Equation Preliminaries Choose two safe prime numbers p and q, form , and determine . Safe prime numbers are of the form , where p is also a prime. Define the function Equation Note: that is usually an exponential . The notation used is a little awkward because only the exponential should be calculated . The division by cannot be accomplished because has no MMI . The numerator should be a multiple of , and the “normal” division should result in an integer with no residue. Choose a generator value such that Equation Note: See section 6.12 regarding choosing values of . The public key is . The private key is λ. Encrypt The plaintext message is . Choose a random number . Calculate the encrypted message Equation Decrypt Plaintext Equation Explanation The Generator g Starting from the Carmichael function Equation 63. Equation If we use binomial expansion of the polynomial, we get where
Equation Preliminaries Choose two safe prime numbers p and q, form , and determine . Safe prime numbers are of the form , where p is also a prime. Define the function Equation Note: that is usually an exponential . The notation used is a little awkward because only the exponential should be calculated . The division by cannot be accomplished because has no MMI . The numerator should be a multiple of , and the “normal” division should result in an integer with no residue. Choose a generator value such that Equation Note: See section 6.12 regarding choosing values of . The public key is . The private key is λ. Encrypt The plaintext message is . Choose a random number . Calculate the encrypted message Equation Decrypt Plaintext Equation Explanation The Generator g Starting from the Carmichael function Equation 63. Equation If we use binomial expansion of the polynomial, we get where
AlgebraOfEncryption_v4.docx