Earn beer money! If you spot an error, send it my way. Each technical error earns $5. Grammar errors may earn an award, but they're harder to define and so I'm not making guarantees. I reserve the right to decide what constitutes an error and the right to award multiple prizes in the case of a tie. Thanks to: John Viega. Omissions and Errors: Page Old New Fixed in version vii http://www.wayner.org/books/pogs/ http:/www.wayner.org/books/pog/ 1.01 10 Hash functions are pure blenders that accept a file Hash functions are pure blenders that accept a string of bits 1.01 10 .. are MD5 and its newer cousin the Secure Hash Algorithm ... are MD5 and it's newer and stronger cousin, the Secure Hash Algorithm 1.01 11 ...The nature of hash functions means that only someone who knows this can generate this value. It should be practically impossible to start with $h(key| file)$ and the file itself and find the value of the $key$. It should be practically impossible to start with $h(key| file)$ and the file itself and find the value of the $key$. In many simple cases, it should also be practically impossible to create a value of $h(key,file)$ without knowing $key$. A more sophisticated protocol known as HMAC offers more strength. 1.01 11 Some avoid this problem by applying the DES algorithm two or three times with different keys effectively doubling or tripling the size of the key. Some avoid this problem by applying the DES algorithm three times with different keys effectively tripling the size of the key. 1.01 12 In simple cases when public key algorithms like RSA are used, digital signatures will be denoted as $f_d(x)$ where $d$ is the decryption key which is normally kept private.  If hash functions are used, the digital signature will be denoted as $h(key,x)$ where the value of $key$ must be known to compute it. In simple cases when public key algorithms like RSA are used, digital signatures will be denoted as $f_d(x)$ where $d$ is the decryption key which is normally kept private. This privacy offers a degree of \newterm{non-reputability}, a term that means that it's difficult for someone to deny signing a document. If hash functions are used, the digital signature will be denoted as $h(key,x)$ where the value of $key$ must be known to compute it. Both the signer and the verifier must know the same value of $key$ preventing any non-repudiation. 1.01 18 If you need more understanding, please consult the basic references like the {\em Handbook of Applied Cryptography} . If you need more understanding, please consult the basic references like the {\em Handbook of Applied Cryptography} or {\em Modern Cryptography}. 1.01