Given some text you suspect has been encrypted with a Vigenère cipher, extract the key and plaintext. There are several methods for doing this. See the Wikipedia entry for more information. Use the following encrypted text:

MOMUD EKAPV TQEFM OEVHP AJMII CDCTI FGYAG JSPXY ALUYM NSMYH
VUXJE LEPXJ FXGCM JHKDZ RYICU HYPUS PGIGM OIYHF WHTCQ KMLRD
ITLXZ LJFVQ GHOLW CUHLO MDSOE KTALU VYLNZ RFGBX PHVGA LWQIS
FGRPH JOOFW GUBYI LAPLA LCAFA AMKLG CETDW VOELJ IKGJB XPHVG
ALWQC SNWBU BYHCU HKOCE XJEYK BQKVY KIIEH GRLGH XEOLW AWFOJ
ILOVV RHPKD WIHKN ATUHN VRYAQ DIVHX FHRZV QWMWV LGSHN NLVZS
JLAKI FHXUF XJLXM TBLQV RXXHR FZXGV LRAJI EXPRV OSMNP KEPDT
LPRWM JAZPK LQUZA ALGZX GVLKL GJTUI ITDSU REZXJ ERXZS HMPST
MTEOE PAPJH SMFNB YVQUZ AALGA YDNMP AQOWT UHDBV TSMUE UIMVH
QGVRW AEFSP EMPVE PKXZY WLKJA GWALT VYYOB YIXOK IHPDS EVLEV
RVSGB JOGYW FHKBL GLXYA MVKIS KIEHY IMAPX UOISK PVAGN MZHPW
TTZPV XFCCD TUHJH WLAPF YULTB UXJLN SIJVV YOVDJ SOLXG TGRVO
SFRII CTMKO JFCQF KTINQ BWVHG TENLH HOGCS PSFPV GJOKM SIFPR
ZPAAS ATPTZ FTPPD PORRF TAXZP KALQA WMIUD BWNCT LEFKO ZQDLX
BUXJL ASIMR PNMBF ZCYLV WAPVF QRHZV ZGZEF KBYIO OFXYE VOWGB
BXVCB XBAWG LQKCM ICRRX MACUO IKHQU AJEGL OIJHH XPVZW JEWBA
FWAML ZZRXJ EKAHV FASMU LVVUT TGK

Letter frequencies for English can be found here.

Specifics for this task:

 Take only the ciphertext as input. You can assume it's all capitalized and has no punctuation, but it might have whitespace.
 Assume the plaintext is written in English.
 Find and output the key.
 Use that key to decrypt and output the original plaintext. Maintaining the whitespace from the ciphertext is optional.
 The algorithm doesn't have to be perfect (which may not be possible) but it should work when given enough ciphertext. The example above is fairly long, and should be plenty for any algorithm.
# from Wikipedia
constant %English-letter-freq = (
     E => 12.70,  L => 4.03,  Y => 1.97,  P => 1.93,  T => 9.06,  A => 8.17,  O => 7.51,  I => 6.97,  N => 6.75,
     S =>  6.33,  H => 6.09,  R => 5.99,  D => 4.25,  C => 2.78,  U => 2.76,  M => 2.41,  W => 2.36,  F => 2.23,
     G =>  2.02,  B => 1.29,  V => 0.98,  K => 0.77,  J => 0.15,  X => 0.15,  Q => 0.10,  Z => 0.07
);
constant @alphabet = %English-letter-freq.keys.sort;
constant max_key_lengths = 5; # number of keylengths to try
 
sub myguess ($text) {
    my ($seqtext, @spacing, @factors, $pos, %freq, %Keys);
 
    # Kasiski examination
    $seqtext = $text;
    while ($seqtext ~~ /$<sequence>=[...].*$<sequence>/) {
        $seqtext = substr($seqtext, 1+index($seqtext, $<sequence>));
        push @spacing, 1 + index($seqtext, $<sequence>);
    }
    for @spacing -> $j {
        %freq{$_}++ for grep { $j %% $_ }, 2..$j;
    }
 
    # discard very short keys, and test only the most likely remaining key lengths
    (%freq.keys.grep(* > 3).sort({%freq{$_}}).tail(max_key_lengths)).race(:1batch).map: -> $keylen {
        my $key-guess = '';
        loop (my $i = 0; $i < $keylen; $i++) {
            my ($mykey, %chi-square, $best-guess);
            loop (my $j = 0; $j < $text.chars; $j += $keylen) {
                $mykey ~= substr($text, ($j+$i) % $text.chars, 1);
            }
 
            for @alphabet -> $subkey {
                my $decrypted = mycrypt($mykey, $subkey);
                my $length    = $decrypted.chars;
                for @alphabet -> $char {
                    my $expected = %English-letter-freq{$char} * $length / 100;
                    my $observed = $decrypted.comb.grep(* eq $char).elems;
                    %chi-square{$subkey} += ($observed - $expected)² / $expected if $observed;
                }
            }
            %Keys{$keylen}{'score'} = %chi-square{@alphabet[0]};
            for %chi-square.keys.sort -> $sk {
                if (%chi-square{$sk} <= %Keys{$keylen}{'score'}) {
                    $best-guess = $sk;
                    %Keys{$keylen}{'score'} = %chi-square{$sk};
                }
            }
            $key-guess ~= $best-guess;
        }
        %Keys{$keylen}{'key'} = $key-guess;
    }
    %Keys.keys.sort({ %Keys{$_}{'score'} }).map:{ %Keys{$_}{'key'} };
}
 
sub mycrypt ($text, $key) {
    constant %values-numbers = @alphabet Z=> ^@alphabet;
    constant %values-letters = %values-numbers.invert;
 
    my ($new-text);
    my $keylen = $key.chars;
    loop (my $i = 0; $i < $text.chars; $i++) {
        my $val =  -1 * %values-numbers{substr( $key, $i%$keylen, 1)} # negative shift for decode
                 +      %values-numbers{substr($text, $i,         1)};
        $new-text ~= %values-letters{ $val % @alphabet };
    }
    return $new-text;
}
 
my $cipher-text = .uc.trans(@alphabet => '', :c) given q:to/EOD/;
    MOMUD EKAPV TQEFM OEVHP AJMII CDCTI FGYAG JSPXY ALUYM NSMYH
    VUXJE LEPXJ FXGCM JHKDZ RYICU HYPUS PGIGM OIYHF WHTCQ KMLRD
    ITLXZ LJFVQ GHOLW CUHLO MDSOE KTALU VYLNZ RFGBX PHVGA LWQIS
    FGRPH JOOFW GUBYI LAPLA LCAFA AMKLG CETDW VOELJ IKGJB XPHVG
    ALWQC SNWBU BYHCU HKOCE XJEYK BQKVY KIIEH GRLGH XEOLW AWFOJ
    ILOVV RHPKD WIHKN ATUHN VRYAQ DIVHX FHRZV QWMWV LGSHN NLVZS
    JLAKI FHXUF XJLXM TBLQV RXXHR FZXGV LRAJI EXPRV OSMNP KEPDT
    LPRWM JAZPK LQUZA ALGZX GVLKL GJTUI ITDSU REZXJ ERXZS HMPST
    MTEOE PAPJH SMFNB YVQUZ AALGA YDNMP AQOWT UHDBV TSMUE UIMVH
    QGVRW AEFSP EMPVE PKXZY WLKJA GWALT VYYOB YIXOK IHPDS EVLEV
    RVSGB JOGYW FHKBL GLXYA MVKIS KIEHY IMAPX UOISK PVAGN MZHPW
    TTZPV XFCCD TUHJH WLAPF YULTB UXJLN SIJVV YOVDJ SOLXG TGRVO
    SFRII CTMKO JFCQF KTINQ BWVHG TENLH HOGCS PSFPV GJOKM SIFPR
    ZPAAS ATPTZ FTPPD PORRF TAXZP KALQA WMIUD BWNCT LEFKO ZQDLX
    BUXJL ASIMR PNMBF ZCYLV WAPVF QRHZV ZGZEF KBYIO OFXYE VOWGB
    BXVCB XBAWG LQKCM ICRRX MACUO IKHQU AJEGL OIJHH XPVZW JEWBA
    FWAML ZZRXJ EKAHV FASMU LVVUT TGK
EOD
 
for myguess($cipher-text) -> $key {
    say "Key        $key\n" ~
        "Key length {$key.chars}\n" ~
        "Plaintext  {substr(mycrypt($cipher-text, $key), 0, 80)}...\n";
}