# Re: How to construct such one-way key chain without hash function

*From*: "laicko" <yichun.zhang@xxxxxxxxx>*Date*: 24 Apr 2006 00:39:22 -0700

You could let F() be any trapdoor one-way permutation.I'm trying to use DL follow your instructions. As to ElGamal scheme,

(g^r, (g^x)^r *m)

every encryption needs a fresh exponent r and keep it in secret. If

it's a constant and

known to the public, how to retain the one-way charateristic?

For instance,

F(x) = x^2 (mod N), where N=PQ is a Blum integer (P,Q = 3 (mod 4)) whose

factorization is known only to the authority. I would recommend using

SHA1(K_i) as the i-th key, instead of using K_i directly.

to use SHA1 here is for CCA security, right?

However, I insist on constructing it without any hash , since I need to

keep

the algebraic charateristic of K_i for further processing.

In someway, I'd like the scheme could follow this condition:

E_{K_i+j}(M)= A_e( E_{K_i}{M}, j) for i,j >=0

E is the encryption algorithm, A is function, e is public known

parameter

.

**Follow-Ups**:**Re: How to construct such one-way key chain without hash function***From:*David Wagner

**References**:**How to construct such one-way key chain without hash function***From:*laicko

**Re: How to construct such one-way key chain without hash function***From:*David Wagner

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