Introduction to Hash Functions - Revision history

JAumasson: HashIntro moved to Introduction to Hash Functions: Add blank spaces.

2008-11-02T16:17:43Z

HashIntro moved to Introduction to Hash Functions: Add blank spaces.

Crechberger at 08:49, 17 March 2008

2008-03-17T08:49:23Z

Crechberger at 07:59, 17 March 2008

2008-03-17T07:59:29Z

Crechberger at 20:35, 16 March 2008

2008-03-16T20:35:12Z

Crechberger at 19:46, 16 March 2008

2008-03-16T19:46:33Z

Crechberger at 10:25, 11 March 2008

2008-03-11T10:25:59Z

Crechberger at 15:27, 10 March 2008

2008-03-10T15:27:09Z

New page

=== Security Requirements ===

The security properties that hash functions are expected to provide,
are summarized in the following three basic requirements:

- '''Collision resistance''': it is infeasible in practice to find two messages m and m^* != m such that h(m) = h(m^*).

- '''Second preimage resistance''': for a given message m, it is infeasible in practice to find a second message m^* != m such that h(m) = h(m^*).

- '''Preimage resistance''': it is infeasible in practice to find, for a given hash value y, a message m such that h(m) = y.

In practice there are several other requirements, but for sake of
simplicity we stick to them.

@@ Line 4: / Line 4: @@
 are summarized in the following three basic requirements:
-- '''Collision resistance''': it is infeasible in practice to find two messages m and <math>2^{62}</math> != m such that h(m) = h(m^*).
+- '''Collision resistance''': it is infeasible in practice to find two messages m and m* != m such that h(m) = h(m*).
-<math>2^{63}</math>
+- '''Second preimage resistance''': for a given message m, it is infeasible in practice to find a second message m* != m such that h(m) = h(m*).
 - '''Preimage resistance''': it is infeasible in practice to find, for a given hash value y, a message m such that h(m) = y.

@@ Line 4: / Line 4: @@
 are summarized in the following three basic requirements:
-- '''Collision resistance''': it is infeasible in practice to find two messages m and <math>m^*</math> != m such that h(m) = h(m^*).
+- '''Collision resistance''': it is infeasible in practice to find two messages m and <math>2^{62}</math> != m such that h(m) = h(m^*).
 - '''Second preimage resistance''': for a given message m, it is infeasible in practice to find a second message m^* != m such that h(m) = h(m^*).

@@ Line 16: / Line 16: @@
 Most hash functions in use today are designed following the
-Damg{\aa}rd-Merkle design principle
+Damgaard-Merkle design principle
 The idea is
-to split the input message $m$ into $\ell$-bit blocks, which are
+to split the input message m into l-bit blocks, which are
 then processed one after another by iterating a compression function
-$f$. Messages whose length is not a multiple of $\ell$ bits need to
+f. Messages whose length is not a multiple of l bits need to
 be padded first.

← Older revision	Revision as of 16:17, 2 November 2008
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@@ Line 1: / Line 1: @@
-=== Security Requirements ===
+= Security Requirements =
 The security properties that hash functions are expected to provide,
@@ Line 12: / Line 12: @@
 In practice there are several other requirements, but for sake of
 simplicity we stick to them.