A Polyalphabetic substitution cipher is simply a substitution cipher with an alphabet that changes. For example one could have two alphabets:
Plain Alphabet: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Cipher Alphabet #1: B D F H J L N P R T V X Z A C E G I K M O Q S U W Y Cipher Alphabet #2: Z Y X W V U T S R Q P O N M L K J I H G F E D C B A
Now to encrypt the message ``The quick brown fox jumped over the lazy dogs" we would alternate between the two cipher alphabets, using #1 for every first letter and #2 for every second, to get: ``Msj joxfp dicda ucu tfzkjw ceji msj xzyb hln".
Polyalphabetic substitution ciphers are useful because the are less easily broken by frequency analysis, however if an attacker knows for instance that the message has a period n, then he simply can individually frequency analyze each cipher alphabet.
The number of letters encrypted before a polyalphabetic substitution cipher returns to its first cipher alphabet is called its period. The larger the period, the stronger the cipher. Of course, this method of encryption is certainly not secure by any definition and should not be applied to any real-life scenarios.