MASH-1

For a cryptographic hash function (a mathematical algorithm), a MASH-1 (Modular Arithmetic Secure Hash) is a hash function based on modular arithmetic.

History

Despite many proposals, few hash functions based on modular arithmetic have withstood attack, and most that have tend to be relatively inefficient. MASH-1 evolved from a long line of related proposals successively broken and repaired.

Standard

Committee Draft ISO/IEC 10118-4 (Nov 95)

Description

MASH-1 involves use of an RSA-like modulus $N$, whose bitlength affects the security. $N$ is a product of two prime numbers and should be difficult to factor, and for $N$ of unknown factorization, the security is based in part on the difficulty of extracting modular roots.

Let $L$ be the length of a message block in bit. $N$ is chosen to have a binary representation a few bits longer than $L$, typically $L < , N, \leq L+16$.

The message is padded by appending the message length and is separated into blocks $D_1, \cdots, D_q$ of length $L/2$. From each of these blocks $D_i$, an enlarged block $B_i$ of length $L$ is created by placing four bits from $D_i$ in the lower half of each byte and four bits of value 1 in the higher half. These blocks are processed iteratively by a compression function:

:$H_0 = IV$
:$H_i = f(B_i, H_) = ((((B_i \oplus H_) \vee E)^e \bmod N) \bmod 2^L) \oplus H_; \quad i=1,\cdots,q$

Where $E=15 \cdot 2^$ and $e=2$. $\vee$ denotes the bitwise OR and $\oplus$ the bitwise XOR.

From $H_q$ are now calculated more data blocks $D_,\cdots,D_$ by linear operations (where $\,$ denotes concatenation):

:$H_q = Y_1 \,\, \, Y_3 \,\, \, Y_0 \,\, \, Y_2; \quad , Y_i, = L/4$
:$Y_i = Y_ \oplus Y_; \quad i=4,\cdots,15$
:$D_ = Y_ \,\, \, Y_; \quad i=1,\cdots,8$

These data blocks are now enlarged to $B_,\cdots,B_$ like above, and with these the compression process continues with eight more steps:
:$H_i = f(B_i, H_); \quad i=q+1,\cdots,q+8$

Finally the hash value is $H_ \bmod p$, where $p$ is a prime number with $7\cdot 2^ < p < 2^$.Smashing MASH-1, Vladimir Antipkin
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MASH-2

There is a newer version of the algorithm called MASH-2 with a different exponent. The original $e=2$ is replaced by $e=2^8+1$. This is the only difference between these versions.

References

* A. Menezes, P. van Oorschot, S. Vanstone, ''Handbook of Applied Cryptography'',

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