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(Tcl) Diffie-Hellman Key Exchange (DH)Diffie-Hellman key exchange (DH) is a cryptographic protocol that allows two parties that have no prior knowledge of each other to jointly establish a shared secret key. This example demonstrates how two parties (Alice and Bob) can compute an N-bit shared secret key without the key ever being transmitted.
load ./chilkat.dll # This example requires the Chilkat API to have been previously unlocked. # See Global Unlock Sample for sample code. # Create two separate instances of the DH object. set dhBob [new_CkDh] set dhAlice [new_CkDh] # The DH algorithm begins with a large prime, P, and a generator, G. # These don't have to be secret, and they may be transmitted over an insecure channel. # The generator is a small integer and typically has the value 2 or 5. # The Chilkat DH component provides the ability to use known # "safe" primes, as well as a method to generate new safe primes. # This example will use a known safe prime. Generating # new safe primes is a time-consuming CPU intensive task # and is normally done offline. # Bob will choose to use the 2nd of our 8 pre-chosen safe primes. # It is the Prime for the 2nd Oakley Group (RFC 2409) -- # 1024-bit MODP Group. Generator is 2. # The prime is: 2^1024 - 2^960 - 1 + 2^64 * { [2^894 pi] + 129093 } CkDh_UseKnownPrime $dhBob 2 # The computed shared secret will be equal to the size of the prime (in bits). # In this case the prime is 1024 bits, so the shared secret will be 128 bytes (128 * 8 = 1024). # However, the result is returned as an SSH1-encoded bignum in hex string format. # The SSH1-encoding prepends a 2-byte count, so the result is going to be 2 bytes # longer: 130 bytes. This results in a hex string that is 260 characters long (two chars # per byte for the hex encoding). # Bob will now send P and G to Alice. set p [CkDh_p $dhBob] set g [CkDh_get_G $dhBob] # Alice calls SetPG to set P and G. SetPG checks # the values to make sure it's a safe prime and will # return 0 if not. set success [CkDh_SetPG $dhAlice $p $g] if {$success != 1} then { puts "P is not a safe prime" delete_CkDh $dhBob delete_CkDh $dhAlice exit } # Each side begins by generating an "E" # value. The CreateE method has one argument: numBits. # It should be set to twice the size of the number of bits # in the session key. # Let's say we want to generate a 128-bit session key # for AES encryption. The shared secret generated by the Diffie-Hellman # algorithm will be longer, so we'll hash the result to arrive at the # desired session key length. However, the length of the session # key we'll utlimately produce determines the value that should be # passed to the CreateE method. # In this case, we'll be creating a 128-bit session key, so pass 256 to CreateE. # This setting is for security purposes only -- the value # passed to CreateE does not change the length of the shared secret # that is produced by Diffie-Hellman. # Also, there is no need to pass in a value larger # than 2 times the expected session key length. It suffices to # pass exactly 2 times the session key length. # Bob generates a random E (which has the mathematical # properties required for DH). set eBob [CkDh_createE $dhBob 256] # Alice does the same: set eAlice [CkDh_createE $dhAlice 256] # The "E" values are sent over the insecure channel. # Bob sends his "E" to Alice, and Alice sends her "E" to Bob. # Each side computes the shared secret by calling FindK. # "K" is the shared-secret. # Bob computes the shared secret from Alice's "E": set kBob [CkDh_findK $dhBob $eAlice] # Alice computes the shared secret from Bob's "E": set kAlice [CkDh_findK $dhAlice $eBob] # Amazingly, kBob and kAlice are identical and the expected # length (260 characters). The strings contain the hex encoded bytes of # our shared secret: puts "Bob's shared secret:" puts "$kBob" puts "Alice's shared secret (should be equal to Bob's)" puts "$kAlice" # To arrive at a 128-bit session key for AES encryption, Bob and Alice should # both transform the raw shared secret using a hash algorithm that produces # the size of session key desired. MD5 produces a 16-byte (128-bit) result, so # this is a good choice for 128-bit AES. # To produce the session key: set crypt [new_CkCrypt2] CkCrypt2_put_EncodingMode $crypt "hex" CkCrypt2_put_HashAlgorithm $crypt "md5" set sessionKey [CkCrypt2_hashStringENC $crypt $kBob] puts "128-bit Session Key:" puts "$sessionKey" # Encrypt something... CkCrypt2_put_CryptAlgorithm $crypt "aes" CkCrypt2_put_KeyLength $crypt 128 CkCrypt2_put_CipherMode $crypt "cbc" # Use an IV that is the MD5 hash of the session key... set iv [CkCrypt2_hashStringENC $crypt $sessionKey] # AES uses a 16-byte IV: puts "Initialization Vector:" puts "$iv" CkCrypt2_SetEncodedKey $crypt $sessionKey "hex" CkCrypt2_SetEncodedIV $crypt $iv "hex" # Encrypt some text: CkCrypt2_put_EncodingMode $crypt "base64" set cipherText64 [CkCrypt2_encryptStringENC $crypt "The quick brown fox jumps over the lazy dog"] puts "$cipherText64" set plainText [CkCrypt2_decryptStringENC $crypt $cipherText64] puts "$plainText" delete_CkDh $dhBob delete_CkDh $dhAlice delete_CkCrypt2 $crypt |
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