LectureNote19-MsgDigests

LectureNote19-MsgDigests - M ESSAGE D IGESTS AND C...

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Unformatted text preview: M ESSAGE D IGESTS AND C ERTIFICATES P UBLIC K EY C RYPTOGRAPHY I NTRO . TO N UMBER T HEORY D IFFIE-H ELLMAN C RYPTOSYSTEM RSA C RYPTOSYSTEM O THER P UBLIC K EY C RYPTOSYSTEMS M ESSAGE D IGESTS AND C ERTIFICATES CS 556 - Computer Security - c circlecopyrt 2009 Colorado State University 68 / 93 Message Digests P UBLIC K EY C RYPTOGRAPHY I NTRO . TO N UMBER T HEORY D IFFIE-H ELLMAN C RYPTOSYSTEM RSA C RYPTOSYSTEM O THER P UBLIC K EY C RYPTOSYSTEMS M ESSAGE D IGESTS AND C ERTIFICATES CS 556 - Computer Security - c circlecopyrt 2009 Colorado State University 69 / 93 Motivation Public-key technology is very slow Cannot sign big messages Signed message is at least as long as original message, often longer Message digests are one way hash values of original messages that represent concisely the message from which it was computed Message Digests P UBLIC K EY C RYPTOGRAPHY I NTRO . TO N UMBER T HEORY D IFFIE-H ELLMAN C RYPTOSYSTEM RSA C RYPTOSYSTEM O THER P UBLIC K EY C RYPTOSYSTEMS M ESSAGE D IGESTS AND C ERTIFICATES CS 556 - Computer Security - c circlecopyrt 2009 Colorado State University 70 / 93 Easy to Compute Hard to Compute Properties of Cryptographic Hash Functions P UBLIC K EY C RYPTOGRAPHY I NTRO . TO N UMBER T HEORY D IFFIE-H ELLMAN C RYPTOSYSTEM RSA C RYPTOSYSTEM O THER P UBLIC K EY C RYPTOSYSTEMS M ESSAGE D IGESTS AND C ERTIFICATES CS 556 - Computer Security - c circlecopyrt 2009 Colorado State University 71 / 93 The hash function H(x) is relatively easy to compute for any given x H(x) is one-way hard to invert, that is given a hash value h, it is computationally infeasible to find some input x such that H(x) = h H(x) is collision-free Weakly Collision Free P UBLIC K EY C RYPTOGRAPHY I NTRO . TO N UMBER T HEORY D IFFIE-H ELLMAN C RYPTOSYSTEM RSA C RYPTOSYSTEM O THER P UBLIC K EY C RYPTOSYSTEMS M ESSAGE D IGESTS AND C ERTIFICATES CS 556 - Computer Security - c circlecopyrt 2009 Colorado State University 72 / 93 Given a message M, it is computationally infeasible to find a message M prime negationslash = M such that H(M) = H(M prime ) Given M, m = H(M) try messages at random to find M prime with H(M prime ) = m 2 k trials on an average for messages of size k bits Strongly Collision Free P UBLIC K EY C RYPTOGRAPHY I NTRO . TO N UMBER T HEORY D IFFIE-H ELLMAN C RYPTOSYSTEM RSA C RYPTOSYSTEM O THER P UBLIC K EY C RYPTOSYSTEMS M ESSAGE D IGESTS AND C ERTIFICATES CS 556 - Computer Security - c circlecopyrt 2009 Colorado State University 73 / 93 It is computationally infeasible to find any two messages M and M prime such that H(M) = H(M prime ) Try pairs of messages at random to find M and M prime such that H(M prime ) = H(M) 2 k / 2 trials on an average Current Generation Algorithms P UBLIC K EY C RYPTOGRAPHY I NTRO . TO N UMBER T HEORY D IFFIE-H ELLMAN C RYPTOSYSTEM RSA C RYPTOSYSTEM O THER P UBLIC K EY C RYPTOSYSTEMS M ESSAGE D IGESTS AND C ERTIFICATES CS 556 - Computer Security -...
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LectureNote19-MsgDigests - M ESSAGE D IGESTS AND C...

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