ISDA Legal Entity Identifier (LEI) hash. Takes 20 digit LEI to a 10 digit Unique Trade Identifier (UTI) prefix

gistfile1.txt

ISDA_PERMITTED_CHARS = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ'
ISDA_PRIME = 59575553

def leiHash( lei, permittedChars = ISDA_PERMITTED_CHARS ):
    """ Shorten 20 character alpha-numeric Legal Entity Identifier into 10 character alpha-numeric "short LEI" that 
        can be used as a Unique Trade Identifier (UTI) prefix. The algorithm is simply the modulo operation lifted from
        integers to the space of alpha-numeric case-insensitive strings. 

         Argument
         --------
         s          str     (length 20 typically)

         Returns
         -------
         str                (length 10)

    """
    # This will break a combination of issuer and firm identifiers into two eight char strings, compress each down to five, and join
    # LEI = LEI Issuer (4 char alphanumeric)" ++ "2 reserved characters always same" 00 ++ firm identifier (12 char alphanumeric) + 2 check digits.
    if len(lei)==20:
        issuer = lei[:4]
        firm   = lei[6:18]
        leiWithoutRedundantChars = issuer + firm
    else:
        leiWithoutRedundantChars = lei

    h = len( leiWithoutRedundantChars )/2
    firstHalf  = leiWithoutRedundantChars[:h]
    secondHalf = leiWithoutRedundantChars[h:]

    firstHalfHash  = _primeHash( s = firstHalf,  newLen = 5, prime = ISDA_PRIME, permittedChars = permittedChars )
    secondHalfHash = _primeHash( s = secondHalf, newLen = 5, prime = ISDA_PRIME, permittedChars = permittedChars )

    return firstHalfHash + secondHalfHash

def leiHashCollisionProbability( nLei, nPermittedChars = 36, firstPrime = ISDA_PRIME, secondPrime = ISDA_PRIME ):
    """ Probability of at least one collision if (>=20 character) LEI's are drawn from uniform distribution with replacement nLei times """
    nPossibilities = firstPrime*secondPrime
    return 1- math.exp( -nLei*(nLei-1.)/(2.*nPossibilities) )

@func.memoize_plus
def _powersModP( nPermittedChars, p ):
    """ Cached powers of nPermittedChars mod p """
    return [ pow( nPermittedChars, k ) % p for k in xrange( 25 ) ]

def _intFromAlphaModP( s, permittedChars = ISDA_PERMITTED_CHARS, p = ISDA_PRIME ):
    """ Convert alpha-numeric to integer modulo p """
    # We merge the operations of converting to an int and taking mod p not because python can't handle large numbers, which
    # it does perfectly well, but to make translation to Excel/VBA straightforward. {n^k mod p} are cached for the same reason,
    # and are hardwired in the VBA version provided to ISDA. 
    i = 0
    nPermittedChars = len( permittedChars )
    for k, char in enumerate( reversed(s) ):
        digit     = permittedChars.find( char )
        i        += _powersModP( nPermittedChars, p )[k]*digit
        i         = i % p
    return i

def _alphaFromInt( i, permittedChars = ISDA_PERMITTED_CHARS ):
    """ Convert back again """
    # (This is an injection from 0..PRIME into the space of alpha-numeric strings)
    a = ''
    nPermittedChars = len( permittedChars )
    while i:
        a = permittedChars[i % nPermittedChars] + a
        i = i // nPermittedChars
    if not a:
        a = permittedChars[0]
    return a

def _primeHash( s, permittedChars = ISDA_PERMITTED_CHARS, prime = ISDA_PRIME, newLen = 5 ):
    """ Hash case-insensitive string to one of shorter length by applying modulus operation """
    # (Doesn't really have to be a prime)
    nPermittedChars = len( permittedChars )
    if pow( nPermittedChars, newLen ) < prime:
        raise ValueError("You may wish to choose a larger prime so the map from integers mod p to alpha-numeric strings is an injection")

    iModP = _intFromAlphaModP( s, permittedChars = permittedChars, p = prime )
    alf   = _alphaFromInt( iModP, permittedChars )
    return alf.ljust( 5, 'Z' )