BBS32BIT, a 32 Bits Cipher

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Network Working Group T. Moreau Request for Comments: <to be assigned> CONNOTECH Experts-conseils Inc. Category: Informational December 1994 BBS32BIT, a 32 Bits Cipher Based on the BBS Pseudo-Random Number Generator Status of this Memo This memo provides information for the Internet community. This memo does not specify an Internet standard of any kind. Distribution of this memo is unlimited. Export Control Restrictions Notice This software for information security may be subject to export control restrictions. Before you do anything that causes or assists the export of this software outside of Canada and the United States, you should consider the implications of the Export and Import Permits Act and the Export Control List of Canada and the International Traffic In Arms Regulations of the United States. Disclaimer and Software Licensing This software and related documentation is provided as is with no guarantee of any kind. CONNOTECH Experts-conseils Inc. deliberately publishes the description of the BBS32BIT cipher and the source code of its version 1.0 implementation. You are granted a license to use the BBS32BIT cipher software version 1.0 on two computer systems. Copyright notices are affixed to the source code, and to the executable programs. CONNOTECH Experts-conseils Inc. is the owner of the rights granted by the applicable copyright laws. If you intend to use any or all of this copyrighted material beyond two computer systems, contact CONNOTECH Experts-conseils Inc. to obtain the required licenses. Moreau [Page 1] RFC <t.b.d.> BBS32BIT, a 32 bit cipher ... December 1994 Table of Contents Status of this Memo . . . . . . . . . . . . . . . . . . . . . . . . . 1 Export Control Restrictions Notice . . . . . . . . . . . . . . . . . 1 Disclaimer and Software License Agreement . . . . . . . . . . . . . . 1 Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Design Objectives . . . . . . . . . . . . . . . . . . . . . 5 2.3 Purpose of this Document . . . . . . . . . . . . . . . . . 6 3 The Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1 Ciphers based on Pseudo-random Number Generators . . . . . 7 3.2 The BBS Pseudo-random Number Generator . . . . . . . . . . 7 3.3 Application of the BBS Generator with 32 Bits Arithmetic . 8 3.4 Key Selection Process . . . . . . . . . . . . . . . . . . . 9 3.5 Effective Key Size . . . . . . . . . . . . . . . . . . . . 10 3.6 Open Questions . . . . . . . . . . . . . . . . . . . . . . 10 4 User Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . 12 4.1.1 The Missing Part: a True Random Bit Source . . . 12 4.2 Possible Key Management Procedures . . . . . . . . . . . . 13 4.2.1 Isolated Encipherment Procedure . . . . . . . . . 13 4.2.2 Recurrent Encipherment Procedure . . . . . . . . 13 4.3 The BBS32KEY utility synopsis . . . . . . . . . . . . . . . 15 4.4 The BBS32ENC utility synopsis . . . . . . . . . . . . . . . 17 4.5 The BBS32DEC utility synopsis . . . . . . . . . . . . . . . 19 4.6 The BBS32DEL utility synopsis . . . . . . . . . . . . . . . 21 4.7 The BBS32ACC utility synopsis . . . . . . . . . . . . . . . 22 5 Implementation in C++ . . . . . . . . . . . . . . . . . . . . . 23 6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 7 Author's Address . . . . . . . . . . . . . . . . . . . . . . . . 26 Moreau [Page 2] RFC <t.b.d.> BBS32BIT, a 32 bit cipher ... December 1994 1 Preface According to the Webster's dictionary, a "cipher" is a method for transforming a text in order to conceal its meaning. The BBS32BIT software is a cipher based on mathematical theory formulated by L. Blum, M. Blum, and M. Shub (see [1]). The BBS32BIT cipher presented here is fully disclosed. This document describes its mathematical foundation in a simple language intended for a typical computer programmer to understand. The difficulty of breaking this cipher does not rely on hiding the method itself, but on hiding two secret numbers used in the method. These two numbers are referred to as the "secret key" of an enciphered message. The BBS32BIT software may find practical applications where confidentiality of computer files is important. It exhibits the following interesting characteristics: Strength It is estimated that 1.3x10**13 tries would be required to break this cipher (an effective secret key size of 44 bits). Yet this claim has to stand up to review by specialists in the field. See the section 3.6 for more details. Possible candidate for exportable cryptographic software or equipment Currently, cryptographic equipment providing confidentiality protection with key sizes up to 40 bits are normally not subject to export restrictions. With the expected trend towards lesser restrictions on export of cryptography, the BBS32BIT cipher may be a good candidate for exportable cryptographic equipment. Speed Encipherment speed is about 2 mega-bits per second on an Intel 80486DX2-66 processor. This is based on software written in high level language (except for one simple mathematical function written in assembly language). Direct access capability For direct access to a given record in a file, the decipherment process is equally fast irrespective of the record position in the file. The BBS32BIT cipher is a packaged as a set of computer utilities for enciphering and deciphering files. In addition, this document suggests procedures for managing secret keys in a way to provide effective confidentiality protection. These procedures are included Moreau [Page 3] RFC <t.b.d.> BBS32BIT, a 32 bit cipher ... December 1994 to demonstrate that a practical cipher system is feasible using a simple mathematical foundation. The BBS32BIT cipher has limitations that the reader should be aware of: A truly random bit source is missing To provide effective security, a cipher system must randomly pick up secret keys from a large set of possible value. This requires a true random bit source. See section 4.1.1 for more details. A subtle key management trap With the BBS32BIT cipher, a given secret key should not be used twice to encipher different data. The implications of this restriction on any specific application should be fully understood. Not a public key cipher Generally speaking, securing information is a labour intensive activity providing little immediate and tangible benefits. The BBS32BIT cipher does not alleviate this fact of life. Other directions in the field of cryptology better address this issue in the case of communications security: the ciphers based on public key cryptography reduces the key management overhead when deployed on a large scale. An abundant literature on contemporary cryptology describe the public key ciphers. The main interest of CONNOTECH Experts-conseils Inc. is to get a review of the design principles behind the BBS32BIT cipher, and to foster acceptance of ciphers based on the BBS pseudo-random number generator. Reader's comments are welcome. You may contact the author at the address indicated at the end of this document. Moreau [Page 4] RFC <t.b.d.> BBS32BIT, a 32 bit cipher ... December 1994 2 Introduction 2.1 Background Modern cryptology is based on applying theoretical results obtained by mathematicians into practical systems. This document is an account of such an attempt. The cryptographic properties the x**2 mod N pseudo-random number generator were studied by three mathematicians, L. Blum, M. Blum, and M. Shub [1]. A recent review of the BBS pseudo-random generator and related work can be found in [3]. An overview of the field of cryptology may be found in [4]. The subject matter of this document is a simple cipher software based on a 32 bits arithmetic implementation of the BBS pseudo- random generator. 2.2 Design Objectives The main objective of this initiative is to foster acceptance of ciphers based on the BBS pseudo-random generator. To achieve this objective, a complete cipher software is presented and fully disclosed. The BBS32BIT cipher software version 1.0 is limited to encipherment of computer files. Although limited in scope, this application has practical uses. The BBS32BIT cipher has the following design goals: 1) Demonstration of encipherment with the BBS pseudo-random generator. 2) Secret key cipher with no attempt to benefit from public key cryptography. 3) Encipherment of computer files in the personal computer DOS environment. 4) Providing effective security. 5) Simple implementation to facilitate review of the security provided by the cypher software. 6) Practical system, ready to use. Design goals 6 and 4 are contradictory when it comes to secret key selection. Effective security can be achieved only if secret keys are randomly chosen from a large set of possible values. A true random process is hard to implement in a personal computer environment without special hardware. Design goal 6 is compromised in this respect: no easy to use secret key selection process is offered. Moreau [Page 5] RFC <t.b.d.> BBS32BIT, a 32 bit cipher ... December 1994 Design goals 5 and 6 are contradictory. To be user friendly, a cipher should be integrated with a file management tool. Such tools are involved software applications. Design goal 6 is compromised in this respect: the BBS32BIT cipher software version 1.0 supports encipherment of multiple related files using batch command files, which is not a user friendly way. The use of the PKZIP utility from PKWARE Inc., 9025 North Deerwood Drive, Brown Deer, WI 53233, USA, may be an attractive alternative. 2.3 Purpose of this Document This document is intended to provide instructions for a programmer to implement the BBS32BIT cipher without having to review the references to the mathematical theory. This document is also intended to allow mathematicians to review these instructions to make sure they abide by the theory. For a security officer or a software designer, the BBS32BIT cipher may be considered to provide confidentiality protection in actual applications. Reader's comments are welcome. Moreau [Page 6] RFC <t.b.d.> BBS32BIT, a 32 bit cipher ... December 1994 3 The Theory 3.1 Ciphers based on Pseudo-random Number Generators A one-time pad is a cipher in which a purely random stream of bits is used as a secret key. This secret key must be as long as the message itself and used only once. The encipherment algorithm is a simple exclusive or operation between the cleartext message and the secret key. The legitimate recipient of the message knows the secret key and applies the same exclusive or operation between the ciphertext and the secret key to recover the cleartext message. This type of cipher is impossible to break according to the information theory. Practical difficulties with the one-time pad cipher are related to secret key management, including: a) the length of the key, b) the requirement of key transmission between the sender and the receiver with a secured communications channel, c) the requirement to establish different keys with each correspondent, and d) the requirement to establish a different key for each message sent or received. Items b) and c) are common to all ciphers based on secret keys, by opposition with public key cryptography. The key length issue is addressed with the use of a pseudo-random number generator. For our purpose, a pseudo-random number generator is a mathematical algorithm producing a long sequence of bits from a short "seed". The pseudo-random sequence is completely determined by the mathematical algorithm and the value of the seed. Yet, no statistical test can differentiate the output sequence from a purely random sequence of bits. By substituting a purely random stream of bits with a pseudo-random sequence, the strong theoretic foundation of the one-time pad is traded for easier key management. The cipher described in this document uses the a secret key approach. In addition, it requires the establishment of a different key for each message sent or received. 3.2 The BBS Pseudo-random Number Generator The BBS pseudo-random number generator is introduced in this section. Notation: x[i] is an integer x of index i in a sequence. N is a parameter of the BBS generator (explained hereafter). Given a seed x[0], the sequence x[1], x[2], x[3], ... is computed with the formula Moreau [Page 7] RFC <t.b.d.> BBS32BIT, a 32 bit cipher ... December 1994 x[i+1] = x[i]**2 mod N The seed x[0] must be of the form x[0] = x**2 mod N where x is an integer relatively prime to N. At some point, this sequence is returning to x[0]. The period is the smallest index p where x[p] = x[0] The period p is dependent on N and x[0]. Only a subset of the sequence x[1], x[2], x[3], ... is retained as a pseudo-random bit string. This subset is the sequence w[1], w[2], w[3], ... where w[i] = x[i] mod 2**k where k is a parameter of the BBS generator representing the number of least significant bits retained at each iteration. The parameter k is less than the number of bits required to represent N as described hereafter. For completeness of the specification, the conversion of the sequence w[1], w[2], w[3], ... into a sequence of computer bytes must be specified. Mathematical properties of the BBS generator are discussed in [1]. The valid range of k is discussed in [2]. 3.3 Application of the BBS Generator with 32 Bits Arithmetic For the BBS32BIT cipher described in this document, the following properties are mandated. The parameter N must be of the form N = P * Q P = 2 * P1 + 1 P1 = 2 * P2 + 1 Q = 2 * Q1 + 1 Q1 = 2 * Q2 + 1 P2 > Q2 where P, P1, P2, Q, Q1, and Q2 are prime numbers. Moreau [Page 8] RFC <t.b.d.> BBS32BIT, a 32 bit cipher ... December 1994 These rules ensure that the period of the resulting sequence is a divisor of 2*P2*Q2. Consequently, the full set of possible periods for any x[0] is {1, 2, Q2, 2*Q2, P2, 2*P2, Q2*P2, 2*Q2*P2} Knowing the factors P and Q of the parameter N, it is possible to find the value x[i] quickly irrespective of the value of i, using the formula x[i] = x[0]**(2**i mod ((P-1)*(Q-1))) mod N It is then easy to find the value of the period p by looking for the smallest possible value of p for which x[p] = x[0]. Given P, Q must be the largest possible value for which N < 2**32. This rule forces N to be fairly close to 2**32, allowing the fullest exploitation of the natural size of arithmetic registers in most computer architectures. From 2**16 to 2**32, there are exactly 48410 possible P ranging from 65587 up to 390446879 with the corresponding Q ranging from 64007 down to 11. The parameter k is set to 4, so that the 4 least significant bits of each x[i] is retained. This follows the findings of [2] where it is shown that for a N of 32 bits, the 5 least significant bits could be retained at each step. The bytes B[0], B[1], B[2], ... required to encipher or decipher a message expressed as a byte stream are taken from the sequence w[1], w[2], w[3], ... with the formula B[j] = 16 * w[2*j+1] + w[2*j+2] 3.4 Key Selection Process For the 32 bits cipher described in this document, the secret key is an indication of both the parameter N and the seed x[0]. This pair (N,x[0]) should be selected by an algorithm giving a fairly equal probability for all pairs in the set of acceptable pairs. For a cipher to offer practical security, it must be difficult to guess the secret key. The key selection process must be done by a computer program from random selections of integers within a specified range with uniform distribution, and not from a choice from the part of the user. This requirement also stems from the difficulty of expressing the pair (N,x[0]) in a meaningful alphanumeric sequence given the constraints on the values of N and x[0]. The key selection program starts with the choice of N, and then proceed with the selection of x[0]. Constraints on x[0] may force Moreau [Page 9] RFC <t.b.d.> BBS32BIT, a 32 bit cipher ... December 1994 the program to start over with a new choice of N. A candidate parameter N should be selected with a uniform probability distribution of the 48410 possible values. A candidate seed x[0] should be derived from a random integer x relatively prime to N with a uniform distribution of the (P-1)*(Q- 1) possible values for x. The candidate seed x[0] is then computed with x[0] = x**2 mod N There are (P-1)*(Q-1)/4 possible values for x[0] (for each x[0], there are exactly 4 possible x). Then the period p of x[0] such that x[p] = x[0] should be found by trying each possible value for the period p, as explained above. The candidate seed x[0] is a good candidate seed only if p = 2*P2*Q2. Experimentation showed that about 76.3% of randomly selected pairs (N,x[0]) have a good candidate seed x[0]. 3.5 Effective Key Size The effective key size is directly related to the number of pairs (N,x[0]) that can be selected as a key. Selection of N has 48410 possible outcomes. Selection of a candidate x[0] has (P-1)*(Q-1)/4 possible outcomes, which is 730940290 on average for all possible N. As stated above, only 76.3% of the pairs (N,x[0]) will be retained. The effective key size is then 48410 * 730940290 * 0.763 = 2.7 * 10**13 which is between 2**44 and 2**45. In summary, the key size is 44 bits. By comparison, the key size of the DES cipher is 56 bits. This key size is a reliable indication of the effective strength of the cipher only if a through review of the cipher is performed by the cryptographic community. See the section 3.6 for more details. 3.6 Open Questions Moreau [Page 10] RFC <t.b.d.> BBS32BIT, a 32 bit cipher ... December 1994 With limited mathematical skills, the author sees three open questions to make a fair assessment of the value of the 32 bits cipher described in this document: 1) Is there any weak keys left when following the proposed key selection process? Maybe the values of N with a small exponent like 11 of 23 produce keys which are easier to break, due to some mathematical properties unknown to the author. 2) The reference [5] describes an optimization to the brute force attack to a stream cipher where the period is an exact power of 2. How this contribution can be applied to break the 32 bits cipher described in this document? 3) Is there any assumptions of the references [1] and [2] which were overlooked in the design of the 32 bits cipher described in this document? If such is the case, chances are that any theorical weakness would create an opportunity to break the cipher. Moreau [Page 11] RFC <t.b.d.> BBS32BIT, a 32 bit cipher ... December 1994 4 User Guide 4.1 Overview The BBS32BIT cipher software version 1.0 contains some of the required tools for enciphering and deciphering computer files. It comprises a set of 3 command line utilities, BBS32KEY, BBS32ENC, and BBS32DEC, respectively for generating a secret key, enciphering, and deciphering. This package is targeted to the DOS file directory format (DOS diskettes and DOS disk partitions). At a minimum, it requires a 80386 processor. It is supplied for the MsDOS or the OS/2 operating system, respectively from Microsoft Corporation and International Business Machines Corporation. An additional utility, BBS32DEL, is provided to delete a file containing sensitive data. This utility writes zeroes in the file before removing it. Any subsequent un-delete attempt will fail to recover the file contents. The BBS32KEY secret key generation utility requires a random data file of a special format (see also section 4.1.1). A few bytes of this random data file are consumed each time the BBS32KEY utility is run. Somebody responsible for computer security or system administration should provide you with the random data file required by the BBS32KEY utility. When multiple related files are to be enciphered in a single operation, the BBS32BIT cipher software version 1.0 is meant to be used in customized batch command files. A single secret key may be used to encipher multiple related files. See the description of the utilities for important details on how to proceed. The person responsible for computer security or system administration should indicate the procedures applicable in each case. Alternatively, the files may be merged in a single file using a file compression utility before encipherment. 4.1.1 The Missing Part: a True Random Bit Source To provide effective security, a cipher system must randomly pick up secret keys from a large set of possible value. This requires a random bit source with properties difficult to obtain in a computer environment. The random bit source must be unpredictable and uniformly distributed. By comparison, the pseudo-random number generator available in a typical run time support library of a programming language is totally predictable (even if its output is statistically undistinguishable from a truly random bit source). As CONNOTECH is dedicated to offering sound solutions, it can not suggest any trade-off as a true random bit source. Internally, the Moreau [Page 12] RFC <t.b.d.> BBS32BIT, a 32 bit cipher ... December 1994 CONNOTECH development team uses a special electronic circuit as a true random bit source. CONNOTECH is planning to sell this true random bit source as a Serial Electronic Coin Flipping Device that can easily be connected to any computer serial port. Contact CONNOTECH for further details. 4.2 Possible Key Management Procedures There are two suggested ways of managing cryptographic keys. The first one is applicable when an isolated encipherment operation is needed between the sender of computer files and the receiver. The second one is appropriate when encipherment of computer files is recurrent, either between a sender and a receiver or in other circumstances. With either method, if multiple files are enciphered, the BBS32ENC utility is invoked for each file in sequence and the standard output of one invocation is used as the standard input of the next one. A batch command file with multiple invocation of the BBS32DEC utility should be prepared with the same file processing order, again with chaining of standard output and standard input. This decipherment batch command file should follow the set of enciphered files on a single storage media. 4.2.1 Isolated Encipherment Procedure When there is an isolated requirement for encipherment of one or more files, the BBS32KEY utility should be invoked to create a secret key which is passed to the BBS32ENC utility and written on a piece of paper. If multiple files are enciphered, this secret key is used for the first invocation of the BBS32ENC utility. The enciphered file, or the set of enciphered files with the decipherment batch command file, are transmitted to the legitimate receiver on a storage media or via a communications mean. An eavesdropper not knowing the secret key can not decipher the contents of the enciphered files. The secret key is transmitted to the legitimate receiver using a different communications channel than the enciphered files. If there is a single enciphered file, the legitimate receiver recovers its contents by invoking the BBS32DEC utility and manually entering the secret key value. If there are multiple files, the decipherment batch command file is invoked instead. 4.2.2 Recurrent Encipherment Procedure When the encipherment requirement occurs on a regular basis, a more convenient and possibly more secure procedure is suggested. The following descriptions may be adapted to the exact circumstances encountered. Either the sender or the receiver invokes the BBS32KEY utility to Moreau [Page 13] RFC <t.b.d.> BBS32BIT, a 32 bit cipher ... December 1994 generate a number of secret keys stored in a shared secret key file. This file is enciphered using the procedure for isolated encipherment of a single file and copied on a 3.5 inches computer diskettes which is write protected. This is done twice, each time with a different secret key from the BBS32KEY utility. Then any version of the shared secret key file is removed from the computer system using the BBS32DEL utility. One of the two diskettes is sent to the other party, again using the isolated encipherment procedure. The other one is kept in a safe location when not in use and its decipherment key is kept as the "master key". Upon reception of the diskette, the other party may elect to decipher the file and re-encipher it with a locally selected master key, again using the BBS32KEY utility. From this point on, either party may send an enciphered file, or a set of enciphered files with a decipherment batch command file, along with a secret key reference, indicating which secret key was used for encipherment. This indication may be included in the decipherment batch command file. Any secret key reference must be used only once, otherwise the confidentiality of the data is seriously imperilled. The exact procedure for the sender is as with the isolated encipherment procedure except that the BBS32KEY utility is replaced by the BBS32ACC utility specifying the shared secret key file and a new record number each time the BBS32ACC utility is run. When the BBS32ACC utility is invoked, the master key of the sender must be manually entered. There is no need to take note of the key extracted by the BBS32ACC utility from the shared secret key file. The record number is a sufficient information as a secret key reference since the receiver has access to the same shared secret key file. The procedure for the receiver is also based on the BBS32ACC utility. This utility replaces the manual entry of the shared secret key. When the BBS32ACC is invoked by the receiver, the receiver master key must be manually entered. Moreau [Page 14] RFC <t.b.d.> BBS32BIT, a 32 bit cipher ... December 1994 4.3 The BBS32KEY utility synopsis: Purpose: To generate one or more secret keys of a format appropriate for the BBS32ENC and BBS32DEC utilities. Warning: A secret key generated by the BBS32KEY utility must be used only once. If two files are enciphered with the same key, the confidentiality of your data is seriously imperilled. See the description of the BBS32ENC and BBS32DEC utilities about how to encipher and decipher multiple files from a single secret key. Command line syntax: BBS32KEY {random file name} [{count}] Command line parameter: {random file name} The file name of the random data file of a special format for the BBS32KEY utility. This file is opened in the update mode. The BBS32KEY utility consumes a few bytes from this file to produce a unique secret key. The consumed bytes are zeroed-out in the file before it is closed. {count} This optional parameter is a decimal integer indicating the requested count of secret keys to generate. The default value is one. Standard file processing: Standard Output: The secret key in decimal notation, for instance "15741 1898436789". If more than one key is requested, each one is output on a separate line. Each line has the same length, so the standard output may be redirected to a file to be enciphered and then processed by the BBS32ACC utility. If a single key is requested, the output format is acceptable as the standard input to the BBS32ENC utility. It is recommended to redirect this standard output to a file to be passed later to the BBS32ENC utility. This intermediate file should be deleted with the BBS32DEL utility. Moreau [Page 15] RFC <t.b.d.> BBS32BIT, a 32 bit cipher ... December 1994 Standard Error: If a single key is requested, the same secret key revealed in a human readable message. It is recommended to take note of the value of the key and treat it with the precautions deserved by the sensitivity of the files to be enciphered with the key. Usually, it should not be stored on the same storage media as the enciphered files. Moreau [Page 16] RFC <t.b.d.> BBS32BIT, a 32 bit cipher ... December 1994 4.4 The BBS32ENC utility synopsis: Purpose: To encipher a computer file. Command line syntax: BBS32ENC {cleartext file} [{ciphertext file}] [/b] [/f] Command line parameter: {cleartext file} The file name of the file to encipher. This file is opened in the read mode. {ciphertext file} This optional parameter pertains to the ciphertext file to be created. Four cases are possible: 1) this parameter explicitly specifies the name and extension of the ciphertext file to be created, 2) this parameter explicitly specifies the directory where a ciphertext file with the same name and extension as the cleartext file is to be created, 3) this parameter is absent and there is a subdirectory named "ENCIPHRD" in the same directory as the cleartext file, in which case the ciphertext file is created in this directory with the same name and extension as the cleartext file, 4) this parameter is absent and there is no subdirectory named "ENCIPHRD" in the same directory as the cleartext file, in which case this directory is created and the ciphertext file is created in it with the same name and extension as the cleartext file. The ciphertext file is opened in the write mode. If a file with the same name exists, the BBS32ENC utility fails unless the /b or /f options are specified. /b This optional parameter tells the BBS32ENC utility to make a backup of the ciphertext file if it already exists. This backup has the same name as the existing file, but with the extension changed to ".BAK". If both the /b and /f parameters are present, /b takes precedence. /f This optional parameter tells the BBS32ENC utility to overwrite the ciphertext file if it Moreau [Page 17] RFC <t.b.d.> BBS32BIT, a 32 bit cipher ... December 1994 already exists. If both the /b and /f parameters are present, /b takes precedence. Standard file processing: Standard Input: The BBS32ENC expects a single line of text on the standard input file. This line of text must contain exactly two decimal numbers valid as a secret key. They can be provided by the BBS32KEY secret key generation utility, by a previous execution of the BBS32ENC utility, or from records of previously generated keys. Standard Output: The next secret key that can be used to resume encryption of another file in a subsequent execution of the BBS32ENC utility. This next secret key is dependent on the initial key passed to the BBS32ENC utility and the cleartext file size. This next secret key is output in a decimal notation acceptable as input to the subsequent execution of the BBS32ENC utility. If you encipher a single file, this output should be ignored or redirected to the NUL device. If you encipher multiple files, it is recommended to redirect this standard output to a file to be passed to the subsequent execution of the BBS32ENC utility. This intermediate file should be deleted with the BBS32DEL utility. Moreau [Page 18] RFC <t.b.d.> BBS32BIT, a 32 bit cipher ... December 1994 4.5 The BBS32DEC utility synopsis: Purpose: To decipher a computer file. Command line syntax: BBS32DEC {cleartext file} [{ciphertext file}] [/b] [/f] Command line parameter: {cleartext file} The file name of the deciphered file to be created. This file is opened in the write mode. If a file with the same name exists, the BBS32DEC utility fails unless the /b or /f options are specified. {ciphertext file} This optional parameter pertains to the ciphertext file to be deciphered. Three cases are possible: 1) this parameter explicitly specifies the name and extension of the ciphertext file to be deciphered, 2) this parameter explicitly specifies the directory where a ciphertext file with the same name and extension as the cleartext file is to be located and deciphered, 3) this parameter is absent and there is a subdirectory named "ENCIPHRD" in the same directory as the cleartext file, in which case a ciphertext file in this directory with the same name and extension as the cleartext file is located and deciphered. The ciphertext file is opened in the read mode. /b This optional parameter tells the BBS32DEC utility to make a backup copy of the cleartext file if it already exists. This backup has the same name as the existing file, but with the extension changed to ".BAK". If both the /b and /f parameters are present, /b takes precedence. /f This optional parameter tells the BBS32DEC utility to overwrite the cleartext file if it already exists. If both the /b and /f parameters are present, /b takes precedence. Standard file processing: Moreau [Page 19] RFC <t.b.d.> BBS32BIT, a 32 bit cipher ... December 1994 Standard Input: The BBS32DEC expects a single line of text on the standard input file. This line of text must contain exactly two decimal numbers valid as a secret key. They can be provided by manual entry of a secret key stored outside of the computer system, by a previous execution of the BBS32DEC utility, or from records of previously generated keys. For the manual entry of a secret key, be sure to type the secret key value correctly as two decimal numbers separated by a space, all in a single line ended by the Enter key. Standard Output: The next secret key that can be used to resume decryption of another file in a subsequent execution of the BBS32DEC utility. This next secret key is dependent on the initial key passed to the BBS32DEC utility and the ciphertext file size. This next secret key is output in a decimal notation acceptable as input to the subsequent execution of the BBS32DEC utility. If you decipher a single file, this output should be ignored or redirected to the NUL device. If you decipher multiple files, it is recommended to redirect this standard output to a file to be passed to the subsequent execution of the BBS32DEC utility. This intermediate file should be deleted with the BBS32DEL utility. Warning: If you decipher multiple files, the order in which the files are deciphered must be the same as the original encipherment order. Moreau [Page 20] RFC <t.b.d.> BBS32BIT, a 32 bit cipher ... December 1994 4.6 The BBS32DEL utility synopsis: Purpose: To delete a file containing sensitive data. This delete operation leaves no recoverable file contents on disk. This utility writes zeroes in the file before removing it. Command line syntax: BBS32DEL {file name} Command line parameter: {file name} The name of the file to be deleted. Moreau [Page 21] RFC <t.b.d.> BBS32BIT, a 32 bit cipher ... December 1994 4.7 The BBS32ACC utility synopsis: Purpose: To decipher a single record in a direct access file. Each record in this file is of a fixed size. Command line syntax: BBS32ACC {file name} {record number} [{record size}] Command line parameter: {file name} The name of the direct access file from which a record is to be deciphered. This file is opened in read mode. Unless otherwise stated, this file is accessed in binary mode. {record number} The record number to be deciphered, as a decimal integer value starting at zero for the first record in the file. {record size} This optional parameter indicates the record size in the direct access file. If absent, the value of this parameter is obtained by reading the first text line in the deciphered direct access file, as if it was a text file. The record length is equal to the length of this first line, including the end of line marker. Standard file processing: Standard Input: The BBS32ACC expects a single line of text on the standard input file. This line of text must contain exactly two decimal numbers valid as a secret key. They can be provided by manual entry of a secret key stored outside of the computer system. For the manual entry of a secret key, be sure to type the secret key value correctly as two decimal numbers separated by a space, all in a single line ended by the Enter key. Standard Output: The standard output receives the deciphered record indicated by the record number command line parameter. Moreau [Page 22] RFC <t.b.d.> BBS32BIT, a 32 bit cipher ... December 1994 5 Implementation in C++ Enclosed on the BBS32BIT software distribution diskette is the source code in the C++ programming language for all utilities. There is a single mathematical function programmed in the assembler language. The computation of a*b mod n where n is close to 2**32 is best done in assembler language where the temporary result a*b occupying 64 bits is directly accessible in a pair of 32 bits registers (see the source file "modulo.asm"). With the source files, there is a "makefile" allowing reconstruction of the whole BBS32BIT software using a C++ compiler and a "make" utility. All source files but two should be highly portable between C++ compilers for the DOS and OS/2 environments. The two exceptions are the assembler function in the source file modulo.asm and the file makefile which are dependent on a specific compiler, namely the Borland C++ for OS/2 version 1.5 from Borland International, Inc. Adaptation to another compiler should be fairly easy. The only tricks are the creation of the source file "modulo.asm" and the accomodation of more than 64 K-bytes of initialized tables (mainly in the source files "getspecp.cpp" and "extspecp.cpp"). Some elementary mathematical algorithms from the number theory are assumed to be known by the programmer. This includes a test of whether a number is prime or composite by exhaustive search of all prime factors, and an efficient way of computing a**b mod n with the fast modular exponentiation (see [4], page 21). The secret keys of the BBS32BIT cipher are pair of numbers representing respectively N and x[0]. To minimize the size of secret keys in human readable format, the actual value of N is replaced by the rank of the factor P among the 48410 possible values in increasing order. Thus there is a requirement of a compressed table of the 48410 possible values for P. See the source file getspecp.cpp. For the preparation of this compressed table and a table of all prime numbers below 2**16, there are three compile-time only executable files, namely allspecp.exe, specprim.exe, and prime64k.exe. The source code for these compile-time only utilities is included and the file makefile contains the information required to re-create them and to use them to re-create the BBS32BIT utilities. To slightly reduce the size of x[0] when displayed in human readable form, it is replaced by its rank among the (P-1)*(Q-1) numbers which are relatively prime to N. See the source file re

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