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/********************************************************************************/
/* */
/* Math functions performed with canonical integers in byte buffers */
/* Written by Ken Goldman */
/* IBM Thomas J. Watson Research Center */
/* $Id: MathOnByteBuffers.c 1519 2019-11-15 20:43:51Z kgoldman $ */
/* */
/* Licenses and Notices */
/* */
/* 1. Copyright Licenses: */
/* */
/* - Trusted Computing Group (TCG) grants to the user of the source code in */
/* this specification (the "Source Code") a worldwide, irrevocable, */
/* nonexclusive, royalty free, copyright license to reproduce, create */
/* derivative works, distribute, display and perform the Source Code and */
/* derivative works thereof, and to grant others the rights granted herein. */
/* */
/* - The TCG grants to the user of the other parts of the specification */
/* (other than the Source Code) the rights to reproduce, distribute, */
/* display, and perform the specification solely for the purpose of */
/* developing products based on such documents. */
/* */
/* 2. Source Code Distribution Conditions: */
/* */
/* - Redistributions of Source Code must retain the above copyright licenses, */
/* this list of conditions and the following disclaimers. */
/* */
/* - Redistributions in binary form must reproduce the above copyright */
/* licenses, this list of conditions and the following disclaimers in the */
/* documentation and/or other materials provided with the distribution. */
/* */
/* 3. Disclaimers: */
/* */
/* - THE COPYRIGHT LICENSES SET FORTH ABOVE DO NOT REPRESENT ANY FORM OF */
/* LICENSE OR WAIVER, EXPRESS OR IMPLIED, BY ESTOPPEL OR OTHERWISE, WITH */
/* RESPECT TO PATENT RIGHTS HELD BY TCG MEMBERS (OR OTHER THIRD PARTIES) */
/* THAT MAY BE NECESSARY TO IMPLEMENT THIS SPECIFICATION OR OTHERWISE. */
/* Contact TCG Administration (admin@trustedcomputinggroup.org) for */
/* information on specification licensing rights available through TCG */
/* membership agreements. */
/* */
/* - THIS SPECIFICATION IS PROVIDED "AS IS" WITH NO EXPRESS OR IMPLIED */
/* WARRANTIES WHATSOEVER, INCLUDING ANY WARRANTY OF MERCHANTABILITY OR */
/* FITNESS FOR A PARTICULAR PURPOSE, ACCURACY, COMPLETENESS, OR */
/* NONINFRINGEMENT OF INTELLECTUAL PROPERTY RIGHTS, OR ANY WARRANTY */
/* OTHERWISE ARISING OUT OF ANY PROPOSAL, SPECIFICATION OR SAMPLE. */
/* */
/* - Without limitation, TCG and its members and licensors disclaim all */
/* liability, including liability for infringement of any proprietary */
/* rights, relating to use of information in this specification and to the */
/* implementation of this specification, and TCG disclaims all liability for */
/* cost of procurement of substitute goods or services, lost profits, loss */
/* of use, loss of data or any incidental, consequential, direct, indirect, */
/* or special damages, whether under contract, tort, warranty or otherwise, */
/* arising in any way out of use or reliance upon this specification or any */
/* information herein. */
/* */
/* (c) Copyright IBM Corp. and others, 2016 - 2019 */
/* */
/********************************************************************************/
/* 9.11 MathOnByteBuffers.c */
/* 9.11.1 Introduction */
/* This file contains implementation of the math functions that are performed with canonical
integers in byte buffers. The canonical integer is big-endian bytes. */
#include "Tpm.h"
/* 9.11.2.1 UnsignedCmpB */
/* This function compare two unsigned values. The values are byte-aligned, big-endian numbers (e.g,
a hash). */
/* Return Values Meaning */
/* 1 if (a > b) */
/* 0 if (a = b) */
/* -1 if (a < b) */
LIB_EXPORT int
UnsignedCompareB(
UINT32 aSize, // IN: size of a
const BYTE *a, // IN: a
UINT32 bSize, // IN: size of b
const BYTE *b // IN: b
)
{
UINT32 i;
if(aSize > bSize)
return 1;
else if(aSize < bSize)
return -1;
else
{
for(i = 0; i < aSize; i++)
{
if(a[i] != b[i])
return (a[i] > b[i]) ? 1 : -1;
}
}
return 0;
}
/* 9.11.2.2 SignedCompareB() */
/* Compare two signed integers: */
/* Return Values Meaning */
/* 1 if a > b */
/* 0 if a = b */
/* -1 if a < b */
int
SignedCompareB(
const UINT32 aSize, // IN: size of a
const BYTE *a, // IN: a buffer
const UINT32 bSize, // IN: size of b
const BYTE *b // IN: b buffer
)
{
int signA, signB; // sign of a and b
// For positive or 0, sign_a is 1
// for negative, sign_a is 0
signA = ((a[0] & 0x80) == 0) ? 1 : 0;
// For positive or 0, sign_b is 1
// for negative, sign_b is 0
signB = ((b[0] & 0x80) == 0) ? 1 : 0;
if(signA != signB)
{
return signA - signB;
}
if(signA == 1)
// do unsigned compare function
return UnsignedCompareB(aSize, a, bSize, b);
else
// do unsigned compare the other way
return 0 - UnsignedCompareB(aSize, a, bSize, b);
}
/* 9.11.3.3 ModExpB */
/* This function is used to do modular exponentiation in support of RSA. The most typical uses are:
c = m^e mod n (RSA encrypt) and m = c^d mod n (RSA decrypt). When doing decryption, the e
parameter of the function will contain the private exponent d instead of the public exponent
e. */
/* If the results will not fit in the provided buffer, an error is returned
(CRYPT_ERROR_UNDERFLOW). If the results is smaller than the buffer, the results is
de-normalized. */
/* This version is intended for use with RSA and requires that m be less than n. */
/* Error Returns Meaning */
/* TPM_RC_SIZE number to exponentiate is larger than the modulus */
/* TPM_RC_NO_RESULT result will not fit into the provided buffer */
TPM_RC
ModExpB(
UINT32 cSize, // IN: the size of the output buffer. It will
// need to be the same size as the modulus
BYTE *c, // OUT: the buffer to receive the results
// (c->size must be set to the maximum size
// for the returned value)
const UINT32 mSize,
const BYTE *m, // IN: number to exponentiate
const UINT32 eSize,
const BYTE *e, // IN: power
const UINT32 nSize,
const BYTE *n // IN: modulus
)
{
BN_MAX(bnC);
BN_MAX(bnM);
BN_MAX(bnE);
BN_MAX(bnN);
NUMBYTES tSize = (NUMBYTES)nSize;
TPM_RC retVal = TPM_RC_SUCCESS;
// Convert input parameters
BnFromBytes(bnM, m, (NUMBYTES)mSize);
BnFromBytes(bnE, e, (NUMBYTES)eSize);
BnFromBytes(bnN, n, (NUMBYTES)nSize);
// Make sure that the output is big enough to hold the result
// and that 'm' is less than 'n' (the modulus)
if(cSize < nSize)
ERROR_RETURN(TPM_RC_NO_RESULT);
if(BnUnsignedCmp(bnM, bnN) >= 0)
ERROR_RETURN(TPM_RC_SIZE);
BnModExp(bnC, bnM, bnE, bnN);
BnToBytes(bnC, c, &tSize);
Exit:
return retVal;
}
/* 9.11.2.4 DivideB() */
/* Divide an integer (n) by an integer (d) producing a quotient (q) and a remainder (r). If q or r
is not needed, then the pointer to them may be set to NULL. */
/* Error Returns Meaning */
/* TPM_RC_NO_RESULT q or r is too small to receive the result */
LIB_EXPORT TPM_RC
DivideB(
const TPM2B *n, // IN: numerator
const TPM2B *d, // IN: denominator
TPM2B *q, // OUT: quotient
TPM2B *r // OUT: remainder
)
{
BN_MAX_INITIALIZED(bnN, n);
BN_MAX_INITIALIZED(bnD, d);
BN_MAX(bnQ);
BN_MAX(bnR);
//
// Do divide with converted values
BnDiv(bnQ, bnR, bnN, bnD);
// Convert the BIGNUM result back to 2B format using the size of the original
// number
if(q != NULL)
if(!BnTo2B(bnQ, q, q->size))
return TPM_RC_NO_RESULT;
if(r != NULL)
if(!BnTo2B(bnR, r, r->size))
return TPM_RC_NO_RESULT;
return TPM_RC_SUCCESS;
}
/* 9.11.2.5 AdjustNumberB() */
/* Remove/add leading zeros from a number in a TPM2B. Will try to make the number by adding or
removing leading zeros. If the number is larger than the requested size, it will make the number
as small as possible. Setting requestedSize to zero is equivalent to requesting that the number
be normalized. */
UINT16
AdjustNumberB(
TPM2B *num,
UINT16 requestedSize
)
{
BYTE *from;
UINT16 i;
// See if number is already the requested size
if(num->size == requestedSize)
return requestedSize;
from = num->buffer;
if (num->size > requestedSize)
{
// This is a request to shift the number to the left (remove leading zeros)
// Find the first non-zero byte. Don't look past the point where removing
// more zeros would make the number smaller than requested, and don't throw
// away any significant digits.
for(i = num->size; *from == 0 && i > requestedSize; from++, i--);
if(i < num->size)
{
num->size = i;
MemoryCopy(num->buffer, from, i);
}
}
// This is a request to shift the number to the right (add leading zeros)
else
{
MemoryCopy(&num->buffer[requestedSize - num->size], num->buffer, num->size);
MemorySet(num->buffer, 0, requestedSize- num->size);
num->size = requestedSize;
}
return num->size;
}
/* 9.11.2.6 ShiftLeft() */
/* This function shifts a byte buffer (a TPM2B) one byte to the left. That is, the most significant
bit of the most significant byte is lost. */
TPM2B *
ShiftLeft(
TPM2B *value // IN/OUT: value to shift and shifted value out
)
{
UINT16 count = value->size;
BYTE *buffer = value->buffer;
if(count > 0)
{
for(count -= 1; count > 0; buffer++, count--)
{
buffer[0] = (buffer[0] << 1) + ((buffer[1] & 0x80) ? 1 : 0);
}
*buffer <<= 1;
}
return value;
}
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