ibe.txt

大数运算库miracl。有了miracl这样的函数库

IBE

This Identity Based Encryption method was invented by Boneh & Franklin. See 
http://crypto.stanford.edu/ibe/ for more details.

This demonstration implementation consists of four programs that implement 
each of the four steps in the algorithm. The source code is intended to be 
read in conjunction with the academic paper which describes the method. The 
clarity of C++ make the code very readable, and easy to associate with the 
mathematical description.


Tested with MS C++, Borland C++ and the DJGPP port of gcc


Function: SETUP

Source File: ibe_set.cpp

This program generates suitable random global domain parameters, and stores 
them in the file common.ibe. The Master key is stored in master.ibe

Compile as (for example with MS C++)

cl /O2 /GX ibe_set.cpp zzn2.cpp big.cpp monty.cpp elliptic.cpp miracl.lib



Function: EXTRACT

Source File: ibe_ext.cpp

This program extracts a private (secret) key from the proffered identity 
string, and stores it in the file private.ibe

Compile as 

cl /O2 /GX ibe_ext.cpp big.cpp monty.cpp elliptic.cpp miracl.lib



Function: ENCRYPT

Source File: ibe_enc.cpp

This program accepts the identity of the recipient (which is his public key), 
and encrypts a file.

Compile as 

cl /O2 /GX ibe_enc.cpp zzn2.cpp big.cpp monty.cpp elliptic.cpp miracl.lib



Function: DECRYPT

Source File: ibe_dec.cpp

This program decrypts a file using the private key from private.ibe

Compile as (for example with MS C++)

cl /O2 /GX ibe_dec.cpp zzn2.cpp big.cpp monty.cpp elliptic.cpp miracl.lib



Run the four programs in the order above, and encrypt a file to yourself!


For fastest speed on a 32-bit processor, select a Comba build in config.c, 
optimized for a 512-bit modulus. Also use the /DBIGS=n flag when compiling, to 
allocate space for Big variables from the stack.  

Several optimizations suggested by the inventors themselves have been 
implemented

(1) : This implementation uses a 512-bit prime p (for effective 1024-bit 
      security).
(2) : We use the faster Tate pairing
(3) : A small 160-bit sub-group q is used, where p=aq-1


New idea - Use a fixed simple group order q = 2^159+2^17+1
To use this define SIMPLE in ibe_set.cpp/ibe_enc.cpp/ibe_dec.cpp

This simplifies and speeds the code by about 20%

Also notice that in the final exponentiation in the Tate Pairing, we are 
calculating

res^(p-1) mod p, where res = (u,v) is in Fp2

This can be replaced by (u,-v)/(u,v) - which is much faster

Latest idea (thanks for the inspiration Paulo) is to use the alternative curve 
mentioned in the IBE paper, so instead of the supersingular curve y^2=x^3+1, 
use y^2=x^3+x. The isomorphism in this case is (x,y) -> (-x,iy), where i is 
the square root of -1. This keeps x "simple", and in Fp. The "denominator" 
calculation in Miller's algorithm only uses x, and so it too is in Fp. So the 
final exponentiation to the power of p-1 wipes it out - x^p-1 mod p = 1 
(thanks Fermat). So all denominator calculations can be excised.

This is substantially faster, and is implemented in the files ibe_setx.cpp, 
ibe_extx.cpp, ibe_encx.cpp, ibe_decx.cpp.

Further optimizations are based on this alternative curve...

PRECOMPUTATION

ibe_exp.cpp

This version uses precomputation to speed up encryption, based on the fixed
Trusted Authorities Public Key. If encrypting several emails to several 
correspondents, this will be much faster. Downside - 8K words of memory 
required to store tables.

NEW November 2002

New hack speeds up IBE encryption. When mapping an ID to a curve point there 
is a time-consuming point multiplication by a large co-factor cf to make the 
point have the required prime order q. For example when p is 512 bits and q 160 
bits, this requires a point multiplication on a 512-bit curve by a 352-bit 
number c. 

In fact this is not required, as the second argument to the Tate Pairing 
need not be of order q! Bilinearity still holds, so e(P,c.Q) = e(P,Q)^c. 
Therefore the unmapped point can be used directly.