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EEC 693/793 Special Topics in Electrical Engineering Secure and Dependable Computing Lecture 6 Wenbing Zhao Department of Electrical and Computer Engineering Cleveland State University wenbing@ieee.org

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2 Spring 2008EEC693: Secure & Dependable ComputingWenbing Zhao Outline Public-key algorithms Digital signatures Message digest Message authentication code Public key management

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3 Spring 2008EEC693: Secure & Dependable ComputingWenbing Zhao Public-Key Algorithms Distributing keys => the weakest link in most cryptosystems –No matter how strong a cryptosystem was, if an intruder could steal the key, the system was worthless –Cryptologists always took for granted that the encryption key and decryption key were the same Diffie and Hellman (1976) proposed a radically new kind of cryptosystem: encryption and decryption keys were different –D(E(P)) = P –It is exceedingly difficult to deduce D from E –E cannot be broken by a chosen plaintext attack

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4 Spring 2008EEC693: Secure & Dependable ComputingWenbing Zhao Public-Key Algorithms Public-key cryptography: –Encryption algorithm and the encryption key can be made public How to establish a secure channel –Alice and Bob have never had previous contact –Alice sends Bob E B (P) (message P encrypted using Bob’s public encryption key E B ) –Bob receives the encrypted message and retrieves the plaintext by using his private key P = D B (E B (P)) –Bobs then sends a reply E A (R) to Alice

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5 Spring 2008EEC693: Secure & Dependable ComputingWenbing Zhao RSA Rivest, Shamir, Adleman, 1978: a good method for public- key cryptography RSA method: –Choose two large primes, p and q (typically 1024 bits) –Compute n = p q and z = ( p-1 ) ( q-1 ) –Choose a number relatively prime to z and call it d –Find e such that e d = 1 mod z To encrypt a message, P, Compute C = P e (mod n) To decrypt C, compute P = C d (mod n) The public key consists of the pair (e, n) The private key consists of the pair (d, n)

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6 Spring 2008EEC693: Secure & Dependable ComputingWenbing Zhao RSA An example of the RSA algorithm –P = 3, q = 11 => n = 33 and z = 20 –A suitable value for d = 7 –e can be found by solving the eq. 7e = 1 (mod 20) => e = 3 –C = P 3 (mod 33), P = C 7 (mod 33)

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7 Spring 2008EEC693: Secure & Dependable ComputingWenbing Zhao Digital Signatures Requirement on digital signatures: one party can send a signed message to another party in such a way that the following conditions hold: –The receiver can verify the claimed identity of the sender –The sender cannot later repudiate the contents of the message –The receiver cannot possibly have fabricated the message himself

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8 Spring 2008EEC693: Secure & Dependable ComputingWenbing Zhao Symmetric-Key Signatures Big Brother (BB): a central authority that knows everything and whom everyone trusts –Each user chooses a secret key and shares it with BB Digital signatures with Big Brother

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9 Spring 2008EEC693: Secure & Dependable ComputingWenbing Zhao Public-Key Signatures Digital signatures using public-key cryptography –Requires E(D(P)) = P (in addition to D(E(P)) = P)

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10 Spring 2008EEC693: Secure & Dependable ComputingWenbing Zhao Message Digests Message digest (MD): using a one-way hash function that takes an arbitrarily long piece of plaintext and from it computes a fixed-length bit string Requirement on the hash function: –Given P, it is easy to compute MD(P) –Given MD(P), it is effectively impossible to find P –Given P no one can find P’ such that MD(P’) = MD(P) –A change to the input of even 1 bit produces a very different output

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11 Spring 2008EEC693: Secure & Dependable ComputingWenbing Zhao Digital Signatures Using Message Digests

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12 Spring 2008EEC693: Secure & Dependable ComputingWenbing Zhao MD5 One of the most widely used hash functions MD5 is the fifth in a series of message digests designed by Ronald Rivest (1992) It operates by mangling bits in a sufficiently complicated way that every output bit is affected by every input bit MD5 generates a 128-bit fixed value

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13 Spring 2008EEC693: Secure & Dependable ComputingWenbing Zhao SHA-1 SHA-1: Secure Hash Algorithm 1, developed by National Security Agency (NSA) and blessed by NIST. It generates 160-bit message digest Use of SHA-1 and RSA for signing nonsecret messages

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14 Spring 2008EEC693: Secure & Dependable ComputingWenbing Zhao Message Authentication Code MACs are used between two parties that share a secret key in order to validate information transmitted between these parties The MAC mechanism that is based on cryptographic hash functions is called HMAC: –Append the key to the plaintext and generate a digest using a hash function –Ship the plaintext together with the digest

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15 Spring 2008EEC693: Secure & Dependable ComputingWenbing Zhao Management of Public Keys Problem statement Certificates X.509 Public key infrastructure

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16 Spring 2008EEC693: Secure & Dependable ComputingWenbing Zhao Problems with Public-Key Management If Alice and Bob do not know each other, how do they get each other’s public keys to start the communication process ? –It is essential Alice gets Bob’s public key, not someone else’s A way for Trudy to subvert public-key encryption

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17 Spring 2008EEC693: Secure & Dependable ComputingWenbing Zhao Certificates Certification Authority (CA): an organization that certifies public keys –It certifies the public keys belonging to people, companies, or even attributes –CA does not need to be on-line all the time (in ideal scenarios) A possible certificate and its signed hash

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18 Spring 2008EEC693: Secure & Dependable ComputingWenbing Zhao X.509 Devised and approved by ITU The basic fields of an X.509 certificate

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19 Spring 2008EEC693: Secure & Dependable ComputingWenbing Zhao Public-Key Infrastructures A Public-Key Infrastructure (PKI) is needed for reasons of –Availability, Scalability, Ease of management A PKI has multiple components –Users, CAs, Certificates, Directories A PKI provides a way of structuring these components and define standards for the various documents and protocols –A simple form of PKI is hierarchical CAs

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20 Spring 2008EEC693: Secure & Dependable ComputingWenbing Zhao Public-Key Infrastructures Hierarchical PKI A chain of trust/certification path: A chain of certificates going back to the root

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21 Spring 2008EEC693: Secure & Dependable ComputingWenbing Zhao Public-Key Infrastructures Revocation: sometimes certificates can be revoked, due to a number of reasons Reinstatement: a revoked certificate could conceivably be reinstated Each CA periodically issues a CRL (Certificate Revocation List) giving the serial numbers of all certificates that it has revoked –A user who is about to use a certificate must now acquire the CRL to see if the certificate has been revoked Having to deal with revocation (and possibly reinstatement) eliminates one of the best properties of certificates, namely, that they can be used without having to contact a CA

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