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crypto-slides-09-pk1.1x1

# crypto-slides-09-pk1.1x1 - Public Key Cryptography 1 See...

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Public Key Cryptography 1 See: Diffie and Hellman, New Directions in Cryptography , IEEE Transactions on Information Theory, Vol. IT-22, No. 6, Nov. 1976. c circlecopyrt Eli Biham - August 18, 2010 220 Public Key Cryptography 1 (9)

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Trapdoor Problems Basing the solution on the complexity of problems, which are easy to solve for the legal users, but are very difficult to the eavesdroppers. Such problems are called trapdoor problems . They allow to exchange secure common keys using insecure channels! c circlecopyrt Eli Biham - August 18, 2010 221 Public Key Cryptography 1 (9)
Diffie-Hellman Key Exchange Protocol Based on number theory assumptions. The basic idea : 1. It is easy to calculate a x mod q for any a , x and q . (The algorithm is shown in Slide 272). 2. There is no efficient algorithm which computes x given a , q , and a x mod q. This is the discrete logarithm (DLOG) problem. c circlecopyrt Eli Biham - August 18, 2010 222 Public Key Cryptography 1 (9)

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Diffie-Hellman Key Exchange Protocol (cont.) Notations : Denote x in binary representation as x = x n 1 x n 2 ...x 1 x 0 , where x = n 1 i =0 x i 2 i . Let q be a large prime number. All the multiplications from now on are modulo q . c circlecopyrt Eli Biham - August 18, 2010 223 Public Key Cryptography 1 (9)
Diffie-Hellman Key Exchange Protocol (cont.) Preparations : System parameters common to all users : Let q be a large prime number ( q > 2 400 ). Let a an integer 1 < a < q . Public and private keys : Each user U: chooses a random value X U (1 < X U < q ) and keeps it secret. publishes Y U = a X U mod q . c circlecopyrt Eli Biham - August 18, 2010 224 Public Key Cryptography 1 (9)

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Diffie-Hellman Key Exchange Protocol (cont.) The key exchange : Two users A,B who wish to have a common key, known only to them: A calculates K = ( Y B ) X A mod q .
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crypto-slides-09-pk1.1x1 - Public Key Cryptography 1 See...

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