 75 72 65 20 6b | 65 79 20 65 78 63 68 61 |secure k|ey excha|
|00005640| 6e 67 65 20 0a 77 69 74 | 68 6f 75 74 20 70 72 69 |nge .wit|hout pri|
|00005650| 6f 72 20 65 78 63 68 61 | 6e 67 65 20 6f 66 20 73 |or excha|nge of s|
|00005660| 65 63 72 65 74 73 2c 20 | 61 6e 64 20 64 69 67 69 |ecrets, |and digi|
|00005670| 74 61 6c 20 73 69 67 6e | 61 74 75 72 65 73 2e 20 |tal sign|atures. |
|00005680| 46 6f 72 20 65 6e 63 72 | 79 70 74 69 6e 67 0a 6d |For encr|ypting.m|
|00005690| 65 73 73 61 67 65 73 2c | 20 52 53 41 20 61 6e 64 |essages,| RSA and|
|000056a0| 20 44 45 53 20 61 72 65 | 20 75 73 75 61 6c 6c 79 | DES are| usually|
|000056b0| 20 63 6f 6d 62 69 6e 65 | 64 20 61 73 20 66 6f 6c | combine|d as fol|
|000056c0| 6c 6f 77 73 3a 20 66 69 | 72 73 74 20 74 68 65 20 |lows: fi|rst the |
|000056d0| 6d 65 73 73 61 67 65 20 | 69 73 20 0a 65 6e 63 72 |message |is .encr|
|000056e0| 79 70 74 65 64 20 77 69 | 74 68 20 61 20 72 61 6e |ypted wi|th a ran|
|000056f0| 64 6f 6d 20 44 45 53 20 | 6b 65 79 2c 20 61 6e 64 |dom DES |key, and|
|00005700| 20 74 68 65 6e 2c 20 62 | 65 66 6f 72 65 20 62 65 | then, b|efore be|
|00005710| 69 6e 67 20 73 65 6e 74 | 20 6f 76 65 72 20 61 6e |ing sent| over an|
|00005720| 20 69 6e 73 65 63 75 72 | 65 20 0a 63 6f 6d 6d 75 | insecur|e .commu|
|00005730| 6e 69 63 61 74 69 6f 6e | 73 20 63 68 61 6e 6e 65 |nication|s channe|
|00005740| 6c 2c 20 74 68 65 20 44 | 45 53 20 6b 65 79 20 69 |l, the D|ES key i|
|00005750| 73 20 65 6e 63 72 79 70 | 74 65 64 20 77 69 74 68 |s encryp|ted with|
|00005760| 20 52 53 41 2e 20 54 6f | 67 65 74 68 65 72 2c 20 | RSA. To|gether, |
|00005770| 74 68 65 20 0a 44 45 53 | 2d 65 6e 63 72 79 70 74 |the .DES|-encrypt|
|00005780| 65 64 20 6d 65 73 73 61 | 67 65 20 61 6e 64 20 74 |ed messa|ge and t|
|00005790| 68 65 20 52 53 41 2d 65 | 6e 63 72 79 70 74 65 64 |he RSA-e|ncrypted|
|000057a0| 20 44 45 53 20 6b 65 79 | 20 61 72 65 20 73 65 6e | DES key| are sen|
|000057b0| 74 2e 20 54 68 69 73 20 | 70 72 6f 74 6f 63 6f 6c |t. This |protocol|
|000057c0| 20 0a 69 73 20 6b 6e 6f | 77 6e 20 61 73 20 61 6e | .is kno|wn as an|
|000057d0| 20 52 53 41 20 64 69 67 | 69 74 61 6c 20 65 6e 76 | RSA dig|ital env|
|000057e0| 65 6c 6f 70 65 2e 0a 0a | 4f 6e 65 20 6d 61 79 20 |elope...|One may |
|000057f0| 77 6f 6e 64 65 72 2c 20 | 77 68 79 20 6e 6f 74 20 |wonder, |why not |
|00005800| 6a 75 73 74 20 75 73 65 | 20 52 53 41 20 74 6f 20 |just use| RSA to |
|00005810| 65 6e 63 72 79 70 74 20 | 74 68 65 20 77 68 6f 6c |encrypt |the whol|
|00005820| 65 20 6d 65 73 73 61 67 | 65 20 61 6e 64 20 6e 6f |e messag|e and no|
|00005830| 74 20 75 73 65 20 0a 44 | 45 53 20 61 74 20 61 6c |t use .D|ES at al|
|00005840| 6c 3f 20 41 6c 74 68 6f | 75 67 68 20 74 68 69 73 |l? Altho|ugh this|
|00005850| 20 6d 61 79 20 62 65 20 | 66 69 6e 65 20 66 6f 72 | may be |fine for|
|00005860| 20 73 6d 61 6c 6c 20 6d | 65 73 73 61 67 65 73 2c | small m|essages,|
|00005870| 20 44 45 53 20 28 6f 72 | 20 61 6e 6f 74 68 65 72 | DES (or| another|
|00005880| 20 0a 63 69 70 68 65 72 | 29 20 69 73 20 70 72 65 | .cipher|) is pre|
|00005890| 66 65 72 61 62 6c 65 20 | 66 6f 72 20 6c 61 72 67 |ferable |for larg|
|000058a0| 65 72 20 6d 65 73 73 61 | 67 65 73 20 62 65 63 61 |er messa|ges beca|
|000058b0| 75 73 65 20 69 74 20 69 | 73 20 6d 75 63 68 20 66 |use it i|s much f|
|000058c0| 61 73 74 65 72 20 74 68 | 61 6e 20 52 53 41 0a 28 |aster th|an RSA.(|
|000058d0| 73 65 65 20 51 75 65 73 | 74 69 6f 6e 20 32 2e 33 |see Ques|tion 2.3|
|000058e0| 29 2e 0a 0a 49 6e 20 73 | 6f 6d 65 20 73 69 74 75 |)...In s|ome situ|
|000058f0| 61 74 69 6f 6e 73 2c 20 | 52 53 41 20 69 73 20 6e |ations, |RSA is n|
|00005900| 6f 74 20 6e 65 63 65 73 | 73 61 72 79 20 61 6e 64 |ot neces|sary and|
|00005910| 20 44 45 53 20 61 6c 6f | 6e 65 20 69 73 20 73 75 | DES alo|ne is su|
|00005920| 66 66 69 63 69 65 6e 74 | 2e 20 54 68 69 73 20 0a |fficient|. This .|
|00005930| 69 6e 63 6c 75 64 65 73 | 20 6d 75 6c 74 69 2d 75 |includes| multi-u|
|00005940| 73 65 72 20 65 6e 76 69 | 72 6f 6e 6d 65 6e 74 73 |ser envi|ronments|
|00005950| 20 77 68 65 72 65 20 73 | 65 63 75 72 65 20 44 45 | where s|ecure DE|
|00005960| 53 2d 6b 65 79 20 61 67 | 72 65 65 6d 65 6e 74 20 |S-key ag|reement |
|00005970| 63 61 6e 20 74 61 6b 65 | 20 0a 70 6c 61 63 65 2c |can take| .place,|
|00005980| 20 66 6f 72 20 65 78 61 | 6d 70 6c 65 20 62 79 20 | for exa|mple by |
|00005990| 74 68 65 20 74 77 6f 20 | 70 61 72 74 69 65 73 20 |the two |parties |
|000059a0| 6d 65 65 74 69 6e 67 20 | 69 6e 20 70 72 69 76 61 |meeting |in priva|
|000059b0| 74 65 2e 20 41 6c 73 6f | 2c 20 52 53 41 20 69 73 |te. Also|, RSA is|
|000059c0| 20 0a 75 73 75 61 6c 6c | 79 20 6e 6f 74 20 6e 65 | .usuall|y not ne|
|000059d0| 63 65 73 73 61 72 79 20 | 69 6e 20 61 20 73 69 6e |cessary |in a sin|
|000059e0| 67 6c 65 2d 75 73 65 72 | 20 65 6e 76 69 72 6f 6e |gle-user| environ|
|000059f0| 6d 65 6e 74 3b 20 66 6f | 72 20 65 78 61 6d 70 6c |ment; fo|r exampl|
|00005a00| 65 2c 20 69 66 20 79 6f | 75 20 77 61 6e 74 20 0a |e, if yo|u want .|
|00005a10| 74 6f 20 6b 65 65 70 20 | 79 6f 75 72 20 70 65 72 |to keep |your per|
|00005a20| 73 6f 6e 61 6c 20 66 69 | 6c 65 73 20 65 6e 63 72 |sonal fi|les encr|
|00005a30| 79 70 74 65 64 2c 20 6a | 75 73 74 20 64 6f 20 73 |ypted, j|ust do s|
|00005a40| 6f 20 77 69 74 68 20 44 | 45 53 20 75 73 69 6e 67 |o with D|ES using|
|00005a50| 2c 20 73 61 79 2c 20 79 | 6f 75 72 20 0a 70 65 72 |, say, y|our .per|
|00005a60| 73 6f 6e 61 6c 20 70 61 | 73 73 77 6f 72 64 20 61 |sonal pa|ssword a|
|00005a70| 73 20 74 68 65 20 44 45 | 53 20 6b 65 79 2e 20 52 |s the DE|S key. R|
|00005a80| 53 41 2c 20 61 6e 64 20 | 70 75 62 6c 69 63 2d 6b |SA, and |public-k|
|00005a90| 65 79 20 63 72 79 70 74 | 6f 67 72 61 70 68 79 20 |ey crypt|ography |
|00005aa0| 69 6e 20 67 65 6e 65 72 | 61 6c 2c 0a 69 73 20 62 |in gener|al,.is b|
|00005ab0| 65 73 74 20 73 75 69 74 | 65 64 20 66 6f 72 20 61 |est suit|ed for a|
|00005ac0| 20 6d 75 6c 74 69 2d 75 | 73 65 72 20 65 6e 76 69 | multi-u|ser envi|
|00005ad0| 72 6f 6e 6d 65 6e 74 2e | 20 41 6c 73 6f 2c 20 61 |ronment.| Also, a|
|00005ae0| 6e 79 20 73 79 73 74 65 | 6d 20 69 6e 20 77 68 69 |ny syste|m in whi|
|00005af0| 63 68 20 64 69 67 69 74 | 61 6c 0a 73 69 67 6e 61 |ch digit|al.signa|
|00005b00| 74 75 72 65 73 20 61 72 | 65 20 64 65 73 69 72 65 |tures ar|e desire|
|00005b10| 64 20 6e 65 65 64 73 20 | 52 53 41 20 6f 72 20 73 |d needs |RSA or s|
|00005b20| 6f 6d 65 20 6f 74 68 65 | 72 20 70 75 62 6c 69 63 |ome othe|r public|
|00005b30| 2d 6b 65 79 20 73 79 73 | 74 65 6d 2e 0a 0a 0a 32 |-key sys|tem....2|
|00005b40| 2e 33 20 48 6f 77 20 66 | 61 73 74 20 69 73 20 52 |.3 How f|ast is R|
|00005b50| 53 41 3f 0a 0a 41 6e 20 | 60 60 52 53 41 20 6f 70 |SA?..An |``RSA op|
|00005b60| 65 72 61 74 69 6f 6e 2c | 27 27 20 77 68 65 74 68 |eration,|'' wheth|
|00005b70| 65 72 20 66 6f 72 20 65 | 6e 63 72 79 70 74 69 6e |er for e|ncryptin|
|00005b80| 67 20 6f 72 20 64 65 63 | 72 79 70 74 69 6e 67 2c |g or dec|rypting,|
|00005b90| 20 73 69 67 6e 69 6e 67 | 0a 6f 72 20 76 65 72 69 | signing|.or veri|
|00005ba0| 66 79 69 6e 67 2c 20 69 | 73 20 65 73 73 65 6e 74 |fying, i|s essent|
|00005bb0| 69 61 6c 6c 79 20 61 20 | 6d 6f 64 75 6c 61 72 20 |ially a |modular |
|00005bc0| 65 78 70 6f 6e 65 6e 74 | 69 61 74 69 6f 6e 2c 20 |exponent|iation, |
|00005bd0| 77 68 69 63 68 20 63 61 | 6e 20 62 65 20 0a 70 65 |which ca|n be .pe|
|00005be0| 72 66 6f 72 6d 65 64 20 | 62 79 20 61 20 73 65 72 |rformed |by a ser|
|00005bf0| 69 65 73 20 6f 66 20 6d | 6f 64 75 6c 61 72 20 6d |ies of m|odular m|
|00005c00| 75 6c 74 69 70 6c 69 63 | 61 74 69 6f 6e 73 2e 0a |ultiplic|ations..|
|00005c10| 0a 49 6e 20 70 72 61 63 | 74 69 63 61 6c 20 61 70 |.In prac|tical ap|
|00005c20| 70 6c 69 63 61 74 69 6f | 6e 73 2c 20 69 74 20 69 |plicatio|ns, it i|
|00005c30| 73 20 63 6f 6d 6d 6f 6e | 20 74 6f 20 63 68 6f 6f |s common| to choo|
|00005c40| 73 65 20 61 20 73 6d 61 | 6c 6c 20 70 75 62 6c 69 |se a sma|ll publi|
|00005c50| 63 20 0a 65 78 70 6f 6e | 65 6e 74 20 66 6f 72 20 |c .expon|ent for |
|00005c60| 74 68 65 20 70 75 62 6c | 69 63 20 6b 65 79 3b 20 |the publ|ic key; |
|00005c70| 69 6e 20 66 61 63 74 2c | 20 65 6e 74 69 72 65 20 |in fact,| entire |
|00005c80| 67 72 6f 75 70 73 20 6f | 66 20 75 73 65 72 73 20 |groups o|f users |
|00005c90| 63 61 6e 20 75 73 65 20 | 0a 74 68 65 20 73 61 6d |can use |.the sam|
|00005ca0| 65 20 70 75 62 6c 69 63 | 20 65 78 70 6f 6e 65 6e |e public| exponen|
|00005cb0| 74 2e 20 54 68 69 73 20 | 6d 61 6b 65 73 20 65 6e |t. This |makes en|
|00005cc0| 63 72 79 70 74 69 6f 6e | 20 66 61 73 74 65 72 20 |cryption| faster |
|00005cd0| 74 68 61 6e 20 64 65 63 | 72 79 70 74 69 6f 6e 20 |than dec|ryption |
|00005ce0| 0a 61 6e 64 20 76 65 72 | 69 66 69 63 61 74 69 6f |.and ver|ificatio|
|00005cf0| 6e 20 66 61 73 74 65 72 | 20 74 68 61 6e 20 73 69 |n faster| than si|
|00005d00| 67 6e 69 6e 67 2e 20 41 | 6c 67 6f 72 69 74 68 6d |gning. A|lgorithm|
|00005d10| 69 63 61 6c 6c 79 2c 20 | 70 75 62 6c 69 63 2d 6b |ically, |public-k|
|00005d20| 65 79 20 0a 6f 70 65 72 | 61 74 69 6f 6e 73 20 74 |ey .oper|ations t|
|00005d30| 61 6b 65 20 4f 28 6b 5e | 32 29 20 73 74 65 70 73 |ake O(k^|2) steps|
|00005d40| 2c 20 70 72 69 76 61 74 | 65 20 6b 65 79 20 6f 70 |, privat|e key op|
|00005d50| 65 72 61 74 69 6f 6e 73 | 20 74 61 6b 65 20 4f 28 |erations| take O(|
|00005d60| 6b 5e 33 29 20 0a 73 74 | 65 70 73 2c 20 61 6e 64 |k^3) .st|eps, and|
|00005d70| 20 6b 65 79 20 67 65 6e | 65 72 61 74 69 6f 6e 20 | key gen|eration |
|00005d80| 74 61 6b 65 73 20 4f 28 | 6b 5e 34 29 20 73 74 65 |takes O(|k^4) ste|
|00005d90| 70 73 2c 20 77 68 65 72 | 65 20 6b 20 69 73 20 74 |ps, wher|e k is t|
|00005da0| 68 65 20 6e 75 6d 62 65 | 72 20 6f 66 20 0a 62 69 |he numbe|r of .bi|
|00005db0| 74 73 20 69 6e 20 74 68 | 65 20 6d 6f 64 75 6c 75 |ts in th|e modulu|
|00005dc0| 73 3b 20 4f 2d 6e 6f 74 | 61 74 69 6f 6e 20 72 65 |s; O-not|ation re|
|00005dd0| 66 65 72 73 20 74 6f 20 | 74 68 65 20 61 6e 20 75 |fers to |the an u|
|00005de0| 70 70 65 72 20 62 6f 75 | 6e 64 20 6f 6e 20 74 68 |pper bou|nd on th|
|00005df0| 65 20 0a 61 73 79 6d 70 | 74 6f 74 69 63 20 72 75 |e .asymp|totic ru|
|00005e00| 6e 6e 69 6e 67 20 74 69 | 6d 65 20 6f 66 20 61 6e |nning ti|me of an|
|00005e10| 20 61 6c 67 6f 72 69 74 | 68 6d 20 5b 32 32 5d 2e | algorit|hm [22].|
|00005e20| 0a 0a 54 68 65 72 65 20 | 61 72 65 20 6d 61 6e 79 |..There |are many|
|00005e30| 20 63 6f 6d 6d 65 72 63 | 69 61 6c 6c 79 20 61 76 | commerc|ially av|
|00005e40| 61 69 6c 61 62 6c 65 20 | 68 61 72 64 77 61 72 65 |ailable |hardware|
|00005e50| 20 69 6d 70 6c 65 6d 65 | 6e 74 61 74 69 6f 6e 73 | impleme|ntations|
|00005e60| 20 6f 66 20 52 53 41 2c | 20 0a 61 6e 64 20 74 68 | of RSA,| .and th|
|00005e70| 65 72 65 20 61 72 65 20 | 66 72 65 71 75 65 6e 74 |ere are |frequent|
|00005e80| 20 61 6e 6e 6f 75 6e 63 | 65 6d 65 6e 74 73 20 6f | announc|ements o|
|00005e90| 66 20 6e 65 77 65 72 20 | 61 6e 64 20 66 61 73 74 |f newer |and fast|
|00005ea0| 65 72 20 63 68 69 70 73 | 2e 20 54 68 65 20 0a 66 |er chips|. The .f|
|00005eb0| 61 73 74 65 73 74 20 63 | 75 72 72 65 6e 74 20 52 |astest c|urrent R|
|00005ec0| 53 41 20 63 68 69 70 20 | 5b 37 36 5d 20 68 61 73 |SA chip |[76] has|
|00005ed0| 20 61 20 74 68 72 6f 75 | 67 68 70 75 74 20 67 72 | a throu|ghput gr|
|00005ee0| 65 61 74 65 72 20 74 68 | 61 6e 20 36 30 30 20 4b |eater th|an 600 K|
|00005ef0| 62 69 74 73 20 0a 70 65 | 72 20 73 65 63 6f 6e 64 |bits .pe|r second|
|00005f00| 20 77 69 74 68 20 61 20 | 35 31 32 2d 62 69 74 20 | with a |512-bit |
|00005f10| 6d 6f 64 75 6c 75 73 2c | 20 69 6d 70 6c 79 69 6e |modulus,| implyin|
|00005f20| 67 20 74 68 61 74 20 69 | 74 20 70 65 72 66 6f 72 |g that i|t perfor|
|00005f30| 6d 73 20 6f 76 65 72 20 | 31 30 30 30 20 0a 52 53 |ms over |1000 .RS|
|00005f40| 41 20 70 72 69 76 61 74 | 65 2d 6b 65 79 20 6f 70 |A privat|e-key op|
|00005f50| 65 72 61 74 69 6f 6e 73 | 20 70 65 72 20 73 65 63 |erations| per sec|
|00005f60| 6f 6e 64 2e 20 49 74 20 | 69 73 20 65 78 70 65 63 |ond. It |is expec|
|00005f70| 74 65 64 20 74 68 61 74 | 20 52 53 41 20 73 70 65 |ted that| RSA spe|
|00005f80| 65 64 73 20 0a 77 69 6c | 6c 20 72 65 61 63 68 20 |eds .wil|l reach |
|00005f90| 31 20 4d 62 69 74 2f 73 | 65 63 6f 6e 64 20 77 69 |1 Mbit/s|econd wi|
|00005fa0| 74 68 69 6e 20 61 20 79 | 65 61 72 20 6f 72 20 73 |thin a y|ear or s|
|00005fb0| 6f 2e 0a 0a 42 79 20 63 | 6f 6d 70 61 72 69 73 6f |o...By c|ompariso|
|00005fc0| 6e 2c 20 44 45 53 20 69 | 73 20 6d 75 63 68 20 66 |n, DES i|s much f|
|00005fd0| 61 73 74 65 72 20 74 68 | 61 6e 20 52 53 41 2e 20 |aster th|an RSA. |
|00005fe0| 49 6e 20 73 6f 66 74 77 | 61 72 65 2c 20 44 45 53 |In softw|are, DES|
|00005ff0| 20 69 73 20 67 65 6e 65 | 72 61 6c 6c 79 20 61 74 | is gene|rally at|
|00006000| 20 0a 6c 65 61 73 74 20 | 31 30 30 20 74 69 6d 65 | .least |100 time|
|00006010| 73 20 61 73 20 66 61 73 | 74 20 61 73 20 52 53 41 |s as fas|t as RSA|
|00006020| 2e 20 49 6e 20 68 61 72 | 64 77 61 72 65 2c 20 44 |. In har|dware, D|
|00006030| 45 53 20 69 73 20 62 65 | 74 77 65 65 6e 20 31 2c |ES is be|tween 1,|
|00006040| 30 30 30 20 61 6e 64 20 | 31 30 2c 30 30 30 0a 74 |000 and |10,000.t|
|00006050| 69 6d 65 73 20 61 73 20 | 66 61 73 74 2c 20 64 65 |imes as |fast, de|
|00006060| 70 65 6e 64 69 6e 67 20 | 6f 6e 20 74 68 65 20 69 |pending |on the i|
|00006070| 6d 70 6c 65 6d 65 6e 74 | 61 74 69 6f 6e 73 2e 20 |mplement|ations. |
|00006080| 52 53 41 20 77 69 6c 6c | 20 70 72 6f 62 61 62 6c |RSA will| probabl|
|00006090| 79 20 6e 61 72 72 6f 77 | 20 0a 74 68 65 20 67 61 |y narrow| .the ga|
|000060a0| 70 20 61 20 62 69 74 20 | 69 6e 20 63 6f 6d 69 6e |p a bit |in comin|
|000060b0| 67 20 79 65 61 72 73 2c | 20 61 73 20 69 74 20 66 |g years,| as it f|
|000060c0| 69 6e 64 73 20 67 72 6f | 77 69 6e 67 20 63 6f 6d |inds gro|wing com|
|000060d0| 6d 65 72 63 69 61 6c 20 | 6d 61 72 6b 65 74 73 2c |mercial |markets,|
|000060e0| 20 62 75 74 20 0a 77 69 | 6c 6c 20 6e 65 76 65 72 | but .wi|ll never|
|000060f0| 20 6d 61 74 63 68 20 74 | 68 65 20 70 65 72 66 6f | match t|he perfo|
|00006100| 72 6d 61 6e 63 65 20 6f | 66 20 44 45 53 2e 0a 0a |rmance o|f DES...|
|00006110| 0a 32 2e 34 20 48 6f 77 | 20 6d 75 63 68 20 65 78 |.2.4 How| much ex|
|00006120| 74 72 61 20 6d 65 73 73 | 61 67 65 20 6c 65 6e 67 |tra mess|age leng|
|00006130| 74 68 20 69 73 20 63 61 | 75 73 65 64 20 62 79 20 |th is ca|used by |
|00006140| 75 73 69 6e 67 20 52 53 | 41 3f 0a 0a 4f 6e 6c 79 |using RS|A?..Only|
|00006150| 20 61 20 76 65 72 79 20 | 73 6d 61 6c 6c 20 61 6d | a very |small am|
|00006160| 6f 75 6e 74 20 6f 66 20 | 64 61 74 61 20 65 78 70 |ount of |data exp|
|00006170| 61 6e 73 69 6f 6e 20 69 | 73 20 69 6e 76 6f 6c 76 |ansion i|s involv|
|00006180| 65 64 20 77 68 65 6e 20 | 75 73 69 6e 67 20 52 53 |ed when |using RS|
|00006190| 41 2e 20 46 6f 72 20 0a | 65 6e 63 72 79 70 74 69 |A. For .|encrypti|
|000061a0| 6f 6e 2c 20 61 20 6d 65 | 73 73 61 67 65 20 6d 61 |on, a me|ssage ma|
|000061b0| 79 20 62 65 20 70 61 64 | 64 65 64 20 74 6f 20 61 |y be pad|ded to a|
|000061c0| 20 6c 65 6e 67 74 68 20 | 74 68 61 74 20 69 73 20 | length |that is |
|000061d0| 61 20 6d 75 6c 74 69 70 | 6c 65 20 6f 66 20 74 68 |a multip|le of th|
|000061e0| 65 20 0a 62 6c 6f 63 6b | 20 6c 65 6e 67 74 68 2c |e .block| length,|
|000061f0| 20 75 73 75 61 6c 6c 79 | 20 36 34 20 62 69 74 73 | usually| 64 bits|
|00006200| 2c 20 73 69 6e 63 65 20 | 52 53 41 20 69 73 20 75 |, since |RSA is u|
|00006210| 73 75 61 6c 6c 79 20 63 | 6f 6d 62 69 6e 65 64 20 |sually c|ombined |
|00006220| 77 69 74 68 20 61 20 0a | 73 65 63 72 65 74 2d 6b |with a .|secret-k|
|00006230| 65 79 20 62 6c 6f 63 6b | 20 63 69 70 68 65 72 20 |ey block| cipher |
|00006240| 73 75 63 68 20 61 73 20 | 44 45 53 20 28 73 65 65 |such as |DES (see|
|00006250| 20 51 75 65 73 74 69 6f | 6e 20 32 2e 31 32 29 2e | Questio|n 2.12).|
|00006260| 20 45 6e 63 72 79 70 74 | 69 6e 67 20 0a 74 68 65 | Encrypt|ing .the|
|00006270| 20 44 45 53 20 6b 65 79 | 20 74 61 6b 65 73 20 61 | DES key| takes a|
|00006280| 73 20 6d 61 6e 79 20 61 | 64 64 69 74 69 6f 6e 61 |s many a|dditiona|
|00006290| 6c 20 62 69 74 73 20 61 | 73 20 74 68 65 20 73 69 |l bits a|s the si|
|000062a0| 7a 65 20 6f 66 20 74 68 | 65 20 52 53 41 20 6d 6f |ze of th|e RSA mo|
|000062b0| 64 75 6c 75 73 2e 0a 0a | 0a 46 6f 72 20 61 75 74 |dulus...|.For aut|
|000062c0| 68 65 6e 74 69 63 61 74 | 69 6f 6e 2c 20 61 6e 20 |henticat|ion, an |
|000062d0| 52 53 41 20 64 69 67 69 | 74 61 6c 20 73 69 67 6e |RSA digi|tal sign|
|000062e0| 61 74 75 72 65 20 69 73 | 20 61 70 70 65 6e 64 65 |ature is| appende|
|000062f0| 64 20 74 6f 20 61 20 64 | 6f 63 75 6d 65 6e 74 2e |d to a d|ocument.|
|00006300| 0a 41 6e 20 52 53 41 20 | 73 69 67 6e 61 74 75 72 |.An RSA |signatur|
|00006310| 65 2c 20 69 6e 63 6c 75 | 64 69 6e 67 20 69 6e 66 |e, inclu|ding inf|
|00006320| 6f 72 6d 61 74 69 6f 6e | 20 73 75 63 68 20 61 73 |ormation| such as|
|00006330| 20 74 68 65 20 6e 61 6d | 65 20 6f 66 20 74 68 65 | the nam|e of the|
|00006340| 20 73 69 67 6e 65 72 2c | 20 69 73 20 0a 74 79 70 | signer,| is .typ|
|00006350| 69 63 61 6c 6c 79 20 61 | 20 66 65 77 20 68 75 6e |ically a| few hun|
|00006360| 64 72 65 64 20 62 79 74 | 65 73 20 6c 6f 6e 67 2e |dred byt|es long.|
|00006370| 20 4f 6e 65 20 6f 72 20 | 6d 6f 72 65 20 63 65 72 | One or |more cer|
|00006380| 74 69 66 69 63 61 74 65 | 73 20 28 73 65 65 20 51 |tificate|s (see Q|
|00006390| 75 65 73 74 69 6f 6e 20 | 0a 33 2e 35 29 20 6d 61 |uestion |.3.5) ma|
|000063a0| 79 20 62 65 20 69 6e 63 | 6c 75 64 65 64 20 61 73 |y be inc|luded as|
|000063b0| 20 77 65 6c 6c 3b 20 63 | 65 72 74 69 66 69 63 61 | well; c|ertifica|
|000063c0| 74 65 73 20 63 61 6e 20 | 62 65 20 75 73 65 64 20 |tes can |be used |
|000063d0| 69 6e 20 63 6f 6e 6a 75 | 6e 63 74 69 6f 6e 0a 77 |in conju|nction.w|
|000063e0| 69 74 68 20 61 6e 79 20 | 64 69 67 69 74 61 6c 20 |ith any |digital |
|000063f0| 73 69 67 6e 61 74 75 72 | 65 20 6d 65 74 68 6f 64 |signatur|e method|
+--------+-------------------------+-------------------------+--------+--------+