Square Hash with a Small Key Size

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Square Hash with a Small Key Size

• Source IEICE Transactions on Fundamentals,
• Vol. E87-A No. 1 pp.54-59 Jan.
  2004
• Author Swee-Huay HENG and Kaoru KUROSAWA
• Date 3/18/2004
• Speaker Chang-Chu Chen

2
Outline

• Review
• Universal hash function
• Multilinear Modular Hashing
• Square Hash
• Proposed approachSQH
• Discussion
• Conclusions

3
ReviewUniversal hash function

• (Carter and Wegman1979) is a set of
  universal hash functions if probabilitywhere
• Universal hash function can be used for message
  authentication codes (MAC)

transmitter
receiver
mmessage xkey MACSx(m)
If MAC is valid Vx (m, MAC)1 Other Vx (m, MAC)0
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ReviewMultilinear Modular Hashing

• MMH(Halevi et al.1997)where , is a prime
• Key string is the same size as the message string

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ExampleMMH

• MMH32

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ReviewSquare Hash

• SQH(Etzel et al.1999)where , is a prime

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Proposed approach

• Modify the key construction
• Key length is shorten by k times

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Proposed approachSQH

• SQHwhere , is a prime

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Discussion

• We can make security bound smaller without making
  the size of MAC larger.
• If a lower collision probability is desired, we
  can reduce the collision bound by half. We
  choosethat is we double our key size than the
  collision probability is

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Conclusions

• Proposed square hash with k times shorter key
  than original square hash
• Proved this new variant of square hash still
  gives a very good security