CH716263A2 - A method of storing computer data by distributing an encrypted container and its fragmented decryption key on a blockchain network. - Google Patents

Abstract

The invention relates to a method for the secure storage of computer data (15) within a peer-to-peer network (1) composed of a plurality of nodes (2) on which a chain (5) of blocks is distributed. , method in which the data is encrypted within an enclave (8). The data (15) thus encrypted and the fragments (23.i) of a key (23) for decryption thereof are distributed over nodes (2A, 2B) of a peer-to-peer network, and Digital fingerprints of the loading of data into the enclave (8) and their storage are stored in the chain (5) of blocks.

Description

TECHNICAL AREA

The invention relates to the field of computing, and more specifically to the field of secure storage of network computer data.

PRIOR ART

The securing of the network storage of computer data has the dual objective of avoiding the loss of data (that is to say their untimely erasure) and their use (this term including reading as well as partial copying or total data) by unauthorized third parties. In other words, security aims to guarantee the sustainability and confidentiality of data.

[0003] To minimize the risk of data loss (in other words, to maximize the durability of the data), replications are generally carried out, that is to say, the data is distributed among several storage spaces. The data is therefore stored redundantly.

To guarantee (as much as possible) the confidentiality of data stored in the network, two methods are generally used: The first consists in restricting (typically via passwords or electronic certificates) access to a server on which the data is stored, which minimizes the risk of reading or copying; The second is to encrypt the data itself using cryptographic techniques.

[0005] The first method is effective under two main conditions.

[0006] First condition: the risk of loopholes in the restrictions on access to the server must be zero or, at the very least, minimum.

However, experience shows that certain attacks make it possible to circumvent these restrictions, typically by recovering the usernames and passwords of users and by usurping their identity to access their data.

[0008] Second condition: the administrator of the server must himself be trustworthy.

However, experience shows that some online service providers (including social networks), which administer servers on which are stored the personal data of many users, allow themselves to access this data and make it operating on their own account, typically by reselling the data to commercial companies or government agencies, or by analyzing the data themselves.

The second method solves the problems of the first, since unauthorized third parties can not make any use of the data, except to crack the encryption algorithms, which, until now, has proved infeasible for the algorithms most commonly used, such as the RSA algorithm (Rivest, Shamir, Adleman) or the elliptic curves algorithm.

Generally, the data is encrypted locally within a sending terminal (typically a personal computer), then the encrypted data is transmitted to the network to be stored there while a cryptographic key for decryption of the data is stored locally at the network. within the sending terminal.

However, this method presents a risk: the loss of the cryptographic key for decryption of the data, which renders the data permanently unusable (and this by anyone, including their owner), because they cannot be deciphered.

It is conceivable to delegate to the network (typically to a remote proxy server) the task of encrypting the data and administering the cryptographic decryption key.

In this case, the problem again arises of a potential access to the data by the administrator of the proxy server, either that the latter copies them before their encryption, or that he takes the liberty of decrypting them by using the generated cryptographic key. The problem also arises, from the point of view of the sending terminal, of obtaining proof, from the network, that the encryption has indeed been carried out.

The invention aims to offer an effective solution to these problems, in particular to the problem of confidentiality.

SUMMARY OF THE INVENTION

There is proposed a method of secure storage of computer data within a peer-to-peer network composed of a plurality of nodes forming a distributed database on which is stored, by replication on each node, a chain of blocks, this method comprising the operations of: <tb> <SEP> - Send, from a sending terminal in which the data is stored, a storage request to the network; <tb> <SEP> - On receipt of the storage request by at least one node of the network, select within the network at least one node, called an entry node, equipped with a computer processing unit in which is implemented an execution environment secured by cryptography, called an enclave; <tb> <SEP> - Instantiate the enclave; <tb> <SEP> - Load the data, from the transmitting terminal and via a secure communication line, to the enclave of the input node; <tb> <SEP> - Enter in a block of the chain of blocks, by one or more nodes of the network, at least one transaction containing a digital fingerprint of the storage request and / or of the loading thus carried out; <tb> <SEP> - In the enclave: <tb><SEP> <SEP> o Encrypt the data to form an encrypted container, by associating it with a cryptographic decryption key; <tb><SEP> <SEP> o Fragment the cryptographic decryption key to form a predetermined number of fragments; <tb><SEP> <SEP> o Designate, among the network, one or more primary storage nodes and distribute the encrypted container to the primary storage node or nodes; <tb><SEP> <SEP> o Designate, among the network, a group of secondary storage nodes in a number equal to the fragments; <tb><SEP> <SEP> o Distribute each fragment of the cryptographic decryption key to a secondary storage node, each secondary storage node receiving a unique fragment; <tb> <SEP> - Outside the enclave: <tb><SEP> <SEP> o Store the encrypted container within each primary storage node; <tb><SEP> <SEP> o Store each fragment of the cryptographic decryption key within each secondary storage node; <tb> <SEP> - Enter in a block of the chain of blocks, by one or more nodes of the network, at least one transaction containing a digital fingerprint of the distributions or memorizations thus carried out.

BRIEF DESCRIPTION OF THE FIGURES

[0017] Other objects and advantages of the invention will become apparent in the light of the description of an embodiment, given below with reference to the accompanying drawings in which: <tb> <SEP> LaFIG.1 is a simplified block diagram illustrating a peer-to-peer network on which a chain of blocks is distributed; <tb> <SEP> LaFIG.2 is a simplified functional diagram illustrating different components of a computer processing unit involved in the creation and operation of a secure execution environment called an enclave; <tb> <SEP> LaFIG.3 is a functional diagram partly illustrating a network architecture, partly the steps of a storage process, and partly the files produced, exchanged or stored within the network for the needs (or application) of this process.

DETAILED DESCRIPTION OF THE INVENTION

Without being limited thereto, the proposed storage method exploits, by combining them, the functionalities offered by two relatively recent technologies of which it seems useful to make a preliminary description before going into the details of the method, namely: Blockchain technology or, in Anglo-Saxon terminology, blockchain (in what follows, Anglo-Saxon terminology will be preferred, because of its common use in most languages, including French); The technology of the secure execution environment or, in English terminology, of the trusted execution environment (TEE).

[0019] Blockchain technology is organized in layers. She understands : A layer of hardware infrastructure, called a “blockchain network”; A protocol layer called the “blockchain protocol”; An information layer, called the “blockchain register”.

The blockchain network is a decentralized computer network, called a peer-to-peer network (in Peer-to-Peer or P2P terminology), made up of a plurality of computers (in the functional sense of the term: it is a device provided with a programmable computer processing unit, which can be in the form of a smartphone, a tablet, a desktop computer, a workstation, a physical or virtual server, i.e. computing and memory space allocated within a physical server and on which an operating system or operating system emulation runs), called "nodes" with reference to the theory of graphs, capable of communicating with each other (ie exchanging computer data), two by two, by means of wired or wireless links.

A network1blockchain comprising nodes2communicating by links3is illustrated in theFIG.1. For the sake of simplification and conformity with graph theory, on FIG.1, the nodes2 of the network1 are represented by circles; the bonds3, by edges connecting the circles. In order not to overload the drawing with lines, only certain links3 between nodes2 are shown.

[0022] The nodes2 can be scattered over large geographic regions; they can also be grouped into smaller geographic regions.

The blockchain protocol is in the form of a computer program implemented in each node2 of the network1 blockchain, and which includes, in addition to dialogue functions - that is to say exchange of computer data - with the other nodes2 of the network1 , a calculation algorithm which, from input data called "transactions" (which are transcriptions of interactions between one or more transmitting computer terminals and one or more recipient computer terminals): <tb> <SEP> - Builds structured data files4 called "blocks", each block4 including a body4containing digital transaction fingerprints, and a header4Bcontaining: <tb><SEP> <SEP> o A sequence number, or row, or height (height in English), in the form of an integer which designates the position of block4 within a chain in the order growing from an initial block (Genesis block); <tb><SEP> <SEP> o A unique digital fingerprint of body4A data; <tb><SEP> <SEP> o A unique digital fingerprint, called a pointer, of the header of the previous block4, <tb><SEP> <SEP> o A timestamp data; <tb> <SEP> - Implements a mechanism for validating blocks4 by consensus between all or part of the nodes2; <tb> <SEP> - Concatenates validated blocks4 to form a register5 (the blockchain register) in the form of an aggregate in which each block4 is mathematically linked to the previous one by its pointer.

The slightest modification of the data of the body4Aou of the header4B of a bloc4affects the value of its digital fingerprint and consequently breaks the link existing between this bloc4 thus modified and the following block 4 whose pointer no longer corresponds.

[0025] According to a particular embodiment, the digital fingerprint of each bloc4 is a digest (or hash) of the data of bloc4, that is to say the result of a hash function applied to the data of block4 (including body4A and header4B except for the digital fingerprint itself). The hash function is typically SHA-256.

For a bloc4donné of rank N (N an integer), the pointer ensures with the bloc4précè of rank N-1 an unalterable link. Indeed, any modification of the data of block4 of rank N-1 would lead to the modification of its fingerprint, and therefore to a lack of correspondence between this (modified) fingerprint of block4 of rank N-1 and the pointer stored among the metadata of block4 of rank NOT.

The succession of blocks4 linked together two by two by correspondence of the pointer of a bloc4donné of rank N with the digital fingerprint of the previous block of rank N-1 therefore constitutes the register5blockchain in the form of an aggregate of correlated blocks4, in which the slightest modification of the data of a block4 of rank N-1 results in a breaking of the link with the following block4 of rank N - and therefore the breaking of the blockchain register.

It is this particular structure which gives the data contained in the register5blockchain a reputation for immutability, guaranteed by the fact that the register5blockchain is replicated on all the nodes2 of the network1, forcing any attacker, not only to modify all the blocks4 of rank greater than the modified block4, but to deploy these modifications (even though the register5blockchain continues to be constituted by the nodes2 applying the blockchain protocol) to all the nodes2.

Whatever the type of consensus applied by the block validation mechanism4, most blockchain technologies have the primary function of recording, in their blockchain ledger5, transactions between one or more issuing terminals, and one or more receiving terminals, interchangeably called "users".

Each user is associated with an account, called in a simplified manner "electronic wallet" (in English digital wallet), which contains a memory area and a programmatic interface having interaction functions with the 1blockchain network to submit transactions to it, and synchronization functions with the 5blockchain register to register, in the memory area, the transactions validated by registration in the 5blockchain register.

Unless otherwise specified, and for the sake of simplicity, the simple expression "blockchain" or "blockchain" designates the register5blockchain itself.

Some recent blockchain technologies (Ethereum, typically) add to the three hardware (blockchain network), protocol (blockchain protocol) and informational (blockchain register) layers an application layer which takes the form of a development environment for programming applications, called “smart contracts”, which can be deployed on the ledger5blockchain from nodes2.

We will now briefly describe the technology of smart contracts.

[0034] A smart contract comprises two elements: An account, called a “Contract account”, in the memory area of which is written a source code containing computer instructions implementing the functions assigned to the smart contract; An executable code (in English Executable Bytecode) resulting from a compilation of the source code, this executable code being stored or deployed within the register5blockchain, that is to say inserted as a transaction in a block4 of the register5blockchain.

In the blockchain technology proposed by Ethereum, a smart contract is activated by a call (in English Call) sent by another account, said initiator account (which can be a user account or a contract account), this call is presenting in the form of a transaction containing, on the one hand, a reserve fund to be transferred (i.e. a payment) from the initiating account to the contract account and, on the other hand, initial conditions.

This call is recorded as a transaction in the register5blockchain. It triggers: The transfer of the reserve fund from the initiating account to the contract account; The designation, among the network1blockchain, of an execution node associated with a user account; The activation, in a computer processing unit of the execution node, of an execution environment or virtual machine (called Ethereum Virtual Machine or EVM in the case of Ethereum); The step-by-step execution of the steps for calculating the executable code by the virtual machine from the initial conditions, each step of calculation being accompanied by a transfer of a fraction (called gas in the case of Ethereum) of the reserve fund from the contract account to the user account of the execution node, until the calculation steps are exhausted, at the end of which a result is obtained; The recording (possibly in the form of a digital fingerprint) of this result as a transaction in the register 5 blockchain.

The initiating account retrieves (that is to say, in practice, downloads) the result when it is synchronized with the register5blockchain.

We now briefly introduce secure execution environments.

A secure execution environment (Trusted execution environment or TEE) is, within a computer processing unit provided with a processor or CPU (Central Processing Unit) 7, a temporary space for calculation and data storage. , called (by convention) an enclave, or even cryptographic enclave, which is isolated, by cryptographic means, from any unauthorized action resulting from the execution of an application outside this space, typically the operating system.

[0040] Intel®, for example, from 2013 revised the structure and interfaces of its processors to include enclave functions, under the name Software Guard Extension, better known by the acronym SGX. SGX equips most of the XX86 type processors marketed by Intel® since 2015, and more specifically from the sixth generation incorporating the so-called Skylake microarchitecture. The enclave functions offered by SGX are not automatically accessible: they must be activated via the elementary input / output system (Basic Input Output System or BIOS).

It does not come within the requirements of the present description to detail the architecture of the enclaves, insofar as: Despite its relative youth, this architecture is relatively well documented, in particular by Intel® which has filed numerous patents, cf. e.g., among the most recent, the US patent application US 2019/0058696; Processors making it possible to implement them are available on the market - in particular the aforementioned Intel® processors; Only the functionalities allowed by the enclave are of interest to us here, these functionalities being able to be implemented via specific command lines. As such, those skilled in the art may refer to the guide published in 2016 by Intel®: Software Guard Extensions, Developer Guide.

For a more accessible description of the enclaves, and more particularly of Intel® SGX, those skilled in the art can also refer to A. Adamski, Overview of Intel SGX - Part 1, SGX Internal, or to D. Boneh , Nickaming Schemes, Fast Verification, and Applications to SGX Technology, in Topics in Cryptology, CT - RSA 2017, The Cryptographers' Track at the RSA Conférence 2017, San Francisco, CA, USA, Feb. 14-17, 2017, Proceedings, pp. 149-164, or to K. Severinsen, Secure Programming with Intel SGX and Novel Applications, Thesis submitted for the Degree of Master in Programming and Networks, Dept. Of Informatics, Faculty of Mathematics and Natural Science, University of Oslo, Autumn 2017.

To summarize, with reference to theFIG.2, an enclave8 comprises, first of all, a secure memory area 9 (called Enclave Page Cache, in English Enclave Page Cache or EPC), which contains code and related data to the enclave itself, and the content of which is encrypted and decrypted in real time by a dedicated chip called the Memory Encryption Engine (MEE). The EPC9 is implemented within a part of the dynamic random access memory (DRAM) 10 allocated to the processor7, and to which ordinary applications (in particular the operating system) do not have access.

[0044] The enclave8 comprises, secondly, cryptographic keys used to encrypt or sign on the fly the data leaving the EPC9, whereby the enclave8 can be identified (in particular by other enclaves), and the The data it generates can be encrypted to be stored in unprotected memory areas (i.e. outside of the EPC9).

In order to be able to use such an enclave8, an application11 must be segmented into, on the one hand, one or more unsecured parts12 (in English untrusted part (s)), and, on the other hand, one or more secure parts13 (in English trusted part (s)).

Only the processes induced by the secure part (s) 13 of the application11 can access the enclave8. The processes induced by the unsecured part (s) 12 cannot access the enclave8, i.e. they cannot dialogue with the processes induced by the part (s) (s) 13secure (s).

The creation (also called instantiation) of the enclave8 and the flow of processes within it are controlled via a set14d'instructions particular executable by the processor7et called by the part (s) 13secure (s) of the application111.

[0048] Among these instructions: ECREATE commands the creation of an enclave8; EINIT commands the initialization of the enclave8; EADD commands code loading into the enclave8; EENTER commands code execution in the enclave8; ERESUME commands a new execution of code in the enclave8; EEXIT controls the exit of enclave8, typically at the end of a process running in enclave8.

We have, on theFIG.2, functionally represented the enclave 8 in the form of a block (in dotted lines) encompassing the secure part of the application11, the processor7 instruction set14, and the EPC9 . This representation is not realistic; it simply aims to visually group together the elements that make up or exploit the enclave8.

We will explain below how the enclaves are exploited.

The nodes2du network1blockchain are all equipped with memory areas, these can be used as storage space for data15 from a terminal16emitter (here shown in the form of a smartphone) connected to the network1. To minimize the risk of data loss15, it is advantageous to perform a replication of the data, that is to say to make a copy of the data15, and to distribute a copy to several nodes2 of the blockchain network. Data traceability15 can be achieved by entering, in the blockchain register, one or more digital fingerprints of the memorizations thus made.

This distributed storage of data15est advantageously controlled by a smart contract, activated for example by the transmitter terminal16 which, while transmitting the data15 to be stored to the network1, transmits to the smart contract a call by the procedure described above.

If the replication of data15 within the network1blockchain solves the problem of the sustainability of the data15, it does not solve the problem of their confidentiality.

Encrypting the data15 at the level of the sender terminal16 (which would store a data decryption key) would solve the problem of confidentiality vis-à-vis unauthorized third parties (except to admit that the decryption key could be copied by an unauthorized third party from the transmitting terminal16), but would not however guarantee that the data would remain accessible by the transmitting terminal16 itself, in the hypothesis - which is realistic in practice - where the cryptographic key is lost or corrupted.

It is proposed here to distribute on the network1not only the data15 (in encrypted form), but also a decryption key thereof, via an enclave8instantiated on a node2E, called entry node, of the network1 (FIG. 3).

To this end, a preliminary operation consists, from the emitter terminal16 in which the data15 is stored, in transmitting a data storage request15 to the network1, typically by activating a smart contract deployed on the blockchain5.

On receipt of the storage request by at least one node2du network1, the smart contract selects, within the network1at least one input node 2E, equipped with a computer processing unit in which an enclave8 is implemented.

This enclave8est then instantiated in application of the instructions of the smart contract, and the data15y is loaded from the transmitting terminal16 and via a secure communication line (eg using the Transport Layer Security or TLS protocol). For this purpose, the enclave8 can be provided, as soon as it is instantiated, with a communication interface 18 emulation supporting the chosen protocol (here TLS) for the exchange of secure data.

The blockchain protocol is advantageously loaded into the enclave8, to form a module19blockchain able to query the register5blockchain and / or to participate in the process of creation and validation of the blocks4.

A transaction20containing a digital imprint of the data loading thus performed is entered in a bloc4de the blockchain5, for the purposes of traceability.

This transaction20 can be transmitted to the module19blockchain by the emitting terminal16, to be registered by one or more nodes2 of the network (by the process described above) in a new block4 of the register5blockchain. As a variant, the module19blockchain itself issues a transaction20for registration in a new block4.

In the enclave8se then takes place a process which comprises the following operations.

A first operation consists in encrypting the data15 by means of a cryptographic encryption key21 to form an encrypted container22, by associating a decryption cryptographic key23 with it. To this end, the data 15 received from the emitting terminal 16 are relayed by the communication interface 18 to an encryption module 24 implemented in the enclave 8.

According to a preferred embodiment, the encryption is symmetrical. In this case, the encryption key21 and the decryption key23 are one and the same key.

A second operation consists in fragmenting the decryption key. More precisely, the decryption key 23 is fragmented into a predetermined number N of fragments 23.i, (i an integer, 2≤i≤N).

According to a preferred embodiment, N is such that N> 3 and the fragmentation is carried out in application of Shamir's rules (called Shamir's Secret Sharing, in English Shamir's Secret Sharing), and more precisely of the threshold diagram , where a predetermined integer K (1 <K <N) is chosen such that a number K of fragments23.isont sufficient to reconstitute the decryption key23.

A third operation consists in designating, among the network1, one or more primary storage nodes2.

To this end, the enclave8est advantageously provided with a data distribution module25, to which the encryption module24 communicates the encrypted container22 for distribution to the primary storage nodes2.

A fourth operation consists in designating, among the network1, a group of several secondary storage nodes2B, in number N equal to the number of fragments23.ide the decryption key23.

These secondary storage nodes 2B are preferably distinct from the primary storage nodes 2 - in other words, the primary storage nodes 2 and the secondary storage nodes 2 B form two disjoint groups (shown in dotted lines in FIG. 3).

A fifth operation consists in distributing the encrypted container22 to the primary storage node or nodes.

A sixth operation consists in distributing the fragments23.ide the cryptographic decryption key23 to the secondary storage nodes 2B, each secondary storage node 2B receiving a unique fragment23.i.

According to a preferred embodiment, the enclave8 is provided with a fragmentation and key distribution module26, to which the encryption module24 communicates the decryption key23 for fragmentation and distribution to the secondary storage nodes2B.

These operations completed, the enclave8 can be closed.

Outside the enclave8, the following operations are carried out: <tb> <SEP> o The encrypted container22 is stored within each primary storage node2; <tb> <SEP> o Each fragment23.ide the decryption cryptographic key23 is stored within each secondary storage node2Brespective.

To ensure the traceability of these operations, at least one transaction containing a digital imprint of the distributions or memorizations thus carried out is registered in a bloc4de the chain5de blocks, by one or more nodes2 of the network1. This transaction can be initiated by the Primary2 and Secondary2B storage nodes, but it can also be initiated by the enclave8 itself (and more specifically by the module20blockchain) before it closes.

The method which has just been described has the following advantages.

The key 23de decryption of the data not being stored locally at the level of the emitter terminal16, it does not risk being lost with it. The fact that it is fragmented (and stored on nodes distant) makes it much less vulnerable to misappropriation.

Since the data is encrypted within the container22, their access is impossible without obtaining the decryption key23. As this is fragmented, an attacker would be forced to apply brute force techniques by recovering all the fragments and by attempting all possible combinations to reconstitute the decryption key, which requires disproportionate computing resources.

Thanks to the fragmentation of the decryption key23, no storage node2Aou2B has both the container22de of its full decryption key23, which limits the risk of unauthorized decryption of data by a storage node2Aou2B (the other nodes2 do not have them no information).

The fact that the fragments23.is are distributed on 2Bsecondary storage nodes distinct from the primary storage nodes2 on which the container22 is distributed further limits the risk of unauthorized decryption, no node2Aou2Bne having both the container22 and a fragment23.i ( whatever) of the decryption key, each node2A, 2B having only part of the information (the container22 encrypted without fragment23.ide associated key23, or, conversely, a fragment23.ide key23 without the encrypted container22 partner).

As the decryption key has been constituted within an enclave8, it is not known to any third party and is not stored anywhere in its entirety. The only way to get it would be to get (unduly) the fragments23.ides different storage nodes2B and reconstitute key23 from them. In practice, such a maneuver is highly improbable, since it would require, due to ignorance of the identity of the secondary storage nodes2B, to attack all the nodes2 of the network1.

As for the replication of the container22 on the 1blockchain network, it makes it possible to store the data with a good assurance that they can be recovered when the time comes by the persons authorized to also recover (and reconstitute) the decryption key23 from the secondary nodes of the storage.

Claims (3)

1. A method of secure storage of computer data (15) within a peer-to-peer network (1) composed of a plurality of nodes (2) forming a distributed database on which is stored, by replication on each node (2), a chain (5) of blocks, this method comprising the operations of: - Sending, from a sender terminal (16) in which the data (15) are stored, a storage request to the network (1); - On receipt of the storage request by at least one node (2) of the network, select within the network (1) at least one node, called the input node (2E), equipped with a computer processing unit in which is implemented an execution environment secured by cryptography, called an enclave (8); - Instantiate the enclave (8); - Load the data (15), from the sender terminal (16) and via a secure communication line (17), to the enclave (8) of the input node (2E); - Enter in a block (4) of the chain (5) of blocks, by one or more nodes (2) of the network (1), at least one transaction (20) containing a digital fingerprint of the storage request and / or the loading thus carried out; - In the enclave (8): o Encrypt the data (15) to form an encrypted container (22), by associating it with a cryptographic decryption key (23); o Fragment the cryptographic decryption key (23) to form a predetermined number of fragments (23.i); o Designate, among the network (1), one or more primary storage nodes (2A) and distribute the encrypted container (22) to the primary storage node or nodes (2A); o Designate, among the network (1), a group of secondary storage nodes (2B) in a number equal to the fragments (23.i); o Distribute each fragment (23.i) of the cryptographic decryption key (23) to a secondary storage node (2B), each secondary storage node (2B) receiving a single fragment; - Outside the enclave (8): o Store the encrypted container (22) within each primary storage node (2); o Memorizing each fragment (23.i) of the cryptographic decryption key (23) within each secondary storage node (2B); - Enter in a block (4) of the chain (5) of blocks, through one or more nodes (2) of the network (1), at least one transaction containing a digital fingerprint of the distributions or memorizations thus carried out. 2. Method according to claim 1, wherein the primary storage nodes (2A) and the secondary storage nodes (2B) form two disjoint groups. 3. Method according to claim 1 or claim 2, in which the fragmentation of the decryption key (23) is carried out in application of Shamir's rules.