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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 25 "1. An RSA public key has
 " }{TEXT 256 8 "n = 5063" }{TEXT -1 14 " and exponent " }{TEXT 257 4 
"a=49" }{TEXT -1 38 ".  Find the corresponding private key." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "n := 5063; a := 49;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"%j]" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"aG\"#\\" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
12 "ifactor (n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%!G6#\"#h\"\"\"
-F%6#\"#$)F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "p := 61; q \+
:= 83;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG\"#h" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%\"qG\"#$)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 19 "phi := (p-1)*(q-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$phiG\"
%?\\" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "x := modp(1/a, phi)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG\"%4A" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 29 "Private key is: [5063, 2209]." }}}{EXCHG {PARA 
257 "" 0 "" {TEXT -1 22 "2. Encode the integer " }{TEXT 259 2 "39" }
{TEXT -1 97 " using the public key.  What do you get? Decode this usin
g the private key you found. Do you get " }{TEXT 258 2 "39" }{TEXT -1 
6 " back?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "modp(39 &^ a, \+
n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$Q)" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 18 "modp(838 &^ x, n);" }}{PARA 11 "" 1 "" {XPPMATH 
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